A heat engine receives heat from a constant volume tank

You are designing a closed-system, isentropic expansion process using an ideal gas that operates between the pressure limits of \(P_{1}\) and \(P_{2}\). The gases under consideration are hydrogen, nitrogen, air, helium, argon, and carbon dioxide. Which of these gases will produce the greatest amount of work? Which will require the least amount of work in a compression process? Equation Transcription: Text Transcription: P_1 P_2

Problem 1P Does the temperature in the Clausius inequality relation have to be absolute temperature? Why?

Problem 2P Does the cyclic integral of heat have to be zero (i.e., does a system have to reject as much heat as it receives to complete a cycle)? Explain.

Problem 3P Is a quantity whose cyclic integral is zero necessarily a property?

To determine the entropy change for an irreversible process between states 1 and 2, should the integral \(\int_{1}^{2} \delta Q / T\) be performed along the actual process path or an imaginary reversible path? Explain. Equation Transcription: Text Transcription: integral _1^2 delta Q/T

Problem 5P Is an isothermal process necessarily internally reversible? Explain your answer with an example.

How do the values of the integral \(\int_{1}^{2} \delta Q / T\) compare for a reversible and irreversible process between the same end states? Equation Transcription: Text Transcription: integral _1^2 delta Q/T

Problem 8P When a system is adiabatic, what can be said about the entropy change of the substance in the system?

Problem 9P Work is entropy free, and sometimes the claim is made that work will not change the entropy of a fluid passing through an adiabatic steady-flow system with a single inlet and outlet. Is this a valid claim?

Problem 7P The entropy of a hot baked potato decreases as it cools. Is this a violation of the increase of entropy principle? Explain.

Problem 10P A piston-cylinder device contains helium gas. Dur­ing a reversible, isothermal process, the entropy of the helium will (never, sometimes, always) increase.

Problem 11P A piston-cylinder device contains nitrogen gas. During a reversible, adiabatic process, the entropy of the nitrogen will (never, sometimes, always) increase.

Problem 12P A piston-cylinder device contains superheated steam. During an actual adiabatic process, the entropy of the steam will (never, sometimes, always) increase.

Problem 13P The entropy of steam will (increase, decrease, remain the same) as it flows through an actual adiabatic turbine.

Problem 14P The entropy of the working fluid of the ideal Carnot cycle (increases, decreases, remains the same) during the isothermal heat addition process.

Problem 16P During a heat transfer process, the entropy of a sys­tem (always, sometimes, never) increases.

Problem 19P A completely reversible heat engine operates with a source at 1500 R and a sink at 500 R. If the entropy of the sink increases by 10 Btu/R, how much will the entropy of the source decrease? How much heat, in Btu, is transferred from the source?

Problem 18P What three different mechanisms can cause the entropy of a control volume to change?

Heat in the amount of \(100\ kJ\) is transferred directly from a hot reservoir at \(1200\ K\) to a cold reservoir at \(600\ K\). Calculate the entropy change of the two reservoirs and determine if the increase of entropy principle is satisfied. Equation Transcription: Text Transcription: 100 kJ 1200 K 600 K

Problem 15P The entropy of the working fluid of the ideal Carnot cycle (increases, decreases, remains the same) during the isothermal heat rejection process.

Problem 22P In the previous problem, assume that the heat is trans­ferred from the cold reservoir to the hot reservoir contrary to the Clausius statement of the second law. Prove that this vio­lates the increase of entropy principle—as it must according to Clausius.

Air is compressed by a \(15-\mathrm{kW}\) compressor from \(P_{1}\) to \(P_{2}\). The air temperature is maintained constant at \(25^{\circ} \mathrm{C}\) during this process as a result of heat transfer to the surrounding medium at \(20^{\circ} \mathrm{C}\). Determine the rate of entropy change of the air. State the assumptions made in solving this problem. Equation Transcription: 25°C 20°C Text Transcription: 15-kW P_1 P_2 25 degree celsius 20 degree celsius

A completely reversible heat pump produces heat at a rate of \(300\ kW\) to warm a house maintained at \(24^{\circ} \mathrm{C}\). The exterior air, which is at \(7 ^{\circ} \mathrm{C}\), serves as the source. Calculate the rate of entropy change of the two reservoirs and determine if this heat pump satisfies the second law according to the increase of entropy principle. Equation Transcription: 7°C 24°C Text Transcription: 300 kW 7 degree celsius 24 degree celsius

Problem 17P Steam is accelerated as it flows through an actual adiabatic nozzle. The entropy of the steam at the nozzle exit will be (greater than, equal to, less than) the entropy at the nozzle inlet.

Problem 24P During the isothermal heat addition process of a Carnot cycle, 900 kJ of heat is added to the working fluid from a source at 400°C. Determine (a) the entropy change of the working fluid, (b) the entropy change of the source, and (c) the total entropy change for the process.

Problem 27P Refrigerant-134a enters the coils of the evaporator of a refrigeration system as a saturated liquid–vapor mixture at a pressure of 140 kPa. The refrigerant absorbs 180 kJ of heat from the cooled space, which is maintained at -10°C, and leaves as saturated vapor at the same pressure. Determine (a) the entropy change of the refrigerant, (b) the entropy change of the cooled space, and (c) the total entropy change for this process.

Problem 28P Is a process that is internally reversible and adia­batic necessarily isentropic? Explain.

Problem 29P 2-lbm of water at 300 psia fill a weighted piston-cylinder device whose volume is 2.5 ft3. The water is then heated at constant pressure until the temperature reaches 500°F. Determine the resulting change in the water's total entropy.

During the isothermal heat rejection process of a Carnot cycle, the working fluid experiences an entropy change of \(20.7\ Btu/R\). If the temperature of the heat sink is \(95^{\circ} \mathrm{F}\), determine (a) the amount of heat transfer, (b) the entropy change of the sink, and (c) the total entropy change for this process. Equation Transcription: 95°F Text Transcription: 95 degree fahrenheit 20.7 Btu/R

A well-insulated rigid tank contains \(3\ kg\) of a saturated liquid–vapor mixture of water at \(200\ kPa\). Initially, three-quarters of the mass is in the liquid phase. An electric resistance heater placed in the tank is now turned on and kept on until all the liquid in the tank is vaporized. Determine the entropy change of the steam during this process. Equation Transcription: Text Transcription: 3 kg 200 kPa

A rigid tank is divided into two equal parts by a partition. One part of the tank contains \(2.5\ kg\) of compressed liquid water at \(400\ kPa\) and \(60^{\circ} \mathrm{C}\) while the other part is evacuated. The partition is now removed, and the water expands to fill the entire tank. Determine the entropy change of water during this process, if the final pressure in the tank is \(40\ kPa\). Equation Transcription: 60°C Text Transcription: 2.5 kg 400 kPa 60 degree celsius 40 kPa

Problem 33P An insulated piston-cylinder device contains 5 L of saturated liquid water at a constant pressure of 150 kPa. An electric resistance heater inside the cylinder is now turned on, and 2200 kJ of energy is transferred to the steam. Deter­mine the entropy change of the water during this process.

Saturated \(R-134a\) vapor enters a compressor at \(6^{\circ} \mathrm{F}\). At compressor exit, the specific entropy is the same as that at the inlet, and the pressure is \(80\ psia\). Determine the \(R-134a\) exit temperature and the change in the enthalpy of \(R-134a\) . Equation Transcription: 6°F Text Transcription: R-134a 6 degree fahrenheit

Problem 36P 1-kg of R-134a initially at 600 kPa and 25°C under­goes a process during which the entropy is kept constant until the pressure drops to 100 kPa. Determine the final temperature of the R-134a and the final specific internal energy.

Refrigerant-134a is expanded isentropically from \(600 \mathrm{kPa}\) and \(70^{\circ} \mathrm{C}\) at the inlet of a steady-flow turbine to \(100 \mathrm{kPa}\) at the outlet. The outlet area is \(1 \mathrm{~m}^{2}\), and the inlet area is \(0.5 \mathrm{~m}^{2}\). Calculate the inlet and outlet velocities when the mass flow rate is \(0.75 \mathrm{~kg} / \mathrm{s}\). Equation Transcription: 70°C Text Transcription: 134a 600 kPa 70 degree celsius 100 kPa 1 m^2 0.75 kg/s

Problem 35P Water vapor enters a turbine at 6 MPa and 400°C, and leaves the turbine at 100 kPa with the same specific entropy as that at the inlet. Calculate the difference between the spe­cific enthalpy of the water at the turbine inlet and exit.

Problem 31P The radiator of a steam heating system has a volume of 20 L and is filled with superheated water vapor at 200 kPa and 150°C. At this moment both the inlet and the exit valves to the radiator are closed. After a while the temperature of the steam drops to 40°C as a result of heat transfer to the room air. Determine the entropy change of the steam during this process.

Problem 38P A piston-cylinder device contains 1.2 kg of saturated water vapor at 200°C. Heat is now transferred to steam, and steam expands reversibly and isothermally to a final pres­sure of 800 kPa. Determine the heat transferred and the work done during this process.

Refrigerant-\(134a\) at \(320\ kPa\) and \(40^{\circ} \mathrm{C}\) undergoes an isothermal process in a closed system until its quality is 45 percent. On per unit mass basis, determine how much work and heat transfer are required. Equation Transcription: 40°C Text Transcription: 134a 320 kPa 40 degree celsius

Reconsider Prob. 7–38. Using EES (or other) software, evaluate and plot the heat transferred to the steam and the work done as a function of final pressure as the pressure varies from the initial value to the final value of \(800\ kPa\). Equation Transcription: Text Transcription: 800 kPa

A \(0.5-\mathrm{m}^{3}\) rigid tank contains refrigerant- \(134 \mathrm{a}\) initially at \(200 \mathrm{kPa}\) and 40 percent quality. Heat is transferred now to the refrigerant from a source at \(35^{\circ} \mathrm{C}\) until the pressure rises to \(400 \mathrm{kPa}\). Determine (a) the entropy change of the refrigerant, (b) the entropy change of the heat source, and (c) the total entropy change for this process. Equation Transcription: 35°C Text Transcription: 0.5-m^3 134a 200 kPa 35 degree celsius 400 kPa

Calculate the heat transfer, in \(Btu/lbm\), for the reversible process 1-3 shown in Fig. P7–45E. Equation Transcription: Text Transcription: Btu/lbm

Determine the heat transfer, in \(\mathrm{kJ} / \mathrm{kg}\), for the reversible process 1-3 shown in Fig. P7-44. Equation Transcription: Text Transcription: kJ/kg

Problem 41P A rigid tank contains 5 kg of saturated vapor steam at 100°C. The steam is cooled to the ambient temperature of 25°C. (a) Sketch the process with respect to the saturation lines on a T-v diagram. (b) Determine the entropy change of the steam, in kJ/K. (c) For the steam and its surroundings, determine the total entropy change associated with this process, in kJ/K.

Problem 46P Steam enters an adiabatic diffuser at 150 kPa and 120°C with a velocity of 550 m/s. Determine the minimum velocity that the steam can have at the outlet when the outlet pressure is 300 kPa.

An isentropic steam turbine processes \(2\ kg/s\) of steam at \(3\ MPa\), which is exhausted at \(50\ kPa\) and \(100^{\circ} \mathrm{C}\). 5 percent of this flow is diverted for feedwater heating at \(500\ kPa\). Determine the power produced by this turbine, in \(kW\). Equation Transcription: 100°C Text Transcription: 2 kg/s 3 MPa 50 kPa 500 kPa kW 100 degree celsius

Problem 47P Steam enters an adiabatic turbine at 800 psia and 900°F and leaves at a pressure of 40 psia. Determine the maximum amount of work that can be delivered by this turbine.

Water at \(70\ kPa\) and \(100^{\circ} \mathrm{C}\) is compressed isentropically in a closed system to \(4\ MPa\). Determine the final temperature of the water and the work required, in \(\mathrm{kJ} / \mathrm{kg}\), for this compression. Equation Transcription: 100°C Text Transcription: 70 kPa 4 MPa kJ/kg 100 degree celsius

Problem 51P 0.7-kg of R-134a is expanded isentropically from 800 kPa and 50°C to 140 kPa. Determine the total heat transfer and work production for this expansion.

Problem 55P In Prob. 7–54, the water is stirred at the same time that it is being heated. Determine the minimum entropy change of the heat-supplying source if 100 kJ of work is done on the water as it is being heated. (Reference Prob. 7–54) A rigid, 20-L steam cooker is arranged with a pressure relief valve set to release vapor and maintain the pressure once the pressure inside the cooker reaches 150 kPa. Initially, this cooker is filled with water at 175 kPa with a quality of 10 percent. Heat is now added until the quality inside the cooker is 40 percent. Determine the minimum entropy change of the thermal energy reservoir supplying this heat.

Problem 54P A rigid, 20-L steam cooker is arranged with a pressure relief valve set to release vapor and maintain the pressure once the pressure inside the cooker reaches 150 kPa. Initially, this cooker is filled with water at 175 kPa with a quality of 10 percent. Heat is now added until the quality inside the cooker is 40 percent. Determine the minimum entropy change of the thermal energy reservoir supplying this heat.

Problem 56P A piston-cylinder device contains 5 kg of steam at 100°C with a quality of 50 percent. This steam undergoes two processes as follows: 1-2 Heat is transferred to the steam in a reversible manner while the temperature is held constant until the steam exists as a saturated vapor. 2-3he steam expands in an adiabatic, reversible process until the pressure is 15 kPa. (a) Sketch these processes with respect to the saturation lines on a single T-sdiagram. (b) Determine the heat transferred to the steam in process 1-2, in kJ. (c) Determine the work done by the steam in process 2-3, inkJ.

A \(0.55-\mathrm{ft}^{3}\) well-insulated rigid can initially contains refrigerant-\(134a\) at \(90\ psia\) and \(30^{\circ} \mathrm{F}\). Now a crack develops in the can, and the refrigerant starts to leak out slowly, Assuming the refrigerant remaining in the can has undergone a reversible, adiabatic process, determine the final mass in the can when the pressure drops to \(20\ psia\). Equation Transcription: 30°F Text Transcription: 134a 0.55-ft^3 30 degree fahrenheit

Problem 58P An electric windshield defroster is used to remove 0.25-in of ice from a windshield. The properties of the ice are Tsat = 32°F, uif = hif =144 Btu/lbm, and v =0.01602 ft3/lbm. Determine the electrical energy required per square foot of windshield surface area to melt this ice and remove it as liquid water at 32°F. What is the mini­mum temperature at which the defroster may be operated? Assume that no heat is transferred from the defroster or ice to the surroundings.

Problem 59P Consider two solid blocks, one hot and the other cold, brought into contact in an adiabatic container. After a while, thermal equilibrium is established in the container as a result of heat transfer. The first law requires that the amount of energy lost by the hot solid be equal to the amount of energy gained by the cold one. Does the second law require that the decrease in entropy of the hot solid be equal to the increase in entropy of the cold one?

A \(50-kg\) copper block initially at \(140^{\circ} \mathrm{C}\) is dropped into an insulated tank that contains \(90\ L\) of water at \(10^{\circ} \mathrm{C}\). Determine the final equilibrium temperature and the total entropy change for this process. Equation Transcription: 140°C 10°C Text Transcription: 50-kg 90 L 140 degree celsius 10 degree celsius

Problem 62P A 25-kg iron block initially at 350°C is quenched in an insulated tank that contains 100 kg of water at 18°C. Assuming the water that vaporizes during the process condenses back in the tank, determine the total entropy change during this process. .

Problem 61P Ten grams of computer chips with a specific heat of 0.3 kJ/kg?K are initially at 20°C. These chips are cooled by placement in 5 grams of saturated liquid R-134a at ?40°C. Presuming that the pressure remains constant while the chips are being cooled, determine the entropy change of (a) the chips, (b) the R-134a, and (c) the entire system. Is this process possible? Why?

Problem 52P 2-kg of saturated water vapor at 600 kPa are contained in a piston-cylinder device. The water expands adiabatically until the pressure is 100 kPa and is said to produce 700 kJ of work output. (a) Determine the entropy change of the water, in kJ/kg·K. (b) Is this process realistic? Using the T-s diagram for the process and the concepts of second law, support your answer.

Reconsider Prob. 7–63. Using EES (or other) software, study the effect of the mass of the iron block on the final equilibrium temperature and the total entropy change for the process. Let the mass of the iron vary from 10 to \(100\ kg\). Plot the equilibrium temperature and the total entropy change as a function of iron mass, and discuss the results. Equation Transcription: Text Transcription: 100 kg

Problem 63P A 30-kg aluminum block initially at 140°C is brought into contact with a 40-kg block of iron at 60°C in an insu­lated enclosure. Determine the final equilibrium temperature and the total entropy change for this process.

An adiabatic pump is to be used to compress saturated liquid water at \(10\ kPa\) to a pressure to \(15\ MPa\) in a reversible manner. Determine the work input using (a) entropy data from the compressed liquid table, (b) inlet specific volume and pressure values, (c) average specific volume and pressure values. Also, determine the errors involved in parts (b) and (c). Equation Transcription: Text Transcription: 10 kPa 15 MPa

A \(30-kg\) iron block and a \(40-kg\) copper block, both initially at \(800^{\circ} \mathrm{C}\), are dropped into a large lake at \(15^{\circ} \mathrm{C}\). Thermal equilibrium is established after a while as a result of heat transfer between the blocks and the lake water. Determine the total entropy change for this process. Equation Transcription: 80°C 15°C Text Transcription: 30-kg 40-kg 80 degree celsius 15 degree celsius

Problem 67P Some properties of ideal gases such as internal energy and enthalpy vary with temperature only [that is, u = u(T) and h = h(T)]. Is this also the case for entropy?

Problem 53P Steam enters a steady-flow adiabatic nozzle with a low inlet velocity as a saturated vapor at 6 MPa and expands to 1.2 MPa. (a) Under the conditions that the exit velocity is to be themaximum possible value, sketch the T-sdiagram with respect to the saturation lines for this process. (b) Determine the maximum exit velocity of the steam, in m/s.

Problem 68P Can the entropy of an ideal gas change during an isothermal process?

Problem 70P Prove that the two relations for entropy change of ideal gases under the constant-specific-heat assumption (Eqs. 7-33 and 7-34) are equivalent.

Problem 69P An ideal gas undergoes a process between two spec­ified temperatures, first at constant pressure and then at con­stant volume. For which case will the ideal gas experience a larger entropy change? Explain.

Problem 72P Which of the two gases—helium or nitrogen experiences the greatest entropy change as its state is changed from 2000 kPa and 427°C to 200 kPa and 27°C?

Problem 71P Starting with the second T dsrelation (Eq. 7-26), obtain Eq. 7-34 for the entropy change of ideal gases under the constant-specific-heat assumption.

Problem 73P Air is expanded from 2000 kPa and 500°C to 100 kPa and 50°C. Assuming constant specific heats, determine the change in the specific entropy of air.

Problem 74P What is the difference between the entropies of air at 15 psia and 90°F and air at 40 psia and 210°F per unit mass basis.

Oxygen gas is compressed in a piston-cylinder device from an initial state of \(0.8 \mathrm{~m}^{3} / \mathrm{kg}\) and \(25^{\circ} \mathrm{C}\) to a final state of \(0.1 \mathrm{~m}^{3} / \mathrm{kg}\) and \(287^{\circ} \mathrm{C}\). Determine the entropy change of the oxygen during this process. Assume constant specific heats. Equation Transcription: 25°C 287°C Text Transcription: 0.8 m^3/kg 0.1 m^3/kg 25 degree celsius 287 degree celsius

A \(1.5-\mathrm{m}^{3}\) insulated rigid tank contains \(2.7 \mathrm{~kg}\) of carbon dioxide at \(100 \mathrm{kPa}\). Now paddle-wheel work is done on the system until the pressure in the tank rises to \(150 \mathrm{kPa}\). Determine the entropy change of carbon dioxide during this process. Assume constant specific heats. Equation Transcription: Text Transcription: 1.5-m^3 2.7 kg 100 kPa 150 kPa

Problem 78P A piston-cylinder device contains 0.75 kg of nitrogen gas at 140 kPa and 37°C. The gas is now compressed slowly in a polytropic process during which PV13 = constant. The process ends when the volume is reduced by one-half. Deter­mine the entropy change of nitrogen during this process.

Problem 77P An insulated piston-cylinder device initially con­tains 300 L of air at 120 kPa and 17°C. Air is now heated for 15 min by a 200-W resistance heater placed inside the cylinder. The pressure of air is maintained constant during this process. Determine the entropy change of air, assuming (a) constant specific heats and (b) variable specific heats.

Air is compressed steadily by a \(5 \mathrm{~kW}\) compressor from \(100 \mathrm{kPa}\) and \(17^{\circ} \mathrm{C}\) to \(600 \mathrm{kPa}\) and \(167^{\circ} \mathrm{C}\) at a rate of \(1.6 \mathrm{~kg} / \mathrm{min}\). During this process, some heat transfer takes place between the compressor and the surrounding medium at \(17^{\circ} \mathrm{C}\). Determine the rate of entropy change of air during this process. Equation Transcription: 17°C Text Transcription: 5-kW 100 kPa 600 kPa 1.6 kg/min 17 degree celsius

Reconsider Prob. 7–78. Using EES (or other) software, investigate the effect of varying the polytropic exponent from 1 to 1.4 on the entropy change of the nitrogen. Show the processes on a common P-v diagram.

Problem 81P Air enters a nozzle steadily at 280 kPa and 77°C with a velocity of 50 m/s and exits at 85 kPa and 320 m/s. The heat losses from the nozzle to the surrounding medium at 20°C are estimated to be 3.2 kJ/kg. Determine (a) the exit temperature and (b) the total entropy change for this process.

A mass of 25 lbm of helium undergoes a process from an initial state of \(50 \mathrm{ft}^{3} / 1 \mathrm{lbm} and 60^{\circ} \mathrm{F}\) to a final state of \(10 \mathrm{ft}^{3} / \mathrm{lbm} and 240^{\circ} \mathrm{F}\). Determine the entropy change of helium during this process, assuming (a) the process is reversible and (b) the process is irreversible. Equation Transcription: Text Transcription: 50 ft3/lbm and 60°F 10 ft3/lbm and 240°F

Problem 85P Nitrogen is compressed isentropically from 100 kPa and 27°C to 1000 kPa in a piston-cylinder device. Determine its final temperature.

Problem 84P 1-kg of air at 200 kPa and 127°C is contained in a piston-cylinder device. Air is now allowed to expand in a reversible, isothermal process until its pressure is 100 kPa. Determine the amount of heat transferred to the air during this expansion.

Problem 86P Air at 3.5 MPa and 500°C is expanded in an adiabatic gas turbine to 0.2 MPa. Calculate the maximum work that this turbine can produce, in kJ/kg.

Air is compressed in an isentropic compressor from 15 psia and \(70^{\circ} \mathrm{F}\) to 200 psia. Determine the outlet temperature and the work consumed by this compressor per unit mass of air. Equation Transcription: Text Transcription: 70°F

Problem 88P An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 12 kmol of an ideal gas at 330 kPa and 50°C, and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Determine the total entropy change during this process.

An insulated rigid tank contains 4 kg of argon gas at \(450 \mathrm{kPa} \text { and } 30^{\circ} \mathrm{C}\). A valve is now opened, and argon is allowed to escape until the pressure inside drops to 200 kPa. Assuming the argon remaining inside the tank has undergone a reversible, adiabatic process, determine the final mass in the tank. Equation Transcription: Text Transcription: 450 kPa and 30°C

Problem 93P Air at 27°C and 100 kPa is contained in a pistoncylinder device. When the air is compressed adiabatically, a minimum work input of 1000 kJ will increase the pressure to 600 kPa. Assuming air has constant specific heats evaluated at 300 K, determine the mass of air in the device.

Reconsider Prob. 7–89. Using EES (or other) software, investigate the effect of the final pressure on the final mass in the tank as the pressure varies from 450 to 150 kPa, and plot the results.

Problem 91P Air enters an adiabatic nozzle at 60 psia, 540°F, and 200 ft/s and exits at 12 psia. Assuming air to be an ideal gas with variable specific heats and disregarding any irreversibil­ities, determine the exit velocity of the air.

Problem 92P Air at 257°C and 400 kPa is contained in a pistoncylinder device. The air expands adiabatically until the pressure is 100 kPa. Determine the mass of air needed to produce maximum work of 1000 kJ. Assume air has constant specific heats evaluated at 300 K.

Problem 94P Air is compressed in a piston-cylinder device from 90 kPa and 20°C to 400 kPa in a reversible isothermal process. Determine (a) the entropy change of air and (b) the work done.

Problem 95P Helium gas is compressed from 90 kPa and 30°C to 450 kPa in a reversible, adiabatic process. Determine the final temperature and the work done, assuming the process takes place (a) in a piston-cylinder device and (b) in a steady flow compressor.

Problem 96P 5-kg of air at 427°C and 600 kPa are contained in a piston-cylinder device. The air expands adiabatically until the pressure is 100 kPa and produces 600 kJ of work output. Assume air has constant specific heats evaluated at 300 K. (a) Determine the entropy change of the air, in kJ/kg?K (b) Since the process is adiabatic, is the process realistic? Using concepts of the second law, support ycur answer.

Problem 99P In large compressors, the gas is frequently cooled while being compressed to reduce the power consumed by the compressor. Explain how cooling the gas during a com­pression process reduces the power consumption.

Problem 100P The turbines in steam power plants operate essen­tially under adiabatic conditions. A plant engineer suggests to end this practice. She proposes to run cooling water through the outer surface of the casing to cool the steam as it flows through the turbine. This way, she reasons, the entropy of the steam will decrease, the performance of the turbine will improve, and as a result the work output of the turbine will increase. How would you evaluate this proposal?

A container filled with 45 kg of liquid water at \(95^{\circ} \mathrm{C}\) is placed in a \(90-m^{3}\) room that is initially at \(12^{\circ} \mathrm{C}\). Thermal equilibrium is established after a while as a result of heat transfer between the water and the air in the room. Using constant specific heats, determine (a) the final equilibrium temperature, (b) the amount of heat transfer between the water and the air in the room, and (c) the entropy generation. Assume the room is well sealed and heavily insulated. Equation Transcription: Text Transcription: 95°C 90-m3 12°C

The well-insulated container shown in Fig. P7–98E is initially evacuated. The supply line contains air that is maintained at 150 psia and \(140^{\circ} \mathrm{F}\). The valve is opened until the pressure in the container is the same as the pressure in the supply line. Determine the minimum temperature in the container when the valve is closed. Equation Transcription: Text Transcription: 140°F

Problem 101P It is well known that the power consumed by a com­pressor can be reduced by cooling the gas during compression. Inspired by this, somebody proposes to cool the liquid as it flows through a pump, in order to reduce the power con­sumption of the pump. Would you support this proposal? Explain.

Problem 102P Air is compressed isothermally from 13 psia and 90°F to 80 psia in a reversible steady-flow device. Calcu­late the work required, in Btu/lbm, for this compression.

Problem 103P Saturated water vapor at 150°C is compressed in a reversible steady-flow device to 1000 kPa while its specific volume remains constant. Determine the work required, in kJ/kg.

Calculate the work produced, in \(B t u / l b m\), for the reversible steady-flow process 1-3 shown in Fig. P7–104E. Equation Transcription: Text Transcription: B t u / l b m

Liquid water enters a \(16-k W\) pump at \(100-k P a\) pressure at a rate of \(5 k g / s\). Determine the highest pressure the liquid water can have at the exit of the pump. Neglect the kinetic and potential energy changes of water, and take the specific volume of water to be \(0.001 m^{3} / k g\) Equation Transcription: Text Transcription: 16-kW 100-kPa 5 kg/s 0.001 m3/kg

Problem 109P Helium gas is compressed from 16 psia and 85°F to 120 psia at a rate of 10 ft3/s. Determine the power input to the compressor, assuming the compression process to be (a) isentropic, (b) polytropic with n= 1.2, (c) isothermal, and (d) ideal two-stage polytropic with n= 1.2.

Reconsider Prob. 7–109E. Using EES (or other) software, evaluate and plot the work of compression and entropy change of the helium as functions of the polytropic exponent as it varies from 1 to 1.667. Discuss your results.

Problem 107P Consider a steam power plant that operates between the pressure limits of 5 MPa and 10 kPa. Steam enters the pump as saturated liquid and leaves the turbine as saturated vapor. Determine the ratio of the work delivered by the tur­bine to the work consumed by the pump. Assume the entire cycle to be reversible and the heat losses from the pump and the turbine to be negligible.

Problem 111P Nitrogen gas is compressed from 80 kPa and 27°C to 480 kPa by a 10-kW compressor. Determine the mass flow rate of nitrogen through the compressor, assuming the compression process to be (a) isentropic, (b) polytropic with n = 1.3, (c) isothermal, and (d) ideal two-stage polytropic with n = 1.3.

Problem 112P Saturated refrigerant-134a vapor at 15 psia is compressed reversibly in an adiabatic compressor to 80 psia. Determine the work input to the compressor. What would your answer be if the refrigerant were first condensed at constant pressure before it was compressed?

Problem 105P Water enters the pump of a steam power plant as saturated liquid at 20 kPa at a rate of 45 kg/s and exits at 6 MPa. Neglecting the changes in kinetic and potential energies and assuming the process to be reversible, determine the power input to the pump.

Problem 113P Describe the ideal process for an (a) adiabatic tur­bine, (b) adiabatic compressor, and (c) adiabatic nozzle, and define the isentropic efficiency for each device.

Problem 116P Steam at 100 psia and 650°F is expanded adiabati­cally in a closed system to 10 psia. Determine the work pro­duced, in Btu/lbm, and the final temperature of steam for an isentropic expansion efficiency of 80 percent.

Problem 114P Is the isentropic process a suitable model for com­pressors that are cooled intentionally? Explain.

Problem 117P Steam enters an adiabatic turbine at 5 MPa, 650°C, and 80 m/s and leaves at 50 kPa, 150°C, and 140 m/s. If the power output of the turbine is 8 MW, determine (a) the mass flow rate of the steam flowing through the turbine and (b) the isentropic efficiency of the turbine.

Steam enters an adiabatic turbine at 8 MPa and \(500^{\circ} \mathrm{C}\) with a mass flow rate of \(3 \mathrm{~kg} / \mathrm{s}\) and leaves at 30 kPa. The isentropic efficiency of the turbine is 0.90. Neglecting the kinetic energy change of the steam, determine (a) the temperature at the turbine exit and (b) the power output of the turbine. Equation Transcription: Text Transcription: 500°C 3 kg/s

Problem 115P On a T-sdiagram, does the actual exit state (state 2) of an adiabatic turbine have to be on the right-hand side of the isentropic exit state (state 2s)? Why?

Problem 118P Combustion gases enter an adiabatic gas turbine at 1540°F and 120 psia and leave at 60 psia with a low velocity.Treating the combustion gases as air and assuming an isentropic efficiency of 82 percent, determine the work output of the turbine.

Steam at 4 MPa and \(350^{\circ} \mathrm{C}\) is expanded in an adiabatic turbine to 120 kPa. What is the isentropic efficiency of this turbine if the steam is exhausted as a saturated vapor? Equation Transcription: Text Transcription: 350°C

Problem 122P Carbon dioxide enters an adiabatic compressor at 100 kPa and 300 K at a rate of 1.8 kg/s and exits at 600 kPa and 450 K. Neglecting the kinetic energy changes, determine the isentropic efficiency of the compressor.

Problem 127P Argon gas enters an adiabatic compressor at 14 psia and 75°F with a velocity of 60 ft/s, and it exits at 200 psia and 240 ft/s. If the isentropic efficiency of the compressor is 87 percent, determine (a) the exit temperature of the argon and (b) the work input to the compressor.

Problem 126P Air is compressed by an adiabatic compressor from 95 kPa and 27°C to 600 kPa and 277°C. Assuming variable specific heats and neglecting the changes in kinetic and potential energies, determine (a) the isentropic efficiency of the compressor and (b) the exit temperature of air if the process were reversible.

Reconsider Prob. 7–128E. Using EES (or other) software, study the effect of varying the nozzle isentropic efficiency from 0.8 to 1.0 on both the exit temperature and pressure of the air, and plot the results.

Problem 123P A refrigeration unit compresses saturated R-134a vapor at 10°C to 1000 kPa. How much power is required to compress 0.9 kg/s of R-134a with a compressor efficiency of 85 percent?

Refrigerant-134a enters an adiabatic compressor as saturated vapor at \(100 \mathrm{kPa}\) at a rate of \(0.7 \mathrm{~m}^{3} / \mathrm{min}\) and exits at 1-MPa pressure. If the isentropic efficiency of the compressor is 87 percent, determine the temperature of the refrigerant at the exit of the compressor and the power input, in . Also, show the process on a diagram with respect to saturation lines. Equation Transcription: Text Transcription: 100kPa 0.7 m3/min

Problem 128P Air enters an adiabatic nozzle at 45 psia and 940°F with low velocity and exits at 650 ft/s. If the isentropic effi­ciency of the nozzle is 85 percent, determine the exit temper­ature and pressure of the air.

Problem 130P The exhaust nozzle of a jet engine expands air at 300 kPa and 180°C adiabatically to 100 kPa. Determine the air velocity at the exit when the inlet velocity is low and the nozzle isentropic efficiency is 96 percent.

An adiabatic diffuser at the inlet of a jet engine increases the pressure of the air that enters the diffuser at 11 psia and 308F to 20 psia. What will the air velocity at the diffuser exit be if the diffuser isentropic efficiency defined as the ratio of the actual kinetic energy change to the isentropic kinetic energy change is 82 percent and the diffuser inlet velocity is \(1200 \mathrm{ft} / \mathrm{s}\)? Equation Transcription: Text Transcription: 1200 ft/s

Problem 134P Oxygen enters an insulated 12-cm-diameter pipe with a velocity of 70 m/s. At the pipe entrance, the oxygen is at 240 kPa and 20°C; and, at the exit, it is at 200 kPa and 18°C. Calculate the rate at which entropy is generated in the pipe.

Problem 135P Nitrogen is compressed by an adiabatic compressor from 100 kPa and 25°C to 600 kPa and 290°C. Calculate the entropy generation for this process, in kJ/kg·K.

Hot combustion gases enter the nozzle of a turbojet engine at \(260 \mathrm{kPa}, 747^{\circ} \mathrm{C} \text {, and } 80 \mathrm{~m} / \mathrm{s}\), and they exit at a pressure of 85 kPa. Assuming an isentropic efficiency of 92 percent and treating the combustion gases as air, determine () the exit velocity and () the exit temperature. Equation Transcription: Text Transcription: 260 kPa, 747°C, and 80 m/s

Steam enters an adiabatic turbine steadily at \(7 M P a, 500^{\circ} \mathrm{C}, \text { and } 45 \mathrm{~m} / \mathrm{s}\), and leaves at 100 kPa and \(75 \mathrm{~m} / \mathrm{s}\). If the power output of the turbine is 5 MW and the isentropic efficiency is 77 percent, determine () the mass flow rate of steam through the turbine, () the temperature at the turbine exit, and () the rate of entropy generation during this process. Equation Transcription: Text Transcription: 7 MPa, 500°C, and 45 m/s 75 m/s

In an ice-making plant, water at \(0^{\circ} \mathrm{C}\) is frozen at atmospheric pressure by evaporating saturated R-134a liquid at \(216^{\circ} \mathrm{C}\). The refrigerant leaves this evaporator as a saturated vapor, and the plant is sized to produce ice at \(0^{\circ} \mathrm{C}\) at a rate of 2500 kg/h. Determine the rate of entropy generation in this plant. Equation Transcription: Text Transcription: 0°C 216°C 0°C

Water at 20 psia and \(50^{\circ} \mathrm{F}\) enters a mixing chamber at a rate of \(300 \mathrm{lbm} / \mathrm{min}\) where it is mixed steadily with steam entering at 20 psia and \(240^{\circ} \mathrm{F}\). The mixture leaves the chamber at 20 psia and \(130^{\circ} \mathrm{F}\), and heat is lost to the surrounding air at \(70^{\circ} \mathrm{F}\) at a rate of \(180 \mathrm{Btu} / \mathrm{min}\). Neglecting the changes in kinetic and potential energies, determine the rate of entropy generation during this process? Equation Transcription: Text Transcription: 50°F 300 lbm/min 240°F 130°F 70°F 180 Btu/min

Problem 140P Steam is to be condensed on the shell side of a heat exchanger at 150°F. Cooling water enters the tubes at 60°F at a rate of 44 lbm/s and leaves at 73°F. Assuming the heat exchanger to be well-insulated, determine (a) the rate of heat transfer in the heat exchanger and (b) the rate of entropy generation in the heat exchanger.

An adiabatic heat exchanger is to cool ethylene glycol \(\left(c_{p}=2.56 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) flowing at a rate of \(2 \mathrm{~kg} / \mathrm{s}\) from \(80 \mathrm{to} 40^{\circ} \mathrm{C}\) by water \(\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) that enters at \(20^{\circ} \mathrm{C}\) and leaves at \(55^{\circ} \mathrm{C}\). Determine the rate of heat transfer and the rate of entropy generation in the heat exchanger. Equation Transcription: Text Transcription: (cp=2.56 kJ/kg°C) 2 kg/s 80 to 40°C (cp=4.18 kJ/kg°C) 20°C 55°C

A well-insulated heat exchanger is to heat water \(\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} C\right)\) from 25 to at a rate of \(0.50 \mathrm{~kg} / \mathrm{s}\) The heating is to be accomplished by geothermal water \(\left(c_{p}=4.13 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) available at at a mass flow rate of \(0.75 \mathrm{~kg} / \mathrm{s}\). Determine the rate of heat transfer and the rate of entropy generation in the heat exchanger. Equation Transcription: Text Transcription: (cp=4.18 kJ/kg°C) 0.50 kg/s (cp=4.13 kJ/kg°C) 0.75 kg/s

A well-insulated, thin-walled, double-pipe, counter-flow heat exchanger is to be used to cool oil \(\left(c_{p}=2.20 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) from \(150^{\circ} \mathrm{C} t o 40^{\circ} \mathrm{C}\) at a rate of \(2 \mathrm{~kg} / \mathrm{s}\) by water \(\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) that enters at \(22^{\circ} \mathrm{C}\) at a rate of \(1.5 \mathrm{~kg} / \mathrm{s}\). Determine the rate of heat transfer and the rate of entropy generation in the heat exchanger. Equation Transcription: Text Transcription: (cp=2.20 kJ/kg°C) 150°C to 40°C 2 kg/s (cp=4.18 kJ/kg°C) 22°C 1.5 kg/s

Problem 136P Air enters a compressor steadily at the ambient conditions of 100 kPa and 22°C and leaves at 800 kPa. Heat is lost from the compressor in the amount of 120 kJ/kg and the air experiences an entropy decrease of 0.40 kJ/kg?K. Using constant specific heats, determine (a) the exit temperature of the air, (b) the work input to the compressor, and (c) the entropy generation during this process.

Problem 146P Chickens with an average mass of 2.2 kg and average specific heat of 3.54 kJ/kg?°C are to be cooled by chilled water that enters a continuous-flow-type immersion chiller at 0.5°C and leaves at 2.5°C. Chickens are dropped into the chiller at a uniform temperature of 15°C at a rate of 250 chickens per hour and are cooled to an average temperature Of 3°C before they are taken out. The chiller gains heat from the surroundings at 25°C at a rate of 150 kJ/h. Determine (a) the rate of heat removal from the chickens, in kW, and (b) the rate of entropy generation during this chilling process.

In a dairy plant, milk at is pasteurized continuously at at a rate of \(12 \mathrm{~L} / \mathrm{s}\) for 24 hours a day and 365 days a year. The milk is heated to the pasteurizing temperature by hot water heated in a natural-gas-fired boiler that has an efficiency of 82 percent. The pasteurized milk is then cooled by cold water at before it is finally refrigerated back to . To save energy and money, the plant installs a regenerator that has an effectiveness of 82 percent. If the cost of natural gas is therm therm \(=105,500 \mathrm{~kJ}\), determine how much energy and money the regenerator will save this company per year and the annual reduction in entropy generation. Equation Transcription: Text Transcription: Equation Transcription: Text Transcription: 12 L/s =105, 500kJ

An ordinary egg can be approximated as a 5.5-cmdiameter sphere. The egg is initially at a uniform temperature of and is dropped into boiling water at . Taking the properties of the egg to be \(\rho=1020 \mathrm{~kg} / \mathrm{m}^{3} \text { and } c_{p}=3.32 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\), determine how much heat is transferred to the egg by the time the average temperature of the egg rises to and the amount of entropy generation associated with this heat transfer process. Equation Transcription: Text Transcription: \rho =1020 kg/m3 and cp=3.32 kJ/kg°C

In a production facility, -in-thick, 2 -ft 2-ft square brass plates \(\left(\rho=532.5 \mathrm{lbm} / \mathrm{ft}^{3} \text { and } c_{p}=0.091 \mathrm{Btu} / \mathrm{lbm} \cdot{ }^{\circ} \mathrm{F}\right)\) that are initially at a uniform temperature of are heated by passing them through an oven at at a rate of 450 per minute. If the plates remain in the oven until their average temperature rises to , determine the rate of heat transfer to the plates in the furnace and the rate of entropy generation associated with this heat transfer process. Equation Transcription: Text Transcription: (\rho=532.5 lbm/ft3 and cp=0.091Btu/lbm°F)

Carbon-steel balls \(\left(\rho=7833 \mathrm{~kg} / \mathrm{m}^{3} \text { and } c_{p}=0.465 \mathrm{~kJ} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right) 8 \mathrm{~mm}\) in diameter are annealed by heating them first to in a furnace and then allowing them to cool slowly to in ambient air at . If 2500 balls are to be annealed per hour, determine the rate of heat transfer from the balls to the air and the rate of entropy generation due to heat loss from the balls to the air. Equation Transcription: Text Transcription: (rho=7833 kg/m3 and cp=0.465 kJ/g°C)8 mm

Long cylindrical steel rods \(\left(\rho=7833 \mathrm{~kg} / \mathrm{m}^{3} \text { and } c_{p}=0.465 \mathrm{~kJ} / \mathrm{kg}^{\circ} \mathrm{C}\right)\) of 10 -cm diameter are heat treated by drawing them at a velocity of through a -long oven maintained at . If the rods enter the oven at and leave at , determine the rate of heat transfer to the rods in the oven and the rate of entropy generation associated with this heat transfer process. Equation Transcription: Text Transcription: (\rho =7833 kg/m3 and cp=0.465 kJ/kg°C)

The inner and outer surfaces of a \(4-m \times 10-m\) brick wall of thickness are maintained at temperatures of and , respectively. If the rate of heat transfer through the wall is , determine the rate of entropy generation within the wall. Equation Transcription: Text Transcription: 4 - m x 10 - m

Problem 152P Steam enters a diffuser at 20 psia and 240°F with a velocity of 900 ft/s and exits as saturated vapor at 240°F and 100 ft/s. The exit area of the diffuser is 1 ft2. Determine (a) the mass flow rate of the steam and (b) the rate of entropy generation during this process. Assume an ambient temperature of 77°F.

Steam enters an adiabatic nozzle at \(2 \mathrm{MP} a and 350^{\circ} \mathrm{C}\) with a velocity of \(55 \mathrm{~m} / \mathrm{s}\) and exits at \(0.8 \mathrm{MPa} and \(390 \mathrm{~m} / \mathrm{s}\) If the nozzle has an inlet area of \(7.5 \mathrm{~cm}^{2}\), determine (a) the exit temperature and the rate of entropy generation for this process. Equation Transcription: m/s Text Transcription: 2MPa and 350°C 55 m/s 0.8MPa and 390m/s 7.5 cm2

Problem 151P A frictionless piston-cylinder device contains satu­rated liquid water at 40-psia pressure. Now 600 Btu of heat is transferred to water from a source at 1000°F, and part of the liquid vaporizes at constant pressure. Determine the total entropy generated during this process, in Btu/R..

Steam expands in a turbine steadily at a rate of \(40,000 \mathrm{~kg} / \mathrm{h}\), entering at \(8.MPa and 500^{\circ} \mathrm{C}\) and leaving at 40 kPa as saturated vapor. If the power generated by the turbine is , determine the rate of entropy generation for this process. Assume the surrounding medium is at \(25^{\circ} \mathrm{C}\). Equation Transcription: Text Transcription: 40, 000 kg/h 8MPa and 500°C 25°C

Problem 155P A hot-water stream at 70°C enters an adiabatic mix­ing chamber with a mass flcw rate of 3.6 kg/s, where it is mixed with a stream of cold water at 20°C. If the mixture leaves the chamber at 42°C, determine (a) the mass flow rate of the cold water and (b) the rate of entropy generation dur­ing this adiabatic mixing process. Assume all the streams are at a pressure of 200 kPa.

Problem 158P An iron block of unknown mass at 185°F is dropped into an insulated tank that contains 0.8 ft3 of water at 70°F. At the same time, a paddle wheel driven by a 200-W motor is activated to stir the water. Thermal equilibrium is established after 10 min- with a final temperature of 75°F. Determine (a) the mass of the iron block and (b) the entropy generated during this process.

Problem 161P A 150-hp compressor in an industrial facility is housed inside the production area where the average temperature during operating hours is 25°C. The average temperature of outdoors during the same hours is 10°C. The compressor operates 4500 h/yr at 85 percent of rated load and is driven by an electric motor that has an efficiency of 90 percent. Taking the price of electricity to be $0.12/kWh, determine the amount of energy and money saved as a result of drawing outside air to the compressor instead of using the inside air.

Problem 159P Compressed air is one of the key utilities in manufacturing facilities, and the total installed power of compressed- air systems in the United States is estimated to be about 20 million horsepower. Assuming the compressors to operate at full load during one-third of the time on average and the average motor efficiency to be 90 percent, determine how much energy and money will be saved per year if the energy consumed by compressors is reduced by 5 percent as a result of implementing some conservation measures. Take the unit cost of electricity to be $0.11/kWh.

Liquid water at \(200 \mathrm{kPa} \text { and } 15^{\circ} \mathrm{C}\) is heated in a chamber by mixing it with superheated steam at \(200 \mathrm{kPa} \text { and } 150^{\circ} \mathrm{C}\). Liquid water enters the mixing chamber at a rate of \(4.3 \mathrm{~kg} / \mathrm{s}\), and the chamber is estimated to lose heat to the surrounding air at \(20^{\circ} \mathrm{C}\) at a rate of 1200 kJ/min. If the mixture leaves the mixing chamber at 200 kPa and \(80^{\circ} \mathrm{C}\), determine () the mass flow rate of the superheated steam and () the rate of entropy generation during this mixing process. Equation Transcription: Text Transcription: 200 kPa and 15°C 200 kPa and 150°C 4.3 kg/s 20°C 80 °C

Problem 160P The compressed-air requirements of a plant at sea level are being met by a 90-hp compressor that takes in air at the local atmospheric pressure of 101.3 kPa and the average temperature of 15°C and compresses it to 1100 kPa. An investigation of the compressed-air system and the equipment using the compressed air reveals that compressing the air to 750 kPa is sufficient for this plant. The compressor operates 3500 h/yr at 75 percent of the rated load and is driven by an electric motor that has an efficiency of 94 percent. Taking the price of electricity to be $0.105/kWh, determine the amount of energy and money saved as a result of reducing the pressure of the compressed air.

Problem 157P A 0.18-m3 rigid tank is filled with saturated liquid water at 120°C. A valve at the bottom of the tank is now opened, and one-half of the total mass is withdrawn from the tank in the liquid form. Heat is transferred to water from a source at 230°C so that the temperature in the tank remains constant. Determine (a) the amount of heat transfer and (b) the total entropy generation for this process.

Problem 162P The compressed-air requirements of a plant are being met by a 100-hp screw compressor that runs at full load during 40 percent of the time and idles the rest of the time during operating hours. The compressor consumes 35 percent of the rated power when idling and 90 percent of the power when compressing air. The annual operating hours of the facility are 3800 h, and the unit cost of electricity is $0.115/kWh. It is determined that the compressed-air requirements of the facility during 60 percent of the time can be met by a 25-hp reciprocating compressor that consumes 95 percent of the rated power when compressing air and no power when not compressing air. It is estimated that the 25-hp compressor runs 85 percent of the time. The efficiencies of the motors of the large and the small compressors at or near full load are 0.90 and 0.88, respectively. The efficiency of the large motor at 35 percent load is 0.82. Determine the amount of energy and money saved as a result of switching to the 25-hp compressor during 60 percent of the time.

Problem 163P The compressed-air requirements of a plant are being met by a 90-hp screw compressor. The facility stops production for one hour every day, including weekends, for lunch break, but the compressor is kept operating. The compressor consumes 35 percent of the rated power when idling, and the unit cost of electricity is $0.11/kWh. Determine the amount of energy and money saved per year as a result of turning the compressor off during lunch break. Take the efficiency of the motor at part load to be 84 percent.

Problem 165P The 1800-rpm, 150-hp motor of a compressor is burned out and is to be replaced by either a standard motor that has a full-load efficiency of 93.0 percent and costs $9031 or a high-efficiency motor that has an efficiency of 96.2 percent and costs $10,942. The compressor operates 4368 h/yr at full load, and its operation at part load is negligible. If the cost of electricity is $0.125/kWh, determine the amount of energy and money this facility will save by purchasing the high-efficiency motor instead of the standard motor. Also, determine if the savings from the high-efficiency motor justify the price differential if the expected life of the motor is 10 years. Ignore any possible rebates from the local power company.

Problem 167P The compressors of a production facility maintain the compressed-air lines at a (gage) pressure of 700 kPa at 1400-m elevation, where the atmospheric pressure is 85.6 kPa. The average temperature of air is 15°C at the compressor inlet and 25°C in the compressed-air lines. The facility operates 4200 h/yr, and the average price of electricity is $0.12/kWh. Taking the compressor efficiency to be 0.8, the motor efficiency to be 0.93, and the discharge coefficient to be 0.65, determine the energy and money saved per year by sealing a leak equivalent to a 3-mm-diameter hole on the compressed-air line.

Problem 166P The space heating of a facility is accomplished by natural gas heaters that are 85 percent efficient. The compressed air needs of the facility are met by a large liquid cooled compressor. The coolant of the compressor is cooled by air in a liquid-to-air heat exchanger whose airflow section is 1.0-m high and 1.0-m wide. During typical operation, the air is heated from 20 to 52°C as it flows through the heat exchanger. The average velocity of air on the inlet side is measured to be 3 m/s. The compressor operates 20 hours a day and 5 days a week throughout the year. Taking the heating season to be 6 months (26 weeks) and the cost of the natural gas to be $1.25/therm (1 therm = 100,000 Btu = 105,500 kJ), determine how much money will be saved by diverting the compressor waste heat into the facility during the heating season.

Problem 164P The compressed-air requirements of a plant are met by a 150-hp compressor equipped with an intercooler, an aftercooler, and a refrigerated dryer. The plant operates 6300 h/yr, but the compressor is estimated to be compressing air during only one-third of the operating hours, that is, 2100 hours a year. The compressor is either idling or is shut off the rest of the time. Temperature measurements and calculations indicate that 25 percent of the energy input to the compressor is removed from the compressed air as heat in the aftercooler. The COP of the refrigeration unit is 2.5, and the cost of electricity is $0.12/kWh. Determine the amount of the energy and money saved per year as a result of cooling the compressed air before it enters the refrigerated dryer.

The energy used to compress air in the United States is estimated to exceed one-half quadrillion \(\left(0.5 \times 10^{15}\right)\)kJ per year. It is also estimated that 10 to 40 percent of the compressed air is lost through leaks. Assuming, on average, 20 percent of the compressed air is lost through air leaks and the unit cost of electricity is $0.13/kWh, determine the amount and cost of electricity wasted per year due to air leaks. Equation Transcription: Text Transcription: (0.5 x 10^15)

Problem 169P A heat engine whose thermal efficiency is 35 percent uses a hot reservoir at 1100 R and a cold reservoir at 550 R. Calculate the entropy change of the two reservoirs when 1 Btu of heat is transferred from the hot reservoir to the engine. Does this engine satisfy the increase of entropy principle? If the thermal efficiency of the heat engine is increased to 60 percent, will the increase of entropy principle still be satisfied?

A refrigerator with a coefficient of performance of 4 transfers heat from a cold region at \(-20^{\circ} \mathrm{C}\) to a hot region at \(30^{\circ} \mathrm{C}\). Calculate the total entropy change of the regions when 1 kJ of heat is transferred from the cold region. Is the second law satisfied? Will this refrigerator still satisfy the second law if its coefficient of performance is 6? Equation Transcription: Text Transcription: -20°C 30°C

Problem 171P It has been suggested that air at 100 kPa and 25°C can be cooled by first compressing it adiabatically in a closed system to 1000 kPa and then expanding it adiabatically back to 100 kPa. Is this possible?

Problem 173P Can saturated water vapor at 200 kPa be condensed to a saturated liquid in an isobaric, closed system process while only exchanging heat with an isothermal energy reservoir at 90°C? (Hint: Determine the entropy generation.)

Problem 174P A 100-lbm block of a solid material whose specific heat is 0.5 Btu/lbm·R is at 80°F. It is heated with 10 lbm of saturated water vapor that has a constant pressure of 20 psia. Determine the final temperature of the block and water, and the entropy change of (a) the block, (b) the water, and (c) the entire system. Is this process possible? Why?

A horizontal cylinder is separated into two compartments by an adiabatic, frictionless piston. One side contains \(0.2 \mathrm{~m}^{3}\) of nitrogen and the other side contains 0.1 kg of helium, both initially at \(20^{\circ} \mathrm{C} \text { and } 95^{\circ} \mathrm{kPa}\). The sides of the cylinder and the helium end are insulated. Now heat is added to the nitrogen side from a reservoir at \(500^{\circ} \mathrm{C}\) until the pressure of the helium rises to 120 kPa. Determine () the final temperature of the helium, () the final volume of the nitrogen, () the heat transferred to the nitrogen, and () the entropy generation during this process. Equation Transcription: Text Transcription: 0.2 m3 20°C and 95°kPa 500°C

A piston-cylinder device contains air that undergoes a reversible thermodynamic cycle. Initially, air is at and with a volume of \(0.3 \mathrm{~m}^{3}\) Air is first expanded isothermally to , then compressed adiabatically to the initial pressure, and finally compressed at the constant pressure to the initial state. Accounting for the variation of specific heats with temperature, determine the work and heat transfer for each process. Equation Transcription: Text Transcription: 0.3 m^3

A piston-cylinder device initially contains \(15 f t^{3}\) of helium gas at 25 psia and \(70^{\circ} \mathrm{F}\). Helium is now compressed in a polytropic process \(\left(P V_{n}=\text { constant }\right)\) to 70 psia and \(300^{\circ} \mathrm{F}\). Determine (a) the entropy change of helium, the entropy change of the surroundings, and whether this process is reversible, irreversible, or impossible. Assume the surroundings are at \(70^{\circ} \mathrm{F}\). Equation Transcription: Text Transcription: 15ft3 70°F (PVn =constant) 300°F 70°F

Problem 172P 1-1bm of air at 10 psia and 70°F is contained in a piston-cylinder device. Next, the air is compressed reversibly to 100 psia while the temperature is maintained constant. Determine the total amount of heat transferred to the air during this compression.

A piston-cylinder device contains steam that undergoes a reversible thermodynamic cycle. Initially the steam is at and with a volume of \(0.3 m^{3}\). The steam is first expanded isothermally to , then compressed adiabatically to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine the net work and heat transfer for the cycle after you calculate the work and heat interaction for each process. Equation Transcription: Text Transcription: 0.3 m^3

A \(0.8-m^{3}\) rigid tank contains carbon dioxide \(\left(C O_{2}\right)\) gas at and . A 500-W electric resistance heater placed in the tank is now turned on and kept on for after which the pressure of \(C O_{2}\) is measured to be . Assuming the surroundings to be at and using constant specific heats, determine the final temperature of \(C O_{2}\), (b) the net amount of heat transfer from the tank, and the entropy generation during this process. Equation Transcription: Text Transcription: 0.8-m3 (CO2) CO2 CO2

Refrigerant-134a enters a compressor as a saturated vapor at 160 kPa at a rate of \(0.03 \mathrm{~m}^{3} / \mathrm{s}\) and leaves at 800 kPa. The power input to the compressor is 10 kW. If the surroundings at \(20^{\circ} \mathrm{C}\) experience an entropy increase of 0.008 kW/K, determine () the rate of heat loss from the compressor, () the exit temperature of the refrigerant, and () the rate of entropy generation. Equation Transcription: Text Transcription: 0.03 m3/s 20°C

Air enters the evaporator section of a window air conditioner at \(100 \mathrm{kP} a and 27{ }^{\circ} \mathrm{C}\) with a volume flow rate of \(6 m^{3} / m i n\). The refrigerant-134a at with a quality of enters the evaporator at a rate of \(2 \mathrm{~kg} / \mathrm{min}\) and leaves as saturated vapor at the same pressure. Determine the exit temperature of the air and the rate of entropy generation for this process, assuming the outer surfaces of the air conditioner are insulated and heat is transferred to the evaporator of the air conditioner from the surrounding medium at \(32^{\circ} \mathrm{C}\) at a rate of \(30 \mathrm{~kJ} / \mathrm{min}\) Equation Transcription: Text Transcription: 100kPa and 27°C 6 m3/min 2 kg/min 32°C 30 kJ/min

Problem 184P 3-kg of helium gas at 100 kPa and 27°C are adiabat­ically compressed to 900 kPa. If the isentropic compression efficiency is 80 percent, determine the required work input and the final temperature of helium.

Problem 180P Helium gas is throttled steadily from 400 kPa and 60°C. Heat is lost from the helium in the amount of 1.75 kJ/kg to the surroundings at 25°C and 100 kPa. If the entropy of the helium increases by 0.34 kJ/kg·K in the valve, determine (a) the exit pressure and temperature and (b) the entropy generation during this process.

Air at 500 kPa and 400 K enters an adiabatic nozzle at a velocity of \(30 \mathrm{~m} / \mathrm{s}\) and leaves at 300 kPa and 350 K. Using variable specific heats, determine () the isentropic efficiency, () the exit velocity, and () the entropy generation. Equation Transcription: Text Transcription: 30 m/s

Problem 185P An inventor claims to have invented an adiabatic steady-flow device with a single inlet-outlet that produces 230 kW when expanding 1 kg/s of air from 1200 kPa and 300°C to 100 kPa. Is this claim valid?

Problem 186P You are to expand a gas adiabatically from 3 MPa and 300°C to 80 kPa in a piston-cylinder device. Which of the two choices - air with an isentropic expansion efficiency of 90 percent or neon with an isentropic expansion efficiency of 80 percent - will produce the most work?

An adiabatic capillary tube is used in some refrigeration systems to drop the pressure of the refrigerant from the condenser level to the evaporator level. R-134a enters the capillary tube as a saturated liquid at \(70^{\circ} \mathrm{C}\), and leaves at \(-20^{\circ} \mathrm{C}\). Determine the rate of entropy generation in the capillary tube for a mass flow rate of \(0.2 \mathrm{~kg} / \mathrm{s}\). Equation Transcription: Text Transcription: 70°C -20°C 0.2 kg/s

Determine the work input and entropy generation during the compression of steam from \(100 \mathrm{kPa} \text { to } 1 \mathrm{MPa}\) in (a) an adiabatic pump and an adiabatic compressor if the inlet state is saturated liquid in the pump and saturated vapor in the compressor and the isentropic efficiency is 85 percent for both devices. Equation Transcription: Text Transcription: 100kPa to 1MPa

Problem 189P Air is compressed steadily by a compressor from 100 kPa and 20°C to 1200 kPa and 300°C at a rate of 0.4 kg/s. The compressor is intentionally cooled by utilizing fins on the surface of the compressor and heat is lost from the compressor at a rate of 15 kW to the surroundings at 20°C. Using constant specific heats at room temperature, determine (a) the power input to the compressor, (b) the isothermal efficiency, and (c) the entropy generation during this process.

Problem 190P Air is compressed steadily by a compressor from 100 kPa and 17°C to 700 kPa at a rate of 5 kg/min. Deter­mine the minimum power input required if the process is (a) adiabatic and (b) isothermal. Assume air to be an ideal gas with variable specific heats, and neglect the changes in kinetic and potential energies.

Problem 193P Refrigerant-134a at 140 kPa and -10°C is compressed by an adiabatic 1.3-kW compressor to an exit state of 700 kPa and 60°C. Neglecting the changes in kinetic and potential energies, determine (a) the isentropic efficiency of the compressor, (b) the volume flow rate of the refrigerant at the compressor inlet, in L/min, and (c) the maximum volume flow rate at the inlet conditions that this adiabatic 1.3-kW compressor can handle without violating the second law.

Air enters a two-stage compressor at \(100 k P a \text { and } 27^{\circ} C\) and is compressed to 625 kPa. The pressure ratio across each stage is the same, and the air is cooled to the initial temperature between the two stages. Assuming the compression process to be isentropic, determine the power input to the compressor for a mass flow rate of \(0.15 \mathrm{~kg} / \mathrm{s}\). What would your answer be if only one stage of compression were used? Equation Transcription: Text Transcription: 100 kPa and 27°C 0.15 kg/s

Problem 194P An adiabatic air compressor is to be powered by a direct-coupled adiabatic steam turbine that is also driving a generator. Steam enters the turbine at 12.5 MPa and 500°C at a rate of 25 kg/s and exits at 10 kPa and a quality of 0.92. Air enters the compressor at 98 kPa and 295 K at a rate of 10 kg/s and exits at 1 MPa and 620 K. Determine (a) the net power delivered to the generator by the turbine and (b) the rate of entropy generation within the tur­bine and the compressor during this process.

Steam at \(6 M P a \text { and } 500^{\circ} C\) enters a two-stage adiabatic turbine at a rate of \(15 \mathrm{~kg} / \mathrm{s}\). 10 percent of the steam is extracted at the end of the first stage at a pressure of 1.2 MPa for other use. The remainder of the steam is further expanded in the second stage and leaves the turbine at 20 kPa. Determine the power output of the turbine, assuming (a) the process is reversible and (b) the turbine has an isentropic efficiency of 88 percent. Equation Transcription: Text Transcription: 6 MPa and 500°C 15 kg/s

Reconsider Prob. 7–194. Using EES (or other) software, determine the isentropic efficiencies for the compressor and turbine. Then use EES to study how varying the compressor efficiency over the range 0.6 to 0.8 and the turbine efficiency over the range 0.7 to 0.95 affect the net work for the cycle and the entropy generated for the process. Plot the net work as a function of the compressor efficiency for turbine efficiencies of 0.7, 0.8, and 0.9, and discuss your results.

Problem 196P Air is expanded in an adiabatic turbine of 85 percent isentropic efficiency from an inlet state of 2200 kPa and 300°C to an outlet pressure of 200 kPa. Calculate the outlet temperature of air and the work produced by this turbine per unit mass of air.

Problem 197P Air is expanded in an adiabatic turbine of 90 percent isentropic efficiency from an inlet state of 2800 kPa and 400°C to an outlet pressure of 150 kPa. Calculate the outlet temperature of air, the work produced by this turbine, and the entropy generation.

Problem 200P A 1200-W electric resistance heating element whose diameter is 0.5 cm is immersed in 40 kg of water initially at 20°C. Assuming the water container is well-insulated, deter­mine how long it will take for this heater to raise the water temperature to 50°C. Also, determine the entropy generated during this process, in kJ/K.

To control the power output of an isentropic steam turbine, a throttle valve is placed in the steam line supplying the turbine inlet, as shown in the figure. Steam at \(6 \mathrm{MPa} \text { and } 400^{\circ} \mathrm{C}\) is supplied to the throttle inlet, and the turbine exhaust pressure is set at 70 kPa. Compare the work produced by this steam turbine, in kJ/kg, when the throttle valve is completely open (so that there is no pressure loss) and when it is partially closed so that the pressure at the turbine inlet is 3 MPa. Equation Transcription: Text Transcription: 6 MPa and 400°C

Problem 202P A passive solar house that is losing heat to the out­doors at 3°C at an average rate of 50,000 kJ/h is maintained, at 22°C at all times during a winter night for 10 h. The house is to be heated by 50 glass containers, each containing 20 L of water that is heated to 80°C during the day by absorbing solar energy. A thermostat controlled 15 kW backup electric resistance heater turns on whenever necessary to keep the house at 22°C. Determine how long the electric heating system was on that night and the amount of entropy generated during the night.

Problem 204P In order to cool 1-ton of water at 20°C in an insulated tank, a person pours 80 kg of ice at -5°C into the water. Determine (a) the final equilibrium temperature in the tank and (b) the entropy generation during this process. The melting temperature and the heat of fusion of ice at atmospheric pressure are 0°C and 333.7 kJ/kg.

Two rigid tanks are connected by a valve. Tank A is insulated and contains \(0.3 m^{3}\) of steam at 400 kPa and 60 percent quality. Tank B is uninsulated and contains 2 kg of steam at 200 kPa and \(250^{\circ} \mathrm{C}\). The valve is now opened, and steam flows from tank A to tank B until the pressure in tank A drops to 200 kPa. During this process 300 kJ of heat is transferred from tank B to the surroundings at \(17^{\circ} \mathrm{C}\). Assuming the steam remaining inside tank A to have undergone a reversible adiabatic process, determine () the final temperature in each tank and () the entropy generated during this process. Equation Transcription: Text Transcription: 0.3 m3 250°C 17°C ________________

A \(5-f t^{3}\) rigid tank initially contains refrigerant-134a at 60 psia and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant-134a at 140 psia and \(80^{\circ} F\) The valve is now opened, allowing the refrigerant to enter the tank, and is closed when it is observed that the tank contains only saturated liquid at 100 psia. Determine () the mass of the refrigerant that entered the tank, () the amount of heat transfer with the surroundings at \(70^{\circ} F\), and () the entropy generated during this process. Equation Transcription: Text Transcription: 5-ft3 80°F 70°F

A \(15-f t^{3}\) steel container that has a mass of 75 lbm when empty is filled with liquid water. Initially, both the steel tank and the water are at \(120^{\circ} \mathrm{F}\). Now heat is transferred, and the entire system cools to the surrounding air temperature of \(70^{\circ} \mathrm{F}\). Determine the total entropy generated during this process. Equation Transcription: Text Transcription: 15-ft3 120°F 70°F

One ton of liquid water at 80°C is brought into a well-insulated and well-sealed \(4-m \times 5-m \times 7-m\) room initially at 22°C and 100 kPa. Assuming constant specific heats for both air and water at room temperature, determine () the final equilibrium temperature in the room and () the total entropy change during this process, in kJ/K. Equation Transcription: Text Transcription: 4-m x 5-m x 7-m

A well-insulated \(4-m \times 4-m \times 5-m\) room initially at is heated by the radiator of a steam heating system. The radiator has a volume of and is filled with superheated vapor at \(200 \mathrm{kP} \text { a and } 200^{\circ} \mathrm{C}\). At this moment both the inlet and the exit valves to the radiator are closed. A fan is used to distribute the air in the room. The pressure of the steam is observed to drop to after 30 min as a result of heat transfer to the room. Assuming constant specific heats for air at room temperature, determine the average temperature of air in the entropy change of the steam, (c) the entropy change of the air in the room, and the entropy generated during this process, in . Assume the air pressure in the room remains constant at at all times. Equation Transcription: Text Transcription: 4-m x 4-m x 5 -m 200 kPa and 200°C

An insulated piston-cylinder device initially contains \(0.02 \mathrm{~m}^{3}\) of saturated liquid-vapor mixture of water with a quality of \(0.1 \mathrm{at} 100^{\circ} \mathrm{C}\). Now some ice at \(-18^{\circ} \mathrm{C}\) is dropped into the cylinder. If the cylinder contains saturated liquid at when thermal equilibrium is established, determine (a) the amount of ice added and the entropy generation during this process. The melting temperature and the heat of fusion of ice at atmospheric pressure are \(0^{\circ} \mathrm{C} \text { and } 333.7 \mathrm{~kJ} / \mathrm{kg}\) Equation Transcription: Text Transcription: 0.02 m3 0.1 at 100°C -18°C 0°C and 333.7 kJ/kg

The inner and outer surfaces of a \(2-m \times 2-m\) window glass in winter are \(10^{\circ} \mathrm{C} \text { and } 3^{\circ} \mathrm{C}\) respectively. If the rate of heat loss through the window is \(3.2 \mathrm{~kJ} / \mathrm{s}\), determine the amount of heat loss, in , through the glass over a period of . Also, determine the rate of entropy generation during this process within the glass. Equation Transcription: Text Transcription: 2 - m x 2 - m 10°C and 3°C 3.2 kJ/s

Using EES (or other) software, determine the work input to a multistage compressor for a given set of inlet and exit pressures for any number of stages. Assume that the pressure ratio across each stage is identical and the compression process is polytropic. List and plot the compressor work against the number of stages for \(P_{1}=100 \mathrm{kP} a, T_{1}=25^{\circ} \mathrm{C}, P_{2}=1000 \mathrm{kP} a \text {, and } n=1.35\) for air. Based on this chart, can you justify using compressors with more than three stages? Equation Transcription: Text Transcription: P1= 100kPa, T1=25°C, P2=1000kPa, and n=1.35

Problem 208P Consider a 50-L evacuated rigid bottle that is surrounded by the atmosphere at 95 kPa and 27°C. A valve at the neck of the bottle is now opened and the atmospheric air is allowed to flow into the bottle. The air trapped in the bottle eventually reaches thermal equilibrium with the atmosphere as a result of heat transfer through the wall of the bottle. The valve remains open during the process so that the trapped air also reaches mechanical equilibrium with the atmosphere. Determine the net heat transfer through the wall of the bottle and the entropy generation during this filling process.

(a) Water flows through a shower head steadily at a rate of \(10 \mathrm{~L} / \mathrm{min}\). An electric resistance heater placed in the water pipe heats the water from \(16 to 43^{\circ} \mathrm{C}\). Taking the density of water to be \(1 \mathrm{~kg} / \mathrm{L}\), determine the electric power input to the heater, in , and the rate of entropy generation during this process, in . (b) In an effort to conserve energy, it is proposed to pass the drained warm water at a temperature of \(39^{\circ} \mathrm{C}\) through a heat exchanger to preheat the incoming cold water. If the heat exchanger has an effectiveness of (that is, it recovers only half of the energy that can possibly be transferred from the drained water to incoming cold water), determine the electric power input required in this case and the reduction in the rate of entropy generation in the resistance heating section. Equation Transcription: Text Transcription: 10 L/min 16 to 43°C 1 kg/L 39°C

The inner and outer glasses of a \(2-m \times 2-m\) double pane window are at \(18^{\circ} \mathrm{C} \text { and } 6^{\circ} \mathrm{C}\), respectively. If the glasses are very nearly isothermal and the rate of heat transfer through the window is , determine the rates of entropy transfer through both sides of the window and the rate of entropy generation within the window, in . Equation Transcription: Text Transcription: 2 - m x 2 - m 18°C and 6°C

Problem 213P A hot-water pipe at 80°C is losing heat to the surrounding air at 5°C at a rate of 2200 W. Determine the rate of entropy generation in the surrounding air, in W/K.

Problem 216P When the transportation of natural gas in a pipeline is not feasible for economic reasons, it is first liquefied using nonconventional refrigeration techniques and then transported in super-insulated tanks. In a natural gas liquefaction plant, the liquefied natural gas (LNG) enters a cryogenic turbine at. 30 bar and - 160°C at a rate of 20 kg/s and leaves at 3 bar. If 115 kW power is produced by the turbine, determine the efficiency of the turbine. Take the density of LNG to be 423.8 kg/m3.

A \(0.40-m^{3}\) insulated piston–cylinder device initially contains 1.3 kg of air at \(30^{\circ} \mathrm{C}\). At this state, the piston is free to move. Now air at 500 kPa and \(70^{\circ} \mathrm{C}\) is allowed to enter the cylinder from a supply line until the volume increases by 50 percent. Using constant specific heats at room temperature, determine () the final temperature, () the amount of mass that has entered, () the work done, and () the entropy generation. Equation Transcription: Text Transcription: 0.40-m3 30°C 70°C

Consider the turbocharger of an internal combustion engine. The exhaust gases enter the turbine at \(450^{\circ} \mathrm{C}\) at a rate of \(0.02 \mathrm{~kg} / \mathrm{s}\) and leave at \(400^{\circ} \mathrm{C}\). Air enters the compressor at \(70^{\circ} \mathrm{C}\) and 95 kPa at a rate of \(0.018 \mathrm{~kg} / \mathrm{s}\) and leaves at 135 kPa. The mechanical efficiency between the turbine and the compressor is 95 percent (5 percent of turbine work is lost during its transmission to the compressor). Using air properties for the exhaust gases, determine () the air temperature at the compressor exit and () the isentropic efficiency of the compressor. Equation Transcription: Text Transcription: 450°C 0.02 kg/s 400°C 70°C 0.018 kg/s

A heat engine receives heat from a constant volume tank filled with 2 kg of air. The engine produces work that is stored in a work reservoir and rejects 400 kJ of heat to a heat reservoir at 300 K. During the process the temperature of the air in the tank decreases to 300 K. () Determine the initial temperature of the air that will maximize the work and the thermal efficiency of the engine. () Evaluate the total entropy change of this isolated system, the work produced, and the thermal efficiency for the initial air temperature in the tank from part () and at 100 K above and below the answer to part (). () Plot the thermal efficiency and the entropy generation as functions of the initial temperature of the air. Comment on your answers. Assume constant specific heats for air at 300 K.

A constant volume tank filled with 2 kg of air rejects heat to a heat reservoir at 300 K. During the process the temperature of the air in the tank decreases to the reservoir temperature. Determine the expressions for the entropy changes for the tank and reservoir and the total entropy change or entropy generated of this isolated system. Plot these entropy changes as functions of the initial temperature of the air. Comment on your results. Assume constant specific heats for air at 300 K.

For an ideal gas with constant specific heats show that the compressor and turbine isentropic efficiencies may be written as \(\eta_{C}=\frac{\left(P_{2} / P_{1}\right)^{(k-1) / k}}{\left(T_{2} / T_{1}\right)-1} \text { and } \eta_{T}=\frac{\left(T_{4} / T_{3}\right)-1}{\left(P_{4} / P_{3}\right)^{(k-1) / k}-1}\) The states 1 and 2 represent the compressor inlet and exit states and the states 3 and 4 represent the turbine inlet and exit states. Equation Transcription: Text Transcription: \eta C=(P2/P1)(k - 1)/k over (T2/T1)-1 and \eta T=(T4/T3)-1 over (P4/P3)(k - 1)/k-1

Problem 221P Starting with the Gibbs equation du = Tds - Pdv,obtain the expression for the change in internal energy of an ideal gas having constant specific heats during the isentropic process PVk= constant.

Consider two bodies of identical mass and specific heat used as thermal reservoirs (source and sink) for a heat engine. The first body is initially at an absolute temperature \(T_{1}\) while the second one is at a lower absolute temperature \(T_{2}\). Heat is transferred from the first body to the heat engine, which rejects the waste heat to the second body. The process continues until the final temperatures of the two bodies \(T_{f}\). become equal. Show that \(T_{f}=\sqrt{T_{1} T_{2}}\) when the heat engine produces the maximum possible work. Equation Transcription: Text Transcription: T_1 T_2 T_{f}=\sqrt T_1 T_2

Problem 222P An initially empty rigid vessel is filled with a fluid from a source whose properties remain constant. Determine the entropy generation if this is done adiabatically and without any work, and the fluid is an ideal gas. Your answer should be in terms of the vessel’s volume, the properties of the gas, the dead state, temperature, the initial and final gas pressure and temperatures, and the pressure and temperature of the gas-supplying source.

The temperature of an ideal gas having constant specific heats is given as a function of specific entropy and specific volume as \(T(s, v)=A v^{1-k} \exp \left(s / c_{v}\right)\) where \(A\) is a constant. For a reversible, constant volume process, find the expression for heat transfer per unit mass as a function of \(C_{v}\) and \(T\) using \(Q=\int T d S\). Compare this result with that obtained by applying the first law to a closed system undergoing a constant volume process. Equation Transcription: Text Transcription: T(s,v)=Av^1-k exp (s/c_v) A c_v T Q=integral TdS

An ideal gas undergoes a reversible, steady-flow process in which pressure and volume are related by the polytropic equation \(P v^{n}=\) constant. Neglecting the changes in kinetic and potential energies of the flow and assuming constant specific heats, ( ) obtain the expression for the heat transfer per unit mass flow for the process and evaluate this expression for the special case where \(n=k=c_{p} / c_{v}\). Equation Transcription: Text Transcription: Pvn= n=k=cp/cv

The polytropic or small stage efficiency of a compressor \(\eta_{x, c}\) is defined as the ratio of the actual differential work done on the fluid to the isentropic differential work done on the flowing through the compressor \(\eta_{\infty, c}=d h_{s} J d h\) Consider an ideal gas with constant specific heats as the working fluid undergoing a process in a compressor in which the polytropic efficiency is constant. Show that the temperature ratio across the compressor is related to the pressure ratio across the compressor by \(\frac{T_{2}}{T_{1}}=\left(\frac{P_{2}}{P_{1}}\right)^{\left(\frac{1}{\eta_{\infty}, C}\right)}\left(\frac{R}{c_{p}}\right)=\left(\frac{P_{2}}{P_{1}}\right)^{\left(\frac{1}{\eta_{\infty, C}}\right)\left(\frac{k-1}{k}\right)}\) Equation Transcription: Text Transcription: \eta_x, c \eta_{\infty, c=d h_s J d h \frac{T_2 T_1=(\frac{P_2 P_1)^(\frac{1\eta_\infty,C\right)(\frac{R c_p\right)=(\frac{P_2 P_1)^\left(\frac{1\eta_\infty, C)(\frac{k-1 k)

Problem 226P Steam is compressed from 6 MPa and 300°C to 10 MPa isentropically. The final temperature of the steam is (a)290°C (b)300°C (c)311°C (d)371°C (e)422°C

Problem 229P Steam expands in an adiabatic turbine from 4 MPa and 500°C to 0.1 MPa at a rate of 2 kg/s. If steam leaves the turbine as saturated vapor, the power output of the turbine is (a) 2058 kW (b) 1910 kW (c) 1780 kW (d) 1674 kW (e) 1542 kW

Problem 228P A piston-cylinder device contains 5 kg of saturated water vapor at 3 MPa. Now heat is rejected from the cylinder at constant pressure until the water vapor completely con­denses so that the cylinder contains saturated liquid at 3 MPa at the end of the process. The entropy change of the system during this process is . (a) 0 kJ/K (b) ?3.5 kJ/K (c) ?12.5 kJ/K (d) ?17.7 kJ/K (e) ?19.5 kJ/K

Problem 227P An apple with an average mass of 0.12 kg and aver­age specific heat of 3.65 kJ/kg °C is cooled from 25°C to 5°C. The entropy change of the apple is (a) ?0.705 kJ/K (b) ?0.254 kJ/K (c) ?0.0304 kJ/K (d) 0 kJ/K (e) 0.348 kJ/K

Problem 230P Argon gas expands, in an adiabatic turbine from 3 MPa and 750°C to 0.2 MPa at a rate of 5 kg/s. The maximum power output of the turbine is (a) 1.06 MW (b) 1.29 MW (c) 1.43 MW (d) 1.76 MW (e) 2.08 MW

Problem 231P A unit mass of a substance undergoes an irreversible process from state 1 to state 2 while gaining heat from the sur­roundings at temperature Tin the amount of q.If the entropy of the substance is S1 at state 1, and s2 at state 2, the entropy change of the. substance ?s during this process is (a) ?s < s2? s1 (b) ?s < s2? s1 (c) ?s = s2? s1 (d) ?s = s2? s1+q/T (e) ?s> s2? s1+q/T

Problem 236P Argon gas expands in an adiabatic turbine steadily from 600 °C and 800 kPa to 80 kPa at a rate of 2.5kg/s. For isentropic efficiency of 88 percent, the power produced by the turbine is (a) 240 kW (b) 361 kW (c) 414 kW (d) 602 kW (e) 111 kW

Problem 234P Heat is lost through a plane wall steadily at a rate of 600 W. If the inner and outer surface temperatures of the wall are 20°C and 5°C, respectively, the rate of entropy generation within the wall is (a) 0.11W/K (b) 4.21 W/K (c) 2.10 W/K (d) 42.1 W/K (e) 90.0 W/K

Problem 233P Helium gas is compressed" from 27°C and 3.50m3/kg to 0.775 m3/kg in a reversible and adiabatic manner,he temperature of helium after compression is (a)74°C (b)122°C (c) 547°C (d)709°C (e) 1082°C

Problem 232P A unit mass of an ideal gas at temperature Tunder­goes a reversible isothermal process from pressure P1 to pres­sure P2 while losing heat to the surroundings at temperature Tin the amount of q.If the gas constant of the gas is R, the entropy change of the gas ?s during this process is (a) ?s = Rln(P2/P1) (b) ?s = Rln(P2/P1) ? q/T (c) ?s = Rln(P1/P2) (d) ?s = Rln(P1/P2) ? q/T (e) ?s = 0

Problem 237P Water enters a pump steadily at 100 kPa at a rate of 35 L/s and leaves at 800 kPa. The flow velocities at the inlet and the exit are the same, but the pump exit where the dis­charge pressure is measured is 6.1 m above the inlet section. The minimum power input to the pump is (a) 34 kW (b) 22 kW (c) 27 kw (d) 52 kW (e) 44 kW

Problem 235P Air is compressed steadily and adiabatically from 17°C and 90 kPa to 200T and 400 kPa. Assuming constant specific heats for air at room temperature, the isentropic effi­ciency of the compressor is (a) 0.76 (b) 0.94 (c)0.86 (d) 0.84 (e) 1.00

Problem 239P Helium gas enters an adiabatic nozzle steadily at 500°C and 600 kPa with a low velocity, and exits at a pres­sure of 90 kPa. The highest possible velocity of helium gas at the nozzle exit is (a) 1475 m/s (b) 1662 m/s (c) 1839 m/s (d) 2066 m/s (e) 3040 m/s

Steam enters an adiabatic turbine steadily at \(400^{\circ} \mathrm{C} \text { and } 5 \mathrm{MPa}\), and leaves at 20 kPa. The highest possible percentage of mass of steam that condenses at the turbine exit and leaves the turbine as a liquid is () 4% () 8% () 12% () 18% (e) 0% Equation Transcription: Text Transcription: 400°C and 5 MPa

Problem 238P Air is to be compressed steadily and isentropically from 1 atm to 16 atm by a two-stage compressor. To mini­mize the total compression work, the intermediate pressure between the two stages must be (a) 3 atm (b) 4 atm (c) 8.5 atm (d) 9 atm (e) 12 atm

Problem 240P Combustion gases with a specific heat ratio of 1.3 enter an adiabatic nozzle steadily at 800°C and 800 kPa with a low velocity, and exit at a pressure of 85 kPa. The lowest possible temperature of combustion gases at the nozzle exit is (a)43°C (b) 237°C (c) 367°C (d) 477°C (e) 640°C

Problem 244P Steam enters an adiabatic turbine at 8 MPa and 500°C at a rate of 18 kg/s, and exits at 0.2 MPa and 300°C. The rate of entropy generation in the turbine is (a)0 kW/K (b)7.2 kW/K (c) 21 kW/K (d)15 kW/K (e)17 kW/K

Problem 245P Helium gas is compressed steadily from 90 kPa and 25°C to 800 kPa at a rate of 2 kg/min by an adiabatic com­pressor. If the compressor consumes 80 kW of power while operating, the isentropic efficiency of this compressor is (a) 54.0% (b) 80.5% (c) 75.8% (d)90.1% (e)100%

Problem 243P Liquid water is to be compressed by a pump whose isentropic efficiency is 75 percent from 0.2 MPa to 5 MPa at a rate of 0.15 m3/min. The required power input to this pump is (a)4.8kW (b)6.4kW (c)9.0kW (d)16.0kW (e)12kW

Problem 242P Liquid water enters an adiabatic piping system at 15°C at a rate of 8 kg/s. If the water temperature rises by 0.2°C during flow due to friction, the rate of entropy genera­tion in the pipe is (a) 23 W/K (b) 55 W/K (c) 68 W/K (d) 220 W/K (e) 443 W/K

Problem 7.71C Starting with the second relation (Eq.7-26), obtain Eq. 7-34 for the entropy change of ideal gases under the constant -specific heat assumption.

Problem 7.72C Which of the two gases-helium or nitrogen-experiences the greatest entropy change as its state is changed from and to and ?

Air is expanded from and to and . Assuming constant specific heats, determine the change in the specific entropy of air

What is the difference between the entropies of air at and and air at and per unit mass basis.

Oxygen gas is compressed in a piston–cylinder device from an initial state of and to a final state of and . Determine the entropy change of the oxygen during this process. Assume constant specific heats.

A insulated rigid tank contains of carbon dioxide at . Now paddle-wheel work is done on the system until the pressure in the tank rises to . Determine the entropy change of carbon dioxide during this process. Assume constant specific heats.

An insulated piston–cylinder device initially contains 300 L of air at and . Air is now heated for 15 min by a 200-W resistance heater placed inside the cylinder. The pressure of air is maintained constant during this process. Determine the entropy change of air, assuming (a) constant specific heats and (b) variable specific heats.

A piston–cylinder device contains of nitrogen gas at and . The gas is now compressed slowly in a polytropic process during which The process ends when the volume is reduced by one-half. Determine the entropy change of nitrogen during this process

Work is entropy free, and sometimes the claim is made that work will not change the entropy of a fluid passing through an adiabatic steady-flow system with a single inlet and outlet. Is this a valid claim?

A piston-cylinder device contains helium gas. During a reversible, isothermal process, the entropy of the helium will (never, sometimes, always) increase.

A piston-cylinder device contains superheated steam. During an actual adiabatic process, the entropy of the steam will (never, sometimes, always) increase.

A piston-cylinder device contains superheated steam. During an actual adiabatic process, the entropy of the steam will (never, sometimes, always) increase.

The entropy of steam will (increase, decrease, remain the same) as it flows through an actual adiabatic turbine.

The entropy of the working fluid of the ideal Carnot cycle (increases, decreases, remains the same) during the isothermal heat addition process.

The entropy of the working fluid of the ideal Carnot cycle (increases, decreases, remains the same) during the isothermal heat rejection process.

During a heat transfer process, the entropy of a system (always, sometimes, never) increases.

Steam is accelerated as it flows through an actual adiabatic nozzle. The entropy of the steam at the nozzle exit will be (greater than, equal to, less than) the entropy at the nozzle inlet.

What three different mechanisms can cause the entropy of a control volume to change?

A completely reversible heat engine operates with a source at and a sink at . If the entropy of the sink increases by , how much will the entropy of the source decrease? How much heat, in Btu, is transferred from the source?

Air is compressed by a 15-kW compressor from P1 to P2. The air temperature is maintained constant at 258C during this process as a result of heat transfer to the surrounding medium at 208C. Determine the rate of entropy change of the air. State the assumptions made in solving this problem.

Heat in the amount of is transferred directly from a hot reservoir at 1200 K to a cold reservoir at 600 K. Calculate the entropy change of the two reservoirs and determine if the increase of entropy principle is satisfied.

In Prob. 7-21, assume that the heat is transferred from the cold reservoir to the hot reservoir contrary to the Clausius statement of the second law. Prove that this violates the increase of entropy principle-as it must according to Clausius.

A completely reversible heat pump produces heat at a rate of 300 kW to warm a house maintained at 248C. The exterior air, which is at 78C, serves as the source. Calculate the rate of entropy change of the two reservoirs and determine if this heat pump satisfies the second law according to the increase of entropy principle.

During the isothermal heat addition process of a Carnot cycle, 900 kJ of heat is added to the working fluid from a source at 4008C. Determine (a) the entropy change of the working fluid, (b) the entropy change of the source, and (c) the total entropy change for the process.

Reconsider Prob. 7-24. Using EES (or other) software, study the effects of the varying heat added to the working fluid and the source temperature on the entropy change of the working fluid, the entropy change of the source, and the total entropy change for the process. Let the source temperature vary from 100 to 10008C. Plot the entropy changes of the source and of the working fluid against the source temperature for heat transfer amounts of 500 kJ, 900 kJ, and 1300 kJ, and discuss the results.

During the isothermal heat rejection process of a Carnot cycle, the working fluid experiences an entropy change of 20.7 Btu/R. If the temperature of the heat sink is 958F, determine (a) the amount of heat transfer, (b) the entropy change of the sink, and (c) the total entropy change for this process.

Refrigerant-134a enters the coils of the evaporator of a refrigeration system as a saturated liquidvapor mixture at a pressure of 140 kPa. The refrigerant absorbs 180 kJ of heat from the cooled space, which is maintained at 2108C, and leaves as saturated vapor at the same pressure. Determine (a) the entropy change of the refrigerant, (b) the entropy change of the cooled space, and (c) the total entropy change for this process.

Is a process that is internally reversible and adiabatic necessarily isentropic? Explain.

2-lbm of water at 300 psia fill a weighted pistoncylinder device whose volume is 2.5 ft3 . The water is then heated at constant pressure until the temperature reaches 5008F. Determine the resulting change in the waters total entropy.

A well-insulated rigid tank contains 3 kg of a saturated liquidvapor mixture of water at 200 kPa. Initially, three-quarters of the mass is in the liquid phase. An electric resistance heater placed in the tank is now turned on and kept on until all the liquid in the tank is vaporized. Determine the entropy change of the steam during this process.

The radiator of a steam heating system has a volume of 20 L and is filled with superheated water vapor at 200 kPa and 1508C. At this moment both the inlet and the exit valves to the radiator are closed. After a while the temperature of the steam drops to 408C as a result of heat transfer to the room air. Determine the entropy change of the steam during this process.

A rigid tank is divided into two equal parts by a partition. One part of the tank contains 2.5 kg of compressed liquid water at 400 kPa and 608C while the other part is evacuated. The partition is now removed, and the water expands to fill the entire tank. Determine the entropy change of water during this process, if the final pressure in the tank is 40 kPa.

An insulated pistoncylinder device contains 5 L of saturated liquid water at a constant pressure of 150 kPa. An electric resistance heater inside the cylinder is now turned on, and 2200 kJ of energy is transferred to the steam. Determine the entropy change of the water during this process.

Saturated R-134a vapor enters a compressor at 68F. At compressor exit, the specific entropy is the same as that at the inlet, and the pressure is 80 psia. Determine the R-134a exit temperature and the change in the enthalpy of R-134a.

Water vapor enters a turbine at 6 MPa and 4008C, and leaves the turbine at 100 kPa with the same specific entropy as that at the inlet. Calculate the difference between the specific enthalpy of the water at the turbine inlet and exit.

1-kg of R-134a initially at 600 kPa and 258C undergoes a process during which the entropy is kept constant until the pressure drops to 100 kPa. Determine the final temperature of the R-134a and the final specific internal energy

Refrigerant-134a is expanded isentropically from 600 kPa and 708C at the inlet of a steady-flow turbine to 100 kPa at the outlet. The outlet area is 1 m2 , and the inlet area is 0.5 m2 . Calculate the inlet and outlet velocities when the mass flow rate is 0.75 kg/s.

A pistoncylinder device contains 1.2 kg of saturated water vapor at 2008C. Heat is now transferred to steam, and steam expands reversibly and isothermally to a final pressure of 800 kPa. Determine the heat transferred and the work done during this process.

Reconsider Prob. 738. Using EES (or other) software, evaluate and plot the heat transferred to the steam and the work done as a function of final pressure as the pressure varies from the initial value to the final value of 800 kPa.

Refrigerant-134a at 320 kPa and 408C undergoes an isothermal process in a closed system until its quality is 45 percent. On per unit mass basis, determine how much work and heat transfer are required.

A rigid tank contains 5 kg of saturated vapor steam at 1008C. The steam is cooled to the ambient temperature of 258C. (a) Sketch the process with respect to the saturation lines on a T-v diagram. (b) Determine the entropy change of the steam, in kJ/K. (c) For the steam and its surroundings, determine the tot

A 0.5-m3 rigid tank contains refrigerant-134a initially at 200 kPa and 40 percent quality. Heat is transferred now to the refrigerant from a source at 358C until the pressure rises to 400 kPa. Determine (a) the entropy change of the refrigerant, (b) the entropy change of the heat source, and (c) the total entropy change for this process.

Reconsider Prob. 742. Using EES (or other) software, investigate the effects of the source temperature and final pressure on the total entropy change for the process. Let the source temperature vary from 30 to 2108C, and the final pressure vary from 250 to 500 kPa. Plot the total entropy change for the process as a function of the source temperature for final pressures of 250 kPa, 400 kPa, and 500 kPa, and discuss the results.

Determine the heat transfer, in kJ/kg, for the reversible process 1-3 shown in Fig. P744.

Calculate the heat transfer, in Btu/lbm, for the reversible process 1-3 shown in Fig. P745E.

Steam enters an adiabatic diffuser at 150 kPa and 1208C with a velocity of 550 m/s. Determine the minimum velocity that the steam can have at the outlet when the outlet pressure is 300 kPa.

Steam enters an adiabatic turbine at 800 psia and 9008F and leaves at a pressure of 40 psia. Determine the maximum amount of work that can be delivered by this turbine.

Reconsider Prob. 747E. Using EES (or other) software, evaluate and plot the work done by the steam as a function of final pressure as it varies from 800 to 40 psia. Also investigate the effect of varying the turbine inlet temperature from the saturation temperature at 800 psia to 9008F on the turbine work.

An isentropic steam turbine processes 2 kg/s of steam at 3 MPa, which is exhausted at 50 kPa and 1008C. 5 percent of this flow is diverted for feedwater heating at 500 kPa. Determine the power produced by this turbine, in kW.

Water at 70 kPa and 1008C is compressed isentropically in a closed system to 4 MPa. Determine the final temperature of the water and the work required, in kJ/kg, for this compression.

0.7-kg of R-134a is expanded isentropically from 800 kPa and 508C to 140 kPa. Determine the total heat transfer and work production for this expansion.

2-kg of saturated water vapor at 600 kPa are contained in a piston-cylinder device. The water expands adiabatically until the pressure is 100 kPa and is said to produce 700 kJ of work output. (a) Determine the entropy change of the water, in kJ/kgK. (b) Is this process realistic? Using the T-s diagram for the process and the concepts of second law, support your answer.

Steam enters a steady-flow adiabatic nozzle with a low inlet velocity as a saturated vapor at 6 MPa and expands to 1.2 MPa. (a) Under the conditions that the exit velocity is to be the maximum possible value, sketch the T-s diagram with respect to the saturation lines for this process. (b) Determine the maximum exit velocity of the steam, in m/s.

A rigid, 20-L steam cooker is arranged with a pressure relief valve set to release vapor and maintain the pressure once the pressure inside the cooker reaches 150 kPa. Initially, this cooker is filled with water at 175 kPa with a quality of 10 percent. Heat is now added until the quality inside the cooker is 40 percent. Determine the minimum entropy change of the thermal energy reservoir supplying this heat.

In Prob. 754, the water is stirred at the same time that it is being heated. Determine the minimum entropy change of the heat-supplying source if 100 kJ of work is done on the water as it is being heated.

A pistoncylinder device contains 5 kg of steam at 1008C with a quality of 50 percent. This steam undergoes two processes as follows: 1-2 Heat is transferred to the steam in a reversible manner while the temperature is held constant until the steam exists as a saturated vapor. 2-3 The steam expands in an adiabatic, reversible process until the pressure is 15 kPa. (a) Sketch these processes with respect to the saturation lines on a single T-s diagram. (b) Determine the heat transferred to the steam in process 1-2, in kJ. (c) Determine the work done by the steam in process 2-3, in kJ.

A 0.55-ft3 well-insulated rigid can initially contains refrigerant-134a at 90 psia and 308F. Now a crack develops in the can, and the refrigerant starts to leak out slowly, Assuming the refrigerant remaining in the can has undergone a reversible, adiabatic process, determine the final mass in the can when the pressure drops to 20 psia.

An electric windshield defroster is used to remove 0.25-in of ice from a windshield. The properties of the ice are Tsat 5 328F, uif 5 hif 5 144 Btu/lbm, and v 5 0.01602 ft3 /lbm. Determine the electrical energy required per square foot of windshield surface area to melt this ice and remove it as liquid water at 328F. What is the minimum temperature at which the defroster may be operated? Assume that no heat is transferred from the defroster or ice to the surroundings.

Consider two solid blocks, one hot and the other cold, brought into contact in an adiabatic container. After a while, thermal equilibrium is established in the container as a result of heat transfer. The first law requires that the amount of energy lost by the hot solid be equal to the amount of energy gained by the cold one. Does the second law require that the decrease in entropy of the hot solid be equal to the increase in entropy of the cold one?

A 50-kg copper block initially at 1408C is dropped into an insulated tank that contains 90 L of water at 108C. Determine the final equilibrium temperature and the total entropy change for this process.

10-grams of computer chips with a specific heat of 0.3 kJ/kgK are initially at 208C. These chips are cooled by placement in 5 grams of saturated liquid R-134a at 2408C. Presuming that the pressure remains constant while the chips are being cooled, determine the entropy change of (a) the chips, (b) the R-134a, and (c) the entire system. Is this process possible? Why?

A 25-kg iron block initially at 3508C is quenched in an insulated tank that contains 100 kg of water at 188C. Assuming the water that vaporizes during the process condenses back in the tank, determine the total entropy change during this process.

A 30-kg aluminum block initially at 1408C is brought into contact with a 40-kg block of iron at 608C in an insulated enclosure. Determine the final equilibrium temperature and the total entropy change for this process.

Reconsider Prob. 763. Using EES (or other) software, study the effect of the mass of the iron block on the final equilibrium temperature and the total entropy change for the process. Let the mass of the iron vary from 10 to 100 kg. Plot the equilibrium temperature and the total entropy change as a function of iron mass, and discuss the results.

A 30-kg iron block and a 40-kg copper block, both initially at 808C, are dropped into a large lake at 158C. Thermal equilibrium is established after a while as a result of heat transfer between the blocks and the lake water. Determine the total entropy change for this process.

An adiabatic pump is to be used to compress saturated liquid water at 10 kPa to a pressure to 15 MPa in a reversible manner. Determine the work input using (a) entropy data from the compressed liquid table, (b) inlet specific volume and pressure values, (c) average specific volume and pressure values. Also, determine the errors involved in parts (b) and (c).

Some properties of ideal gases such as internal energy and enthalpy vary with temperature only [that is, u 5 u(T) and h 5 h(T)]. Is this also the case for entropy?

Can the entropy of an ideal gas change during an isothermal process?

An ideal gas undergoes a process between two specified temperatures, first at constant pressure and then at constant volume. For which case will the ideal gas experience a larger entropy change? Explain.

Prove that the two relations for entropy change of ideal gases under the constant-specific-heat assumption (Eqs. 733 and 734) are equivalent.

Starting with the second T ds relation (Eq. 726), obtain Eq. 734 for the entropy change of ideal gases under the constant-specific-heat assumption.

Which of the two gaseshelium or nitrogen experiences the greatest entropy change as its state is changed from 2000 kPa and 4278C to 200 kPa and 278C?

Air is expanded from 2000 kPa and 5008C to 100 kPa and 508C. Assuming constant specific heats, determine the change in the specific entropy of air.

What is the difference between the entropies of air at 15 psia and 908F and air at 40 psia and 2108F per unit mass basis.

Oxygen gas is compressed in a pistoncylinder device from an initial state of 0.8 m3 /kg and 258C to a final state of 0.1 m3 /kg and 2878C. Determine the entropy change of the oxygen during this process. Assume constant specific heats.

A 1.5-m3 insulated rigid tank contains 2.7 kg of carbon dioxide at 100 kPa. Now paddle-wheel work is done on the system until the pressure in the tank rises to 150 kPa. Determine the entropy change of carbon dioxide during this process. Assume constant specific heats.

An insulated pistoncylinder device initially contains 300 L of air at 120 kPa and 178C. Air is now heated for 15 min by a 200-W resistance heater placed inside the cylinder. The pressure of air is maintained constant during this process. Determine the entropy change of air, assuming (a) constant specific heats and (b) variable specific heats.

A pistoncylinder device contains 0.75 kg of nitrogen gas at 140 kPa and 378C. The gas is now compressed slowly in a polytropic process during which PV1.3 5 constant. The process ends when the volume is reduced by one-half. Determine the entropy change of nitrogen during this process.

Reconsider Prob. 778. Using EES (or other) software, investigate the effect of varying the polytropic exponent from 1 to 1.4 on the entropy change of the nitrogen. Show the processes on a common P-v diagram.

Air is compressed steadily by a 5-kW compressor from 100 kPa and 178C to 600 kPa and 1678C at a rate of 1.6 kg/min. During this process, some heat transfer takes place between the compressor and the surrounding medium at 178C. Determine the rate of entropy change of air during this process.

Air enters a nozzle steadily at 280 kPa and 778C with a velocity of 50 m/s and exits at 85 kPa and 320 m/s. The heat losses from the nozzle to the surrounding medium at 208C are estimated to be 3.2 kJ/kg. Determine (a) the exit temperature and (b) the total entropy change for this process.

Reconsider Prob. 781. Using EES (or other) software, study the effect of varying the surrounding medium temperature from 10 to 408C on the exit temperature and the total entropy change for this process, and plot the results.

A mass of 25 lbm of helium undergoes a process from an initial state of 50 ft3 /lbm and 608F to a final state of 10 ft3 /lbm and 2408F. Determine the entropy change of helium during this process, assuming (a) the process is reversible and (b) the process is irreversible.

1-kg of air at 200 kPa and 1278C is contained in a piston-cylinder device. Air is now allowed to expand in a reversible, isothermal process until its pressure is 100 kPa. Determine the amount of heat transferred to the air during this expansion

Nitrogen is compressed isentropically from 100 kPa and 278C to 1000 kPa in a piston-cylinder device. Determine its final temperature.

Air at 3.5 MPa and 5008C is expanded in an adiabatic gas turbine to 0.2 MPa. Calculate the maximum work that this turbine can produce, in kJ/kg.

Air is compressed in an isentropic compressor from 15 psia and 708F to 200 psia. Determine the outlet temperature and the work consumed by this compressor per unit mass of air.

An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 12 kmol of an ideal gas at 330 kPa and 508C, and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Determine the total entropy change during this process.

An insulated rigid tank contains 4 kg of argon gas at 450 kPa and 308C. A valve is now opened, and argon is allowed to escape until the pressure inside drops to 200 kPa. Assuming the argon remaining inside the tank has undergone a reversible, adiabatic process, determine the final mass in the tank.

Reconsider Prob. 789. Using EES (or other) software, investigate the effect of the final pressure on the final mass in the tank as the pressure varies from 450 to 150 kPa, and plot the results.

Air enters an adiabatic nozzle at 60 psia, 5408F, and 200 ft/s and exits at 12 psia. Assuming air to be an ideal gas with variable specific heats and disregarding any irreversibilities, determine the exit velocity of the air.

Air at 2578C and 400 kPa is contained in a pistoncylinder device. The air expands adiabatically until the pressure is 100 kPa. Determine the mass of air needed to produce maximum work of 1000 kJ. Assume air has constant specific heats evaluated at 300 K.

Air at 278C and 100 kPa is contained in a pistoncylinder device. When the air is compressed adiabatically, a minimum work input of 1000 kJ will increase the pressure to 600 kPa. Assuming air has constant specific heats evaluated at 300 K, determine the mass of air in the device.

Air is compressed in a piston-cylinder device from 90 kPa and 208C to 400 kPa in a reversible isothermal process. Determine (a) the entropy change of air and (b) the work done

Helium gas is compressed from 90 kPa and 308C to 450 kPa in a reversible, adiabatic process. Determine the final temperature and the work done, assuming the process takes place (a) in a piston-cylinder device and (b) in a steadyflow compressor.

5-kg of air at 4278C and 600 kPa are contained in a piston-cylinder device. The air expands adiabatically until the pressure is 100 kPa and produces 600 kJ of work output. Assume air has constant specific heats evaluated at 300 K. (a) Determine the entropy change of the air, in kJ/kgK (b) Since the process is adiabatic, is the process realistic? Using concepts of the second law, support your answer.

A container filled with 45 kg of liquid water at 958C is placed in a 90-m3 room that is initially at 128C. Thermal equilibrium is established after a while as a result of heat transfer between the water and the air in the room. Using constant specific heats, determine (a) the final equilibrium temperature, (b) the amount of heat transfer between the water and the air in the room, and (c) the entropy generation. Assume the room is well sealed and heavily insulated.

The well-insulated container shown in Fig. P798E is initially evacuated. The supply line contains air that is maintained at 150 psia and 1408F. The valve is opened until the pressure in the container is the same as the pressure in the supply line. Determine the minimum temperature in the container when the valve is closed.

In large compressors, the gas is frequently cooled while being compressed to reduce the power consumed by the compressor. Explain how cooling the gas during a compression process reduces the power consumption

The turbines in steam power plants operate essentially under adiabatic conditions. A plant engineer suggests to end this practice. She proposes to run cooling water through the outer surface of the casing to cool the steam as it flows through the turbine. This way, she reasons, the entropy of the steam will decrease, the performance of the turbine will improve, and as a result the work output of the turbine will increase. How would you evaluate this proposal?

It is well known that the power consumed by a compressor can be reduced by cooling the gas during compression. Inspired by this, somebody proposes to cool the liquid as it flows through a pump, in order to reduce the power consumption of the pump. Would you support this proposal? Explain.

Air is compressed isothermally from 13 psia and 908F to 80 psia in a reversible steady-flow device. Calculate the work required, in Btu/lbm, for this compression.

Saturated water vapor at 1508C is compressed in a reversible steady-flow device to 1000 kPa while its specific volume remains constant. Determine the work required, in kJ/kg.

Calculate the work produced, in Btu/lbm, for the reversible steady-flow process 1-3 shown in Fig. P7104E.

Water enters the pump of a steam power plant as saturated liquid at 20 kPa at a rate of 45 kg/s and exits at 6 MPa. Neglecting the changes in kinetic and potential energies and assuming the process to be reversible, determine the power input to the pump.

Liquid water enters a 16-kW pump at 100-kPa pressure at a rate of 5 kg/s. Determine the highest pressure the liquid water can have at the exit of the pump. Neglect the kinetic and potential energy changes of water, and take the specific volume of water to be 0.001 m3 /kg.

Consider a steam power plant that operates between the pressure limits of 5 MPa and 10 kPa. Steam enters the pump as saturated liquid and leaves the turbine as saturated vapor. Determine the ratio of the work delivered by the turbine to the work consumed by the pump. Assume the entire cycle to be reversible and the heat losses from the pump and the turbine to be negligible.

Reconsider Prob. 7107. Using EES (or other) software, investigate the effect of the quality of the steam at the turbine exit on the net work output. Vary the quality from 0.5 to 1.0, and plot the net work output as a function of this quality.

Helium gas is compressed from 16 psia and 858F to 120 psia at a rate of 10 ft3 /s. Determine the power input to the compressor, assuming the compression process to be (a) isentropic, (b) polytropic with n 5 1.2, (c) isothermal, and (d) ideal two-stage polytropic with n 5 1.2.

Reconsider Prob. 7109E. Using EES (or other) software, evaluate and plot the work of compression and entropy change of the helium as functions of the polytropic exponent as it varies from 1 to 1.667. Discuss your results.

Nitrogen gas is compressed from 80 kPa and 278C to 480 kPa by a 10-kW compressor. Determine the mass flow rate of nitrogen through the compressor, assuming the compression process to be (a) isentropic, (b) polytropic with n 5 1.3, (c) isothermal, and (d) ideal two-stage polytropic with n 5 1.3.

Saturated refrigerant-134a vapor at 15 psia is compressed reversibly in an adiabatic compressor to 80 psia. Determine the work input to the compressor. What would your answer be if the refrigerant were first condensed at constant pressure before it was compressed?

Describe the ideal process for an (a) adiabatic turbine, (b) adiabatic compressor, and (c) adiabatic nozzle, and define the isentropic efficiency for each device.

Is the isentropic process a suitable model for compressors that are cooled intentionally? Explain.

On a T-s diagram, does the actual exit state (state 2) of an adiabatic turbine have to be on the right-hand side of the isentropic exit state (state 2s)? Why?

Steam at 100 psia and 6508F is expanded adiabatically in a closed system to 10 psia. Determine the work produced, in Btu/lbm, and the final temperature of steam for an isentropic expansion efficiency of 80 percent.

Steam enters an adiabatic turbine at 5 MPa, 6508C, and 80 m/s and leaves at 50 kPa, 1508C, and 140 m/s. If the power output of the turbine is 8 MW, determine (a) the mass flow rate of the steam flowing through the turbine and (b) the isentropic efficiency of the turbine.

Combustion gases enter an adiabatic gas turbine at 15408F and 120 psia and leave at 60 psia with a low velocity. Treating the combustion gases as air and assuming an isentropic efficiency of 82 percent, determine the work output of the turbine.

Steam at 4 MPa and 3508C is expanded in an adiabatic turbine to 120 kPa. What is the isentropic efficiency of this turbine if the steam is exhausted as a saturated vapor?

Steam enters an adiabatic turbine at 8 MPa and 5008C with a mass flow rate of 3 kg/s and leaves at 30 kPa. The isentropic efficiency of the turbine is 0.90. Neglecting the kinetic energy change of the steam, determine (a) the temperature at the turbine exit and (b) the power output of the turbine.

Reconsider Prob. 7120. Using EES (or other) software, study the effect of varying the turbine isentropic efficiency from 0.75 to 1.0 on both the work done and the exit temperature of the steam, and plot your results.

Carbon dioxide enters an adiabatic compressor at 100 kPa and 300 K at a rate of 1.8 kg/s and exits at 600 kPa and 450 K. Neglecting the kinetic energy changes, determine the isentropic efficiency of the compressor.

A refrigeration unit compresses saturated R-134a vapor at 108C to 1000 kPa. How much power is required to compress 0.9 kg/s of R-134a with a compressor efficiency of 85 percent?

Refrigerant-134a enters an adiabatic compressor as saturated vapor at 100 kPa at a rate of 0.7 m3 /min and exits at 1-MPa pressure. If the isentropic efficiency of the compressor is 87 percent, determine (a) the temperature of the refrigerant at the exit of the compressor and (b) the power input, in kW. Also, show the process on a T-s diagram with respect to saturation lines.

Reconsider Prob. 7124. Using EES (or other) software, redo the problem by including the effects of the kinetic energy of the flow by assuming an inletto-exit area ratio of 1.5 for the compressor when the compressor exit pipe inside diameter is 2 cm

Air is compressed by an adiabatic compressor from 95 kPa and 278C to 600 kPa and 2778C. Assuming variable specific heats and neglecting the changes in kinetic and potential energies, determine (a) the isentropic efficiency of the compressor and (b) the exit temperature of air if the process were reversible.

Argon gas enters an adiabatic compressor at 14 psia and 758F with a velocity of 60 ft/s, and it exits at 200 psia and 240 ft/s. If the isentropic efficiency of the compressor is 87 percent, determine (a) the exit temperature of the argon and (b) the work input to the compressor.

Air enters an adiabatic nozzle at 45 psia and 9408F with low velocity and exits at 650 ft/s. If the isentropic efficiency of the nozzle is 85 percent, determine the exit temperature and pressure of the air.

Reconsider Prob. 7128E. Using EES (or other) software, study the effect of varying the nozzle isentropic efficiency from 0.8 to 1.0 on both the exit temperature and pressure of the air, and plot the results.

The exhaust nozzle of a jet engine expands air at 300 kPa and 1808C adiabatically to 100 kPa. Determine the air velocity at the exit when the inlet velocity is low and the nozzle isentropic efficiency is 96 percent.

An adiabatic diffuser at the inlet of a jet engine increases the pressure of the air that enters the diffuser at 11 psia and 308F to 20 psia. What will the air velocity at the diffuser exit be if the diffuser isentropic efficiency defined as the ratio of the actual kinetic energy change to the isentropic kinetic energy change is 82 percent and the diffuser inlet velocity is 1200 ft/s?

Hot combustion gases enter the nozzle of a turbojet engine at 260 kPa, 7478C, and 80 m/s, and they exit at a pressure of 85 kPa. Assuming an isentropic efficiency of 92 percent and treating the combustion gases as air, determine (a) the exit velocity and (b) the exit temperature.

Refrigerant-134a is expanded adiabatically from 100 psia and 1008F to a saturated vapor at 10 psia. Determine the entropy generation for this process, in Btu/lbmR.

Oxygen enters an insulated 12-cm-diameter pipe with a velocity of 70 m/s. At the pipe entrance, the oxygen is at 240 kPa and 208C; and, at the exit, it is at 200 kPa and 188C. Calculate the rate at which entropy is generated in the pipe.

Nitrogen is compressed by an adiabatic compressor from 100 kPa and 258C to 600 kPa and 2908C. Calculate the entropy generation for this process, in kJ/kgK.

Air enters a compressor steadily at the ambient conditions of 100 kPa and 228C and leaves at 800 kPa. Heat is lost from the compressor in the amount of 120 kJ/kg and the air experiences an entropy decrease of 0.40 kJ/kg?K. Using constant specific heats, determine (a) the exit temperature of the air, (b) the work input to the compressor, and (c) the entropy generation during this process.

Steam enters an adiabatic turbine steadily at 7 MPa, 5008C, and 45 m/s, and leaves at 100 kPa and 75 m/s. If the power output of the turbine is 5 MW and the isentropic efficiency is 77 percent, determine (a) the mass flow rate of steam through the turbine, (b) the temperature at the turbine exit, and (c) the rate of entropy generation during this process.

In an ice-making plant, water at 08C is frozen at atmospheric pressure by evaporating saturated R-134a liquid at 2168C. The refrigerant leaves this evaporator as a saturated vapor, and the plant is sized to produce ice at 08C at a rate of 2500 kg/h. Determine the rate of entropy generation in this plant.

Water at 20 psia and 508F enters a mixing chamber at a rate of 300 lbm/min where it is mixed steadily with steam entering at 20 psia and 2408F. The mixture leaves the chamber at 20 psia and 1308F, and heat is lost to the surrounding air at 708F at a rate of 180 Btu/min. Neglecting the changes in kinetic and potential energies, determine the rate of entropy generation during this process?

Steam is to be condensed on the shell side of a heat exchanger at 1508F. Cooling water enters the tubes at 608F at a rate of 44 lbm/s and leaves at 738F. Assuming the heat exchanger to be well-insulated, determine (a) the rate of heat transfer in the heat exchanger and (b) the rate of entropy generation in the heat exchanger.

A well-insulated heat exchanger is to heat water (cp 5 4.18 kJ/kg?8C) from 25 to 608C at a rate of 0.50 kg/s. The heating is to be accomplished by geothermal water (cp 5 4.31 kJ/kg?8C) available at 1408C at a mass flow rate of 0.75 kg/s. Determine (a) the rate of heat transfer and (b) the rate of entropy generation in the heat exchanger.

An adiabatic heat exchanger is to cool ethylene glycol (cp 5 2.56 kJ/kg?8C) flowing at a rate of 2 kg/s from 80 to 408C by water (cp 5 4.18 kJ/kg?8C) that enters at 208C and leaves at 558C. Determine (a) the rate of heat transfer and (b) the rate of entropy generation in the heat exchanger.

A well-insulated, thin-walled, double-pipe, counter-flow heat exchanger is to be used to cool oil (cp 5 2.20 kJ/kg?8C) from 1508C to 408C at a rate of 2 kg/s by water (cp 5 4.18 kJ/kg?8C) that enters at 228C at a rate of 1.5 kg/s. Determine (a) the rate of heat transfer and (b) the rate of entropy generation in the heat exchanger.

In a dairy plant, milk at 48C is pasteurized continuously at 728C at a rate of 12 L/s for 24 hours a day and 365 days a year. The milk is heated to the pasteurizing temperature by hot water heated in a natural-gas-fired boiler that has an efficiency of 82 percent. The pasteurized milk is then cooled by cold water at 188C before it is finally refrigerated back to 48C. To save energy and money, the plant installs a regenerator that has an effectiveness of 82 percent. If the cost of natural gas is $1.30/therm (1 therm 5 105,500 kJ), determine how much energy and money the regenerator will save this company per year and the annual reduction in entropy generation.

An ordinary egg can be approximated as a 5.5-cmdiameter sphere. The egg is initially at a uniform temperature of 88C and is dropped into boiling water at 978C. Taking the properties of the egg to be r 5 1020 kg/m3 and cp 5 3.32 kJ/kg8C, determine (a) how much heat is transferred to the egg by the time the average temperature of the egg rises to 708C and (b) the amount of entropy generation associated with this heat transfer process.

Chickens with an average mass of 2.2 kg and average specific heat of 3.54 kJ/kg?8C are to be cooled by chilled water that enters a continuous-flow-type immersion chiller at 0.58C and leaves at 2.58C. Chickens are dropped into the chiller at a uniform temperature of 158C at a rate of 250 chickens per hour and are cooled to an average temperature of 38C before they are taken out. The chiller gains heat from the surroundings at 258C at a rate of 150 kJ/h. Determine (a) the rate of heat removal from the chickens, in kW, and (b) the rate of entropy generation during this chilling process.

Carbon-steel balls (r 5 7833 kg/m3 and cp 5 0.465 kJ/kg?8C) 8 mm in diameter are annealed by heating them first to 9008C in a furnace and then allowing them to cool slowly to 1008C in ambient air at 358C. If 2500 balls are to be annealed per hour, determine (a) the rate of heat transfer from the balls to the air and (b) the rate of entropy generation due to heat loss from the balls to the air.

In a production facility, 1.2-in-thick, 2-ft 3 2-ft square brass plates (r 5 532.5 lbm/ft3 and cp 5 0.091 Btu/lbm?8F) that are initially at a uniform temperature of 758F are heated by passing them through an oven at 13008F at a rate of 450 per minute. If the plates remain in the oven until their average temperature rises to 10008F, determine (a) the rate of heat transfer to the plates in the furnace and (b) the rate of entropy generation associated with this heat transfer process.

Long cylindrical steel rods (r 5 7833 kg/m3 and cp 5 0.465 kJ/kg8C) of 10-cm diameter are heat treated by drawing them at a velocity of 3 m/min through a 7-m-long oven maintained at 9008C. If the rods enter the oven at 308C and leave at 7008C, determine (a) the rate of heat transfer to the rods in the oven and (b) the rate of entropy generation associated with this heat transfer process.

The inner and outer surfaces of a 4-m 3 10-m brick wall of thickness 20 cm are maintained at temperatures of 168C and 48C, respectively. If the rate of heat transfer through the wall is 1250 W, determine the rate of entropy generation within the wall.

A frictionless pistoncylinder device contains saturated liquid water at 40-psia pressure. Now 600 Btu of heat is transferred to water from a source at 10008F, and part of the liquid vaporizes at constant pressure. Determine the total entropy generated during this process, in Btu/R.

Steam enters a diffuser at 20 psia and 2408F with a velocity of 900 ft/s and exits as saturated vapor at 2408F and 100 ft/s. The exit area of the diffuser is 1 ft2 . Determine (a) the mass flow rate of the steam and (b) the rate of entropy generation during this process. Assume an ambient temperature of 778F.

Steam enters an adiabatic nozzle at 2 MPa and 3508C with a velocity of 55 m/s and exits at 0.8 MPa and 390 m/s. If the nozzle has an inlet area of 7.5 cm2 , determine (a) the exit temperature and (b) the rate of entropy generation for this process.

Steam expands in a turbine steadily at a rate of 40,000 kg/h, entering at 8 MPa and 5008C and leaving at 40 kPa as saturated vapor. If the power generated by the turbine is 8.2 MW, determine the rate of entropy generation for this process. Assume the surrounding medium is at 258C.

A hot-water stream at 708C enters an adiabatic mixing chamber with a mass flow rate of 3.6 kg/s, where it is mixed with a stream of cold water at 208C. If the mixture leaves the chamber at 428C, determine (a) the mass flow rate of the cold water and (b) the rate of entropy generation during this adiabatic mixing process. Assume all the streams are at a pressure of 200 kPa.

Liquid water at 200 kPa and 158C is heated in a chamber by mixing it with superheated steam at 200 kPa and 1508C. Liquid water enters the mixing chamber at a rate of 4.3 kg/s, and the chamber is estimated to lose heat to the surrounding air at 208C at a rate of 1200 kJ/min. If the mixture leaves the mixing chamber at 200 kPa and 808C, determine (a) the mass flow rate of the superheated steam and (b) the rate of entropy generation during this mixing process.

A 0.18-m3 rigid tank is filled with saturated liquid water at 1208C. A valve at the bottom of the tank is now opened, and one-half of the total mass is withdrawn from the tank in the liquid form. Heat is transferred to water from a source at 2308C so that the temperature in the tank remains constant. Determine (a) the amount of heat transfer and (b) the total entropy generation for this process.

An iron block of unknown mass at 1858F is dropped into an insulated tank that contains 0.8 ft3 of water at 708F. At the same time, a paddle wheel driven by a 200-W motor is activated to stir the water. Thermal equilibrium is established after 10 min with a final temperature of 758F. Determine (a) the mass of the iron block and (b) the entropy generated during this process.

Compressed air is one of the key utilities in manufacturing facilities, and the total installed power of compressed-air systems in the United States is estimated to be about 20 million horsepower. Assuming the compressors to operate at full load during one-third of the time on average and the average motor efficiency to be 90 percent, determine how much energy and money will be saved per year if the energy consumed by compressors is reduced by 5 percent as a result of implementing some conservation measures. Take the unit cost of electricity to be $0.11/kWh.

The compressed-air requirements of a plant at sea level are being met by a 90-hp compressor that takes in air at the local atmospheric pressure of 101.3 kPa and the average temperature of 158C and compresses it to 1100 kPa. An investigation of the compressed-air system and the equipment using the compressed air reveals that compressing the air to 750 kPa is sufficient for this plant. The compressor operates 3500 h/yr at 75 percent of the rated load and is driven by an electric motor that has an efficiency of 94 percent. Taking the price of electricity to be $0.105/kWh, determine the amount of energy and money saved as a result of reducing the pressure of the compressed air.

A 150-hp compressor in an industrial facility is housed inside the production area where the average temperature during operating hours is 258C. The average temperature of outdoors during the same hours is 108C. The compressor operates 4500 h/yr at 85 percent of rated load and is driven by an electric motor that has an efficiency of 90 percent. Taking the price of electricity to be $0.12/kWh, determine the amount of energy and money saved as a result of drawing outside air to the compressor instead of using the inside air.

The compressed-air requirements of a plant are being met by a 100-hp screw compressor that runs at full load during 40 percent of the time and idles the rest of the time during operating hours. The compressor consumes 35 percent of the rated power when idling and 90 percent of the power when compressing air. The annual operating hours of the facility are 3800 h, and the unit cost of electricity is $0.115/kWh. It is determined that the compressed-air requirements of the facility during 60 percent of the time can be met by a 25-hp reciprocating compressor that consumes 95 percent of the rated power when compressing air and no power when not compressing air. It is estimated that the 25-hp compressor runs 85 percent of the time. The efficiencies of the motors of the large and the small compressors at or near full load are 0.90 and 0.88, respectively. The efficiency of the large motor at 35 percent load is 0.82. Determine the amount of energy and money saved as a result of switching to the 25-hp compressor during 60 percent of the time.

The compressed-air requirements of a plant are being met by a 90-hp screw compressor. The facility stops production for one hour every day, including weekends, for lunch break, but the compressor is kept operating. The compressor consumes 35 percent of the rated power when idling, and the unit cost of electricity is $0.11/kWh. Determine the amount of energy and money saved per year as a result of turning the compressor off during lunch break. Take the efficiency of the motor at part load to be 84 percent.

The compressed-air requirements of a plant are met by a 150-hp compressor equipped with an intercooler, an aftercooler, and a refrigerated dryer. The plant operates 6300 h/yr, but the compressor is estimated to be compressing air during only one-third of the operating hours, that is, 2100 hours a year. The compressor is either idling or is shut off the rest of the time. Temperature measurements and calculations indicate that 25 percent of the energy input to the compressor is removed from the compressed air as heat in the aftercooler. The COP of the refrigeration unit is 2.5, and the cost of electricity is $0.12/kWh. Determine the amount of the energy and money saved per year as a result of cooling the compressed air before it enters the refrigerated dryer.

The 1800-rpm, 150-hp motor of a compressor is burned out and is to be replaced by either a standard motor that has a full-load efficiency of 93.0 percent and costs $9031 or a high-efficiency motor that has an efficiency of 96.2 percent and costs $10,942. The compressor operates 4368 h/yr at full load, and its operation at part load is negligible. If the cost of electricity is $0.125/kWh, determine the amount of energy and money this facility will save by purchasing the high-efficiency motor instead of the standard motor. Also, determine if the savings from the high-efficiency motor justify the price differential if the expected life of the motor is 10 years. Ignore any possible rebates from the local power company.

The space heating of a facility is accomplished by natural gas heaters that are 85 percent efficient. The compressed air needs of the facility are met by a large liquidcooled compressor. The coolant of the compressor is cooled by air in a liquid-to-air heat exchanger whose airflow section is 1.0-m high and 1.0-m wide. During typical operation, the air is heated from 20 to 528C as it flows through the heat exchanger. The average velocity of air on the inlet side is measured to be 3 m/s. The compressor operates 20 hours a day and 5 days a week throughout the year. Taking the heating season to be 6 months (26 weeks) and the cost of the natural gas to be $1.25/therm (1 therm 5 100,000 Btu 5 105,500 kJ), determine how much money will be saved by diverting the compressor waste heat into the facility during the heating season.

The compressors of a production facility maintain the compressed-air lines at a (gage) pressure of 700 kPa at 1400-m elevation, where the atmospheric pressure is 85.6 kPa. The average temperature of air is 158C at the compressor inlet and 258C in the compressed-air lines. The facility operates 4200 h/yr, and the average price of electricity is $0.12/kWh. Taking the compressor efficiency to be 0.8, the motor efficiency to be 0.93, and the discharge coefficient to be 0.65, determine the energy and money saved per year by sealing a leak equivalent to a 3-mm-diameter hole on the compressed-air line.

The energy used to compress air in the United States is estimated to exceed one-half quadrillion (0.5 3 1015) kJ per year. It is also estimated that 10 to 40 percent of the compressed air is lost through leaks. Assuming, on average, 20 percent of the compressed air is lost through air leaks and the unit cost of electricity is $0.13/kWh, determine the amount and cost of electricity wasted per year due to air leaks.

A heat engine whose thermal efficiency is 35 percent uses a hot reservoir at 1100 R and a cold reservoir at 550 R. Calculate the entropy change of the two reservoirs when 1 Btu of heat is transferred from the hot reservoir to the engine. Does this engine satisfy the increase of entropy principle? If the thermal efficiency of the heat engine is increased to 60 percent, will the increase of entropy principle still be satisfied?

A refrigerator with a coefficient of performance of 4 transfers heat from a cold region at 2208C to a hot region at 308C. Calculate the total entropy change of the regions when 1 kJ of heat is transferred from the cold region. Is the second law satisfied? Will this refrigerator still satisfy the second law if its coefficient of performance is 6?

It has been suggested that air at 100 kPa and 258C can be cooled by first compressing it adiabatically in a closed system to 1000 kPa and then expanding it adiabatically back to 100 kPa. Is this possible?

1-1bm of air at 10 psia and 708F is contained in a piston-cylinder device. Next, the air is compressed reversibly to 100 psia while the temperature is maintained constant. Determine the total amount of heat transferred to the air during this compression.

Can saturated water vapor at 200 kPa be condensed to a saturated liquid in an isobaric, closed system process while only exchanging heat with an isothermal energy reservoir at 908C? (Hint: Determine the entropy generation.)

A 100-lbm block of a solid material whose specific heat is 0.5 Btu/lbmR is at 808F. It is heated with 10 lbm of saturated water vapor that has a constant pressure of 20 psia. Determine the final temperature of the block and water, and the entropy change of (a) the block, (b) the water, and (c) the entire system. Is this process possible? Why?

A horizontal cylinder is separated into two compartments by an adiabatic, frictionless piston. One side contains 0.2 m3 of nitrogen and the other side contains 0.1 kg of helium, both initially at 208C and 95 kPa. The sides of the cylinder and the helium end are insulated. Now heat is added to the nitrogen side from a reservoir at 5008C until the pressure of the helium rises to 120 kPa. Determine (a) the final temperature of the helium, (b) the final volume of the nitrogen, (c) the heat transferred to the nitrogen, and (d) the entropy generation during this process.

A pistoncylinder device contains air that undergoes a reversible thermodynamic cycle. Initially, air is at 400 kPa and 300 K with a volume of 0.3 m3 Air is first expanded isothermally to 150 kPa, then compressed adiabatically to the initial pressure, and finally compressed at the constant pressure to the initial state. Accounting for the variation of specific heats with temperature, determine the work and heat transfer for each process.

A pistoncylinder device initially contains 15 ft3 of helium gas at 25 psia and 708F. Helium is now compressed in a polytropic process (PVn 5 constant) to 70 psia and 3008F. Determine (a) the entropy change of helium, (b) the entropy change of the surroundings, and (c) whether this process is reversible, irreversible, or impossible. Assume the surroundings are at 708F.

A pistoncylinder device contains steam that undergoes a reversible thermodynamic cycle. Initially the steam is at 400 kPa and 3508C with a volume of 0.3 m3 . The steam is first expanded isothermally to 150 kPa, then compressed adiabatically to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine the net work and heat transfer for the cycle after you calculate the work and heat interaction for each process.

A 0.8-m3 rigid tank contains carbon dioxide (CO2) gas at 250 K and 100 kPa. A 500-W electric resistance heater placed in the tank is now turned on and kept on for 40 min after which the pressure of CO2 is measured to be 175 kPa. Assuming the surroundings to be at 300 K and using constant specific heats, determine (a) the final temperature of CO2, (b) the net amount of heat transfer from the tank, and (c) the entropy generation during this process.

Helium gas is throttled steadily from 400 kPa and 608C. Heat is lost from the helium in the amount of 1.75 kJ/kg to the surroundings at 258C and 100 kPa. If the entropy of the helium increases by 0.34 kJ/kgK in the valve, determine (a) the exit pressure and temperature and (b) the entropy generation during this process.

Air enters the evaporator section of a window air conditioner at 100 kPa and 278C with a volume flow rate of 6 m3 /min. The refrigerant-134a at 120 kPa with a quality of 0.3 enters the evaporator at a rate of 2 kg/min and leaves as saturated vapor at the same pressure. Determine the exit temperature of the air and the rate of entropy generation for this process, assuming (a) the outer surfaces of the air conditioner are insulated and (b) heat is transferred to the evaporator of the air conditioner from the surrounding medium at 328C at a rate of 30 kJ/min.

Refrigerant-134a enters a compressor as a saturated vapor at 160 kPa at a rate of 0.03 m3 /s and leaves at 800 kPa. The power input to the compressor is 10 kW. If the surroundings at 208C experience an entropy increase of 0.008 kW/K, determine (a) the rate of heat loss from the compressor, (b) the exit temperature of the refrigerant, and (c) the rate of entropy generation.

Air at 500 kPa and 400 K enters an adiabatic nozzle at a velocity of 30 m/s and leaves at 300 kPa and 350 K. Using variable specific heats, determine (a) the isentropic efficiency, (b) the exit velocity, and (c) the entropy generation.

3-kg of helium gas at 100 kPa and 278C are adiabatically compressed to 900 kPa. If the isentropic compression efficiency is 80 percent, determine the required work input and the final temperature of helium.

An inventor claims to have invented an adiabatic steady-flow device with a single inlet-outlet that produces 230 kW when expanding 1 kg/s of air from 1200 kPa and 3008C to 100 kPa. Is this claim valid?

You are to expand a gas adiabatically from 3 MPa and 3008C to 80 kPa in a piston-cylinder device. Which of the two choices air with an isentropic expansion efficiency of 90 percent or neon with an isentropic expansion efficiency of 80 percent will produce the most work?

An adiabatic capillary tube is used in some refrigeration systems to drop the pressure of the refrigerant from the condenser level to the evaporator level. R-134a enters the capillary tube as a saturated liquid at 708C, and leaves at 2208C. Determine the rate of entropy generation in the capillary tube for a mass flow rate of 0.2 kg/s.

Determine the work input and entropy generation during the compression of steam from 100 kPa to 1 MPa in (a) an adiabatic pump and (b) an adiabatic compressor if the inlet state is saturated liquid in the pump and saturated vapor in the compressor and the isentropic efficiency is 85 percent for both devices

Air is compressed steadily by a compressor from 100 kPa and 208C to 1200 kPa and 3008C at a rate of 0.4 kg/s. The compressor is intentionally cooled by utilizing fins on the surface of the compressor and heat is lost from the compressor at a rate of 15 kW to the surroundings at 208C. Using constant specific heats at room temperature, determine (a) the power input to the compressor, (b) the isothermal efficiency, and (c) the entropy generation during this process.

Air is compressed steadily by a compressor from 100 kPa and 178C to 700 kPa at a rate of 5 kg/min. Determine the minimum power input required if the process is (a) adiabatic and (b) isothermal. Assume air to be an ideal gas with variable specific heats, and neglect the changes in kinetic and potential energies.

Air enters a two-stage compressor at 100 kPa and 278C and is compressed to 625 kPa. The pressure ratio across each stage is the same, and the air is cooled to the initial temperature between the two stages. Assuming the compression process to be isentropic, determine the power input to the compressor for a mass flow rate of 0.15 kg/s. What would your answer be if only one stage of compression were used?

Steam at 6 MPa and 5008C enters a two-stage adiabatic turbine at a rate of 15 kg/s. 10 percent of the steam is extracted at the end of the first stage at a pressure of 1.2 MPa for other use. The remainder of the steam is further expanded in the second stage and leaves the turbine at 20 kPa. Determine the power output of the turbine, assuming (a) the process is reversible and (b) the turbine has an isentropic efficiency of 88 percent.

Refrigerant-134a at 140 kPa and 2108C is compressed by an adiabatic 1.3-kW compressor to an exit state of 700 kPa and 608C. Neglecting the changes in kinetic and potential energies, determine (a) the isentropic efficiency of the compressor, (b) the volume flow rate of the refrigerant at the compressor inlet, in L/min, and (c) the maximum volume flow rate at the inlet conditions that this adiabatic 1.3-kW compressor can handle without violating the second law.

An adiabatic air compressor is to be powered by a direct-coupled adiabatic steam turbine that is also driving a generator. Steam enters the turbine at 12.5 MPa and 5008C at a rate of 25 kg/s and exits at 10 kPa and a quality of 0.92. Air enters the compressor at 98 kPa and 295 K at a rate of 10 kg/s and exits at 1 MPa and 620 K. Determine (a) the net power delivered to the generator by the turbine and (b) the rate of entropy generation within the turbine and the compressor during this process.

Reconsider Prob. 7194. Using EES (or other) software, determine the isentropic efficiencies for the compressor and turbine. Then use EES to study how varying the compressor efficiency over the range 0.6 to 0.8 and the turbine efficiency over the range 0.7 to 0.95 affect the net work for the cycle and the entropy generated for the process. Plot the net work as a function of the compressor efficiency for turbine efficiencies of 0.7, 0.8, and 0.9, and discuss your results.

Air is expanded in an adiabatic turbine of 85 percent isentropic efficiency from an inlet state of 2200 kPa and 3008C to an outlet pressure of 200 kPa. Calculate the outlet temperature of air and the work produced by this turbine per unit mass of air.

Air is expanded in an adiabatic turbine of 90 percent isentropic efficiency from an inlet state of 2800 kPa and 4008C to an outlet pressure of 150 kPa. Calculate the outlet temperature of air, the work produced by this turbine, and the entropy generation.

To control the power output of an isentropic steam turbine, a throttle valve is placed in the steam line supplying the turbine inlet, as shown in the figure. Steam at 6 MPa and 4008C is supplied to the throttle inlet, and the turbine exhaust pressure is set at 70 kPa. Compare the work produced by this steam turbine, in kJ/kg, when the throttle valve is completely open (so that there is no pressure loss) and when it is partially closed so that the pressure at the turbine inlet is 3 MPa.

Two rigid tanks are connected by a valve. Tank A is insulated and contains 0.3 m3 of steam at 400 kPa and 60 percent quality. Tank B is uninsulated and contains 2 kg of steam at 200 kPa and 2508C. The valve is now opened, and steam flows from tank A to tank B until the pressure in tank A drops to 200 kPa. During this process 300 kJ of heat is transferred from tank B to the surroundings at 178C. Assuming the steam remaining inside tank A to have undergone a reversible adiabatic process, determine (a) the final temperature in each tank and (b) the entropy generated during this process.

A 1200-W electric resistance heating element whose diameter is 0.5 cm is immersed in 40 kg of water initially at 208C. Assuming the water container is well-insulated, determine how long it will take for this heater to raise the water temperature to 508C. Also, determine the entropy generated during this process, in kJ/K.

A 5-ft3 rigid tank initially contains refrigerant-134a at 60 psia and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant-134a at 140 psia and 808F. The valve is now opened, allowing the refrigerant to enter the tank, and is closed when it is observed that the tank contains only saturated liquid at 100 psia. Determine (a) the mass of the refrigerant that entered the tank, (b) the amount of heat transfer with the surroundings at 708F, and (c) the entropy generated during this process.

A passive solar house that is losing heat to the outdoors at 38C at an average rate of 50,000 kJ/h is maintained at 228C at all times during a winter night for 10 h. The house is to be heated by 50 glass containers, each containing 20 L of water that is heated to 808C during the day by absorbing solar energy. A thermostat controlled 15 kW backup electric resistance heater turns on whenever necessary to keep the house at 228C. Determine how long the electric heating system was on that night and the amount of entropy generated during the night.

A 15-ft3 steel container that has a mass of 75 lbm when empty is filled with liquid water. Initially, both the steel tank and the water are at 1208F. Now heat is transferred, and the entire system cools to the surrounding air temperature of 708F. Determine the total entropy generated during this process.

In order to cool 1-ton of water at 208C in an insulated tank, a person pours 80 kg of ice at 258C into the water. Determine (a) the final equilibrium temperature in the tank and (b) the entropy generation during this process. The melting temperature and the heat of fusion of ice at atmospheric pressure are 08C and 333.7 kJ/kg.

One ton of liquid water at 808C is brought into a well-insulated and well-sealed 4-m 3 5-m 3 7-m room initially at 228C and 100 kPa. Assuming constant specific heats for both air and water at room temperature, determine (a) the final equilibrium temperature in the room and (b) the total entropy change during this process, in kJ/K.

A well-insulated 4-m 3 4-m 3 5-m room initially at 108C is heated by the radiator of a steam heating system. The radiator has a volume of 15 L and is filled with superheated vapor at 200 kPa and 2008C. At this moment both the inlet and the exit valves to the radiator are closed. A 120-W fan is used to distribute the air in the room. The pressure of the steam is observed to drop to 100 kPa after 30 min as a result of heat transfer to the room. Assuming constant specific heats for air at room temperature, determine (a) the average temperature of air in 30 min, (b) the entropy change of the steam, (c) the entropy change of the air in the room, and (d) the entropy generated during this process, in kJ/K. Assume the air pressure in the room remains constant at 100 kPa at all times

An insulated pistoncylinder device initially contains 0.02 m3 of saturated liquidvapor mixture of water with a quality of 0.1 at 1008C. Now some ice at 2188C is dropped into the cylinder. If the cylinder contains saturated liquid at 1008C when thermal equilibrium is established, determine (a) the amount of ice added and (b) the entropy generation during this process. The melting temperature and the heat of fusion of ice at atmospheric pressure are 08C and 333.7 kJ/kg

Consider a 50-L evacuated rigid bottle that is surrounded by the atmosphere at 95 kPa and 278C. A valve at the neck of the bottle is now opened and the atmospheric air is allowed to flow into the bottle. The air trapped in the bottle eventually reaches thermal equilibrium with the atmosphere as a result of heat transfer through the wall of the bottle. The valve remains open during the process so that the trapped air also reaches mechanical equilibrium with the atmosphere. Determine the net heat transfer through the wall of the bottle and the entropy generation during this filling process.

(a) Water flows through a shower head steadily at a rate of 10 L/min. An electric resistance heater placed in the water pipe heats the water from 16 to 438C. Taking the density of water to be 1 kg/L, determine the electric power input to the heater, in kW, and the rate of entropy generation during this process, in kW/K. (b) In an effort to conserve energy, it is proposed to pass the drained warm water at a temperature of 398C through a heat exchanger to preheat the incoming cold water. If the heat exchanger has an effectiveness of 0.50 (that is, it recovers only half of the energy that can possibly be transferred from the drained water to incoming cold water), determine the electric power input required in this case and the reduction in the rate of entropy generation in the resistance heating section.

Using EES (or other) software, determine the work input to a multistage compressor for a given set of inlet and exit pressures for any number of stages. Assume that the pressure ratio across each stage is identical and the compression process is polytropic. List and plot the compressor work against the number of stages for P1 5 100 kPa, T1 5 258C, P2 5 1000 kPa, and n 5 1.35 for air. Based on this chart, can you justify using compressors with more than three stages?

The inner and outer surfaces of a 2-m 3 2-m window glass in winter are 108C and 38C, respectively. If the rate of heat loss through the window is 3.2 kJ/s, determine the amount of heat loss, in kJ, through the glass over a period of 5 h. Also, determine the rate of entropy generation during this process within the glass.

The inner and outer glasses of a 2-m 3 2-m doublepane window are at 188C and 68C, respectively. If the glasses are very nearly isothermal and the rate of heat transfer through the window is 110 W, determine the rates of entropy transfer through both sides of the window and the rate of entropy generation within the window, in W/K.

A hot-water pipe at 808C is losing heat to the surrounding air at 58C at a rate of 2200 W. Determine the rate of entropy generation in the surrounding air, in W/K.

Consider the turbocharger of an internal combustion engine. The exhaust gases enter the turbine at 4508C at a rate of 0.02 kg/s and leave at 4008C. Air enters the compressor at 708C and 95 kPa at a rate of 0.018 kg/s and leaves at 135 kPa. The mechanical efficiency between the turbine and the compressor is 95 percent (5 percent of turbine work is lost during its transmission to the compressor). Using air properties for the exhaust gases, determine (a) the air temperature at the compressor exit and (b) the isentropic efficiency of the compressor.

A 0.40-m3 insulated pistoncylinder device initially contains 1.3 kg of air at 308C. At this state, the piston is free to move. Now air at 500 kPa and 708C is allowed to enter the cylinder from a supply line until the volume increases by 50 percent. Using constant specific heats at room temperature, determine (a) the final temperature, (b) the amount of mass that has entered, (c) the work done, and (d) the entropy generation.

When the transportation of natural gas in a pipeline is not feasible for economic reasons, it is first liquefied using nonconventional refrigeration techniques and then transported in super-insulated tanks. In a natural gas liquefaction plant, the liquefied natural gas (LNG) enters a cryogenic turbine at 30 bar and 21608C at a rate of 20 kg/s and leaves at 3 bar. If 115 kW power is produced by the turbine, determine the efficiency of the turbine. Take the density of LNG to be 423.8 kg/m3 .

A constant volume tank filled with 2 kg of air rejects heat to a heat reservoir at 300 K. During the process the temperature of the air in the tank decreases to the reservoir temperature. Determine the expressions for the entropy changes for the tank and reservoir and the total entropy change or entropy generated of this isolated system. Plot these entropy changes as functions of the initial temperature of the air. Comment on your results. Assume constant specific heats for air at 300 K.

Consider two bodies of identical mass m and specific heat c used as thermal reservoirs (source and sink) for a heat engine. The first body is initially at an absolute temperature T1 while the second one is at a lower absolute temperature T2. Heat is transferred from the first body to the heat engine, which rejects the waste heat to the second body. The process continues until the final temperatures of the two bodies Tf become equal. Show that Tf 5 "T1T2 when the heat engine produces the maximum possible work.

A heat engine receives heat from a constant volume tank filled with 2 kg of air. The engine produces work that is stored in a work reservoir and rejects 400 kJ of heat to a heat reservoir at 300 K. During the process the temperature of the air in the tank decreases to 300 K. (a) Determine the initial temperature of the air that will maximize the work and the thermal efficiency of the engine. (b) Evaluate the total entropy change of this isolated system, the work produced, and the thermal efficiency for the initial air temperature in the tank from part (a) and at 100 K above and below the answer to part (a). (c) Plot the thermal efficiency and the entropy generation as functions of the initial temperature of the air. Comment on your answers. Assume constant specific heats for air at 300 K.

For an ideal gas with constant specific heats show that the compressor and turbine isentropic efficiencies may be written as hC 5 (P2/P1) (k21)/k (T2/T1) 2 1 and hT 5 (T4/T3) 2 1 (P4/P3) (k21)/k 2 1 . The states 1 and 2 represent the compressor inlet and exit states and the states 3 and 4 represent the turbine inlet and exit states.

Starting with the Gibbs equation dh 5 T ds 1 vdP, obtain the expression for the change in enthalpy of an ideal gas having constant specific heats during the isentropic process Pv k 5 constant.

An initially empty rigid vessel is filled with a fluid from a source whose properties remain constant. Determine the entropy generation if this is done adiabatically and without any work, and the fluid is an ideal gas. Your answer should be in terms of the vessels volume, the properties of the gas, the dead state, temperature, the initial and final gas pressure and temperatures, and the pressure and temperature of the gas-supplying source.

The temperature of an ideal gas having constant specific heats is given as a function of specific entropy and specific volume as T(s,v) 5 Av1k exp(s/cv) where A is a constant. For a reversible, constant volume process, find the expression for heat transfer per unit mass as a function of cv and T using Q 5 eT dS. Compare this result with that obtained by applying the first law to a closed system undergoing a constant volume process.

An ideal gas undergoes a reversible, steady-flow process in which pressure and volume are related by the polytropic equation Pv n 5 constant. Neglecting the changes in kinetic and potential energies of the flow and assuming constant specific heats, (a) obtain the expression for the heat transfer per unit mass flow for the process and (b) evaluate this expression for the special case where n 5 k 5 cp /cv.

The polytropic or small stage efficiency of a compressor h`,C is defined as the ratio of the actual differential work done on the fluid to the isentropic differential work done on the flowing through the compressor h`,C 5 dhs/dh. Consider an ideal gas with constant specific heats as the working fluid undergoing a process in a compressor in which the polytropic efficiency is constant. Show that the temperature ratio across the compressor is related to the pressure ratio across the compressor by T2 T1 5 a P2 P1 b a 1 hq,C ba R cp b 5 a P2 P1 b a 1 hq,C bak21 k b

Steam is compressed from 6 MPa and 3008C to 10 MPa isentropically. The final temperature of the steam is (a) 2908C (b) 3008C (c) 3118C (d) 3718C (e) 4228C

An apple with an average mass of 0.12 kg and average specific heat of 3.65 kJ/kg8C is cooled from 258C to 58C. The entropy change of the apple is (a) 20.705 kJ/K (b) 20.254 kJ/K (c) 20.0304 kJ/K (d) 0 kJ/K (e) 0.348 kJ/K

A pistoncylinder device contains 5 kg of saturated water vapor at 3 MPa. Now heat is rejected from the cylinder at constant pressure until the water vapor completely condenses so that the cylinder contains saturated liquid at 3 MPa at the end of the process. The entropy change of the system during this process is (a) 0 kJ/K (b) 23.5 kJ/K (c) 212.5 kJ/K (d) 217.7 kJ/K (e) 219.5 kJ/K

Steam expands in an adiabatic turbine from 4 MPa and 5008C to 0.1 MPa at a rate of 2 kg/s. If steam leaves the turbine as saturated vapor, the power output of the turbine is (a) 2058 kW (b) 1910 kW (c) 1780 kW (d) 1674 kW (e) 1542 kW

Argon gas expands in an adiabatic turbine from 3 MPa and 7508C to 0.2 MPa at a rate of 5 kg/s. The maximum power output of the turbine is (a) 1.06 MW (b) 1.29 MW (c) 1.43 MW (d) 1.76 MW (e) 2.08 MW

A unit mass of a substance undergoes an irreversible process from state 1 to state 2 while gaining heat from the surroundings at temperature T in the amount of q. If the entropy of the substance is s1 at state 1, and s2 at state 2, the entropy change of the substance Ds during this process is (a) Ds , s2 2 s1 (b) Ds . s2 2 s1 (c) Ds 5 s2 2 s1 (d) Ds 5 s2 2 s1 1 q/T (e) Ds . s2 2 s1 1 q/T

A unit mass of an ideal gas at temperature T undergoes a reversible isothermal process from pressure P1 to pressure P2 while losing heat to the surroundings at temperature T in the amount of q. If the gas constant of the gas is R, the entropy change of the gas Ds during this process is (a) Ds 5 R ln(P2/P1) (b) Ds 5 R ln(P2/P1) 2 q/T (c) Ds 5 R ln(P1/P2) (d) Ds 5 R ln(P1/P2) 2 q/T (e) Ds 5 0

Helium gas is compressed from 278C and 3.50 m3 /kg to 0.775 m3 /kg in a reversible and adiabatic manner. The temperature of helium after compression is (a) 748C (b) 1228C (c) 5478C (d) 7098C (e) 10828C

Heat is lost through a plane wall steadily at a rate of 600 W. If the inner and outer surface temperatures of the wall are 208C and 58C, respectively, the rate of entropy generation within the wall is (a) 0.11 W/K (b) 4.21 W/K (c) 2.10 W/K (d) 42.1 W/K (e) 90.0 W/K

Air is compressed steadily and adiabatically from 178C and 90 kPa to 2008C and 400 kPa. Assuming constant specific heats for air at room temperature, the isentropic efficiency of the compressor is (a) 0.76 (b) 0.94 (c) 0.86 (d) 0.84 (e) 1.00

Argon gas expands in an adiabatic turbine steadily from 6008C and 800 kPa to 80 kPa at a rate of 2.5 kg/s. For isentropic efficiency of 88 percent, the power produced by the turbine is (a) 240 kW (b) 361 kW (c) 414 kW (d) 602 kW (e) 777 kW

Water enters a pump steadily at 100 kPa at a rate of 35 L/s and leaves at 800 kPa. The flow velocities at the inlet and the exit are the same, but the pump exit where the discharge pressure is measured is 6.1 m above the inlet section. The minimum power input to the pump is (a) 34 kW (b) 22 kW (c) 27 kW (d) 52 kW (e) 44 kW

Air is to be compressed steadily and isentropically from 1 atm to 16 atm by a two-stage compressor. To minimize the total compression work, the intermediate pressure between the two stages must be (a) 3 atm (b) 4 atm (c) 8.5 atm (d) 9 atm (e) 12 atm

Helium gas enters an adiabatic nozzle steadily at 5008C and 600 kPa with a low velocity, and exits at a pres sure of 90 kPa. The highest possible velocity of helium gas at the nozzle exit is (a) 1475 m/s (b) 1662 m/s (c) 1839 m/s (d) 2066 m/s (e) 3040 m/s

Combustion gases with a specific heat ratio of 1.3 enter an adiabatic nozzle steadily at 8008C and 800 kPa with a low velocity, and exit at a pressure of 85 kPa. The lowest possible temperature of combustion gases at the nozzle exit is (a) 438C (b) 2378C (c) 3678C (d) 4778C (e) 6408C

Steam enters an adiabatic turbine steadily at 4008C and 5 MPa, and leaves at 20 kPa. The highest possible percentage of mass of steam that condenses at the turbine exit and leaves the turbine as a liquid is (a) 4% (b) 8% (c) 12% (d) 18% (e) 0%

Liquid water enters an adiabatic piping system at 158C at a rate of 8 kg/s. If the water temperature rises by 0.28C during flow due to friction, the rate of entropy generation in the pipe is (a) 23 W/K (b) 55 W/K (c) 68 W/K (d) 220 W/K (e) 443 W/K

Liquid water is to be compressed by a pump whose isentropic efficiency is 75 percent from 0.2 MPa to 5 MPa at a rate of 0.15 m3 /min. The required power input to this pump is (a) 4.8 kW (b) 6.4 kW (c) 9.0 kW (d) 16.0 kW (e) 12 kW

Steam enters an adiabatic turbine at 8 MPa and 5008C at a rate of 18 kg/s, and exits at 0.2 MPa and 3008C. The rate of entropy generation in the turbine is (a) 0 kW/K (b) 7.2 kW/K (c) 21 kW/K (d) 15 kW/K (e) 17 kW/K

Helium gas is compressed steadily from 90 kPa and 258C to 800 kPa at a rate of 2 kg/min by an adiabatic compressor. If the compressor consumes 80 kW of power while operating, the isentropic efficiency of this compressor is (a) 54.0% (b) 80.5% (c) 75.8% (d) 90.1% (e) 100%

Compressors powered by natural gas engines are increasing in popularity. Several major manufacturing facilities have already replaced the electric motors that drive their compressors by gas driven engines in order to reduce their energy bills since the cost of natural gas is much lower than the cost of electricity. Consider a facility that has a 130-kW compressor that runs 4400 h/yr at an average load factor of 0.6. Making reasonable assumptions and using unit costs for natural gas and electricity at your location, determine the potential cost savings per year by switching to gas driven engines.

It is well-known that the temperature of a gas rises while it is compressed as a result of the energy input in the form of compression work. At high compression ratios, the air temperature may rise above the autoignition temperature of some hydrocarbons, including some lubricating oil. Therefore, the presence of some lubricating oil vapor in highpressure air raises the possibility of an explosion, creating a fire hazard. The concentration of the oil within the compressor is usually too low to create a real danger. However, the oil that collects on the inner walls of exhaust piping of the compressor may cause an explosion. Such explosions have largely been eliminated by using the proper lubricating oils, carefully designing the equipment, intercooling between compressor stages, and keeping the system clean. A compressor is to be designed for an industrial application in Los Angeles. If the compressor exit temperature is not to exceed 2508C for safety consideration, determine the maximum allowable compression ratio that is safe for all possible weather conditions for that area.

Identify the major sources of entropy generation in your house and propose ways of reducing them.

Obtain the following information about a power plant that is closest to your town: the net power output; the type and amount of fuel; the power consumed by the pumps, fans, and other auxiliary equipment; stack gas losses; temperatures at several locations; and the rate of heat rejection at the condenser. Using these and other relevant data, determine the rate of entropy generation in that power plant.

You are designing a closed-system, isentropicexpansion process using an ideal gas that operates between the pressure limits of P1 and P2. The gases under consideration are hydrogen, nitrogen, air, helium, argon, and carbon dioxide. Which of these gases will produce the greatest amount of work? Which will require the least amount of work in a compression process?