Solved: Air in a pistoncylinder assembly is compressed

Construct a plot, to scale, showing constant-pressure lines of 5.0 and 10 MPa ranging from 100 to \(400^{\circ} \mathrm{C}\) on a T–s diagram for water.

Construct a plot, to scale, showing constant-pressure lines of 1000 and \(1500 \mathrm{\ lbf} / \mathrm{in} .^{2}\) ranging from 300 to \(1000^{\circ} \mathrm{F}\) on a T–s diagram for water.

Using the appropriate table, determine the indicated property. In each case, locate the state on sketches of the T– and T–s diagrams. (a) water at p = 0.20 bar, \(s=4.3703 \mathrm{\ kJ} / \mathrm{kg} \cdot \mathrm{K}\). Find h, in kJ/kg. (b) water at p = 10 bar, u = 3124.4 kJ/kg. Find s, in \(\mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\). (c) Refrigerant 134a at \(T=-28^{\circ} \mathrm{C}\), x=0.8. Find s, in \(\mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\). (d) ammonia at \(T=20^{\circ} \mathrm{C}, s=5.0849 \mathrm{\ kJ} / \mathrm{kg} \cdot \mathrm{K}\). Find u, in kJ/kg.

Using the appropriate tables, determine the change in specific entropy between the specified states, in Btu/lb ? 8R. Show the states on a sketch of the T–s diagram. (a) water, \(p_{1}=10 \mathrm{\ lbf} / \mathrm{in} .\), saturated vapor; \(p_{2}=500 \mathrm{lbf} / \mathrm{in} .^{2}\), \(T_{2}=700^{\circ} \mathrm{F}\). (b) ammonia,\(p_{1}=140 \mathrm{\ lbf} / \mathrm{in} .^{2}, \ T_{1}=160^{\circ} \mathrm{F} ; \ T_{2}=-10^{\circ} \mathrm{F}, \ h_{2}=590 \mathrm{\ Btu} / \mathrm{lb}\). (c) air as an ideal gas, \(T_{1}=80^{\circ} \mathrm{F}, p_{1}=1 \mathrm{\ atm} ; T_{2}=340^{\circ} \mathrm{F}\), p = 5 atm. (d) oxygen as an ideal gas, \(T_{1}=T_{2}=520^{\circ} \mathrm{R}, \ p_{1}=10 \mathrm{\ atm}, \ p_{2}=5 \mathrm{\ atm}\).

Using IT, determine the indicated property for each case in Problem 6.3. Compare the values obtained using the software with the tabular values and discuss.

Using IT, determine the indicated property for each case in Problem 6.4. Compare the values obtained using the software with the tabular values and discuss.

Using steam table data, determine the indicated property data for a process in which there is no change in specific entropy between state 1 and state 2. In each case, locate the states on a sketch of the T–s diagram. (a) \(T_{1}=40^{\circ} \mathrm{C}, x_{1}=100 \%, p_{2}=150 \mathrm{\ kPa}\). Find \(T_{2}\), in \({ }^{\circ} \mathrm{C}\), and \(\Delta h\), in kJ/kg. (b) \(T_{1}=10^{\circ} \mathrm{C}, x_{1}=75 \%, p_{2}=1 \mathrm{MPa}\). Find \(T_{2}\), in \({ }^{\circ} \mathrm{C}\), and \(\Delta u\), in kJ/kg.

Using the appropriate table, determine the indicated property for a process in which there is no change in specific entropy between state 1 and state 2. (a) water, \(p_{1}=14.7 \mathrm{\ lbf} / \mathrm{in} .^{2}, T_{1}=500^{\circ} \mathrm{F}, p_{2}=100 \mathrm{\ lbf} / \mathrm{in} .2\) Find \(T_{2}\) in \({ }^{\circ} \mathrm{F}\). (b) water, \(T_{1}=10^{\circ} \mathrm{C}, \ x_{1}=0.75\), saturated vapor at state 2. Find \(p_{2}\) in bar. (c) air as an ideal gas, \(T_{1}=27^{\circ} \mathrm{C}, \ p_{1}=1.5 \mathrm{\ bar}, \ T_{2}=127^{\circ} \mathrm{C}\). Find \(p_{2}\) in bar. (d) air as an ideal gas, \(T_{1}=100^{\circ} \mathrm{F}, \ p_{1}=3 \mathrm{\ atm}, \ p_{2}=2 \mathrm{\ atm}\). Find \(T_{2}\) in \({ }^{\circ} \mathrm{F}\). (e) Refrigerant 134a, \(T_{1}=20^{\circ} \mathrm{C}, \ p_{1}=5 \text { bar, } p_{2}=1 \text { bar }\). Find \(v_{2}\) in \(\mathrm{m}^{3} / \mathrm{kg}\).

Using IT, obtain the property data requested in (a) Problem 6.7, (b) Problem 6.8, and compare with data obtained from the appropriate table.

Propane undergoes a process from state 1, where \(p_{1}=1.4\) MPa, \(T_{1}=60^{\circ} \mathrm{C}\), to state 2, where \(p_{2}=1.0\) MPa, during which the change in specific entropy is \(s_{2}-s_{1}=-0.035 \mathrm{\ kJ} / \mathrm{kg} \cdot \mathrm{K}\). At state 2, determine the temperature, in \({ }^{\circ} \mathrm{C}\), and the specific enthalpy, in kJ/kg.

Air in a piston–cylinder assembly undergoes a process from state 1, where \(T_{1}=300 \mathrm{\ K}, p_{1}=100 \mathrm{\ kPa}\), to state 2, where \(T_{2}=500 \mathrm{\ K}, p_{2}=650 \mathrm{\ kPa}\). Using the ideal gas model for air, determine the change in specific entropy between these states, in \(\mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\), if the process occurs (a) without internal irreversibilities, (b) with internal irreversibilities.

Water contained in a closed, rigid tank, initially at \(100 \mathrm{\ lbf} /\text { in. }{ }^{2}, \ 800^{\circ} \mathrm{F}\), is cooled to a final state where the pressure is \(20 \mathrm{lbf} / \mathrm{in}^{2}\) Determine the change in specific entropy, in \(\text { Btu/lb • }{ }^{\circ} \mathrm{R}\), and show the process on sketches of the T– and T–s diagrams.

One-quarter lbmol of nitrogen gas \(\left(\mathrm{N}_{2}\right)\) undergoes a process from \(p_{1}=20 \mathrm{\ lbf} / \mathrm{in} .^{2}, \ T_{1}=500^{\circ} \mathrm{R}\) to \(p_{2}=150 \mathrm{\ lbf} / \mathrm{in}^{2}\) For the process W = -500 Btu and Q = -125.9 Btu. Employing the ideal gas model, determine (a) \(T_{2}\), in \({ }^{\circ} \mathrm{R}\). (b) the change in entropy, in \(\mathrm{Btu} /{ }^{\circ} \mathrm{R}\). Show the initial and final states on a T–s diagram.

Five kg of nitrogen \(\left(\mathrm{N}_{2}\right)\) undergoes a process from \(p_{1}=5\) bar, \(T_{1}=400 \mathrm{\ K}\) to \(p_{2}=2 \mathrm{bar}, \ T_{2}=500 \mathrm{\ K}\). Assuming ideal gas behavior, determine the change in entropy, in kJ/K, with (a) constant specific heats evaluated at 450 K. (b) variable specific heats. Compare the results and discuss.

One kilogram of water contained in a piston–cylinder assembly, initially at \(160^{\circ} \mathrm{C}\), 150 kPa, undergoes an isothermal compression process to saturated liquid. For the process, W = -471.5 kJ. Determine for the process (a) the heat transfer, in kJ. (b) the change in entropy, in kJ/K. Show the process on a sketch of the T–s diagram.

One-tenth kmol of carbon monoxide (CO) in a piston–cylinder assembly undergoes a process from \(p_{1}=150 \mathrm{\ kPa}\), \(T_{1}=300 \mathrm{\ K}\) to \(p_{2}=500 \mathrm{\ kPa}, T_{2}=370 \mathrm{\ K}\). For the process, W = -300 kJ. Employing the ideal gas model, determine (a) the heat transfer, in kJ. (b) the change in entropy, in kJ/K. Show the process on a sketch of the T–s diagram.

Argon in a piston–cylinder assembly is compressed from state 1, where \(T_{1}=300 \mathrm{\ K}, V_{1}=1 \mathrm{\ m}^{3}\), to state 2, where \(T_{2}=200 \mathrm{\ K}\). If the change in specific entropy is \(s_{2}-s_{1}=-0.27\mathrm{\ kJ} / \mathrm{kg} \cdot \mathrm{K}\), determine the final volume, in \(\mathrm{m}^{3}\). Assume the ideal gas model with k = 1.67.

Steam enters a turbine operating at steady state at 1 MPa, \(200^{\circ} \mathrm{C}\) and exits at \(40^{\circ} \mathrm{C}\) with a quality of 83%. Stray heat transfer and kinetic and potential energy effects are negligible. Determine (a) the power developed by the turbine, in kJ per kg of steam flowing, (b) the change in specific entropy from inlet to exit, in kJ/K per kg of steam flowing.

Ethylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) enters a compressor operating at steady state at 310 K, 1 bar and is compressed to 600 K, 5 bar. Assuming the ideal gas model, determine the change in specific entropy of the gas from inlet to exit, in \(\mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\).

One kg of water in a piston–cylinder assembly undergoes the two internally reversible processes in series shown in Fig. P6.20. For each process, determine, in kJ, the heat transfer and the work.

One kg of water in a piston–cylinder assembly undergoes the two internally reversible processes in series shown in Fig. P6.21. For each process, determine, in kJ, the heat transfer and the work.

A system consisting of 2 kg of water initially at \160^{\circ} \mathrm{C}\), 10 bar undergoes an internally reversible, isothermal expansion during which there is energy transfer by heat into the system of 2700 kJ. Determine the final pressure, in bar, and the work, in kJ.

One lb of water in a piston–cylinder assembly, initially a saturated liquid at 1 atm, undergoes a constant-pressure, internally reversible expansion to x = 90%. Determine the work and heat transfer, each in Btu. Sketch the process on p–v and T–s coordinates. Associate the work and heat transfer with areas on these diagrams.

A gas within a piston–cylinder assembly undergoes an isothermal process at 400 K during which the change in entropy is -0.3 kJ/K. Assuming the ideal gas model for the gas and negligible kinetic and potential energy effects, evaluate the work, in kJ.

Water within a piston–cylinder assembly, initially at \(10 \mathrm{\ lbf} / \mathrm{in} .^{2}, \ 500^{\circ} \mathrm{F}\), undergoes an internally reversible process to \(80 \mathrm{\ lbf} / \mathrm{in} .^{2}, \ 800^{\circ} \mathrm{F}\), during which the temperature varies linearly with specific entropy. For the water, determine the work and heat transfer, each in Btu/lb. Neglect kinetic and potential energy effects.

A gas initially at 2.8 bar and \(60^{\circ} \mathrm{C}\) is compressed to a final pressure of 14 bar in an isothermal internally reversible process. Determine the work and heat transfer, each in kJ per kg of gas, if the gas is (a) Refrigerant 134a, (b) air as an ideal gas. Sketch the process on p–v and T–s coordinates.

Nitrogen \(\left(\mathrm{N}_{2}\right)\) undergoes an internally reversible process from 6 bar, \(247^{\circ} \mathrm{C}\) during which \(p v^{1.20}=\text { constant }\). The initial volume is \(0.1 \mathrm{\ m}^{3}\) and the work for the process is 121.14 kJ. Assuming ideal gas behavior, and neglecting kinetic and potential energy effects, determine heat transfer, in kJ, and the entropy change, in kJ/K. Show the process on a T–s diagram.

Air in a piston–cylinder assembly and modeled as an ideal gas undergoes two internally reversible processes in series from state 1, where \(T_{1}=290 \mathrm{\ K}, \ p_{1}=1\) bar. Process 1–2: Compression to \(p_{2}=5\) bar during which \(p V^{1.19}=\) constant. Process 2–3: Isentropic expansion to \(p_{3}=1\) bar. (a) Sketch the two processes in series on T–s coordinates. (b) Determine the temperature at state 2, in K. (c) Determine the net work, in kJ/kg

One lb of oxygen, \(\mathrm{O}_{2}\), in a piston–cylinder assembly undergoes a cycle consisting of the following processes: Process 1–2: Constant-pressure expansion from \(T_{1}=450^{\circ} \mathrm{R},\ p_{1}=30 \mathrm{\ lbf} / \mathrm{in}^{2}\)to \(T_{2}=1120^{\circ} \mathrm{R}\). Process 2–3: Compression to \(T_{3}=800^{\circ} \mathrm{R}\) and \(p_{3}=53.3 \mathrm{\ lbf} /\mathrm { in. }{ }^{2}\) with \(Q_{23}=-60\) Btu. Process 3–1: Constant-volume cooling to state 1. Employing the ideal gas model with \(c_{p}\) evaluated at \(T_{1}\), determine the change in specific entropy, in \(\mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\), for each process. Sketch the cycle on p–v and T–s coordinates.

One-tenth kg of a gas in a piston–cylinder assembly undergoes a Carnot power cycle for which the isothermal expansion occurs at 800 K. The change in specific entropy of the gas during the isothermal compression, which occurs at 400 K, is \(-25 \mathrm{\ kJ} / \mathrm{kg} \cdot \mathrm{K}\). Determine (a) the net work developed per cycle, in kJ, and (b) the thermal efficiency

Figure P6.31 provides the T–s diagram of a Carnot refrigeration cycle for which the substance is Refrigerant 134a. Determine the coefficient of performance.

Figure P6.32 provides the T–s diagram of a Carnot heat pump cycle for which the substance is ammonia. Determine the net work input required, in kJ, for 50 cycles of operation and 0.1 kg of substance.

Air in a piston–cylinder assembly undergoes a Carnot power cycle. The isothermal expansion and compression processes occur at 1400 K and 350 K, respectively. The pressures at the beginning and end of the isothermal compression are 100 kPa and 500 kPa, respectively. Assuming the ideal gas model with \(c_{\mathrm{p}}=1.005 \mathrm{\ kJ} / \mathrm{kg} \cdot \mathrm{K}\), determine (a) the pressures at the beginning and end of the isothermal expansion, each in kPa. (b) the heat transfer and work, in kJ/kg, for each process. (c) the thermal efficiency

Water in a piston–cylinder assembly undergoes a Carnot power cycle. At the beginning of the isothermal expansion, the temperature is \(250^{\circ} \mathrm{C}\) and the quality is 80%. The isothermal expansion continues until the pressure is 2 MPa. The adiabatic expansion then occurs to a final temperature of \(175^{\circ} \mathrm{C}\). (a) Sketch the cycle on T–s coordinates. (b) Determine the heat transfer and work, in kJ/kg, for each process. (c) Evaluate the thermal efficiency.

One lb of water contained in a piston–cylinder assembly, initially saturated vapor at 1 atm, is condensed at constant pressure to saturated liquid. Evaluate the heat transfer, in Btu, and the entropy production, in \(\text { Btu } /{ }^{\circ} \mathrm{R}\), for (a) the water as the system. (b) an enlarged system consisting of the water and enough of the nearby surroundings that heat transfer occurs only at the ambient temperature, \(80^{\circ} \mathrm{F}\). Assume the state of the nearby surroundings does not change during the process of the water, and ignore kinetic and potential energy

Five kg of water contained in a piston–cylinder assembly expand from an initial state where \(T_{1}=400^{\circ} \mathrm{C}, p_{1}=700 \mathrm{\ kPa}\) to a final state where \(T_{2}=200^{\circ} \mathrm{C}, p_{2}=300 \mathrm{\ kPa}\), with no significant effects of kinetic and potential energy. The accompanying table provides additional data at the two states. It is claimed that the water undergoes an adiabatic process between these states while developing work. Evaluate this claim.

Two m3 of air in a rigid, insulated container fitted with a paddle wheel is initially at 293 K, 200 kPa. The air receives 710 kJ by work from the paddle wheel. Assuming the ideal gas model with \(c_{v}=0.72 \mathrm{\ kJ} / \mathrm{kg} \cdot \mathrm{K}\), determine for the air (a) the mass, in kg, (b) final temperature, in K, and (c) the amount of entropy produced, in kJ/K.

Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) gas undergoes a process in a closed system from \(T_{1}=100^{\circ} \mathrm{F}, p_{1}=20 \mathrm{lbf} / \mathrm{in} .^{2}\) to \(T_{2}=400^{\circ} \mathrm{R}, \ p_{2}=50 \mathrm{\ lbf} / \mathrm{in} .^{2}\) The entropy produced due to internal irreversibilities during the process is determined to be \(0.15 \mathrm{Btu} /{ }^{\circ} \mathrm{R}\) per lb of gas. The carbon dioxide can be modeled as an ideal gas. Determine if the energy transfer by heat, Q, is positive (into the system), negative (out of the system), or zero.

Air contained in a rigid, insulated tank fitted with a paddle wheel, initially at 1 bar, 330 K and a volume of \(1.93 \mathrm{\ m}^{3}\), receives an energy transfer by work from the paddle wheel in an amount of 400 kJ. Assuming the ideal gas model for the air, determine (a) the final temperature, in K, (b) the final pressure, in bar, and (c) the amount of entropy produced, in kJ/K. Ignore kinetic and potential energy.

Air contained in a rigid, insulated tank fitted with a paddle wheel, initially at 4 bar, \(40^{\circ} \mathrm{C}\) and a volume of \(0.2 \mathrm{\ m}^{3}\), is stirred until its temperature is \(353^{\circ} \mathrm{C}\). Assuming the ideal gas model with k = 1.4 for the air, determine (a) the final pressure, in bar, (b) the work, in kJ, and (c) the amount of entropy produced, in kJ/K. Ignore kinetic and potential energy.

Air contained in a rigid, insulated tank fitted with a paddle wheel, initially at 300 K, 2 bar, and a volume of \(2 \mathrm{\ m}^{3}\), is stirred until its temperature is 500 K. Assuming the ideal gas model for the air, and ignoring kinetic and potential energy, determine (a) the final pressure, in bar, (b) the work, in kJ, and (c) the amount of entropy produced, in kJ/K. Solve using (a) data from Table A-22. (b) constant \(c_{v}\) read from Table A-20 at 400 K. Compare the results of parts (a) and (b).

A rigid, insulated container fitted with a paddle wheel contains 5 lb of water, initially at \(260^{\circ} \mathrm{F}\) and a quality of 60%. The water is stirred until the temperature is \(350^{\circ} \mathrm{F}\). For the water, determine (a) the work, in Btu, and (b) the amount of entropy produced, in \(\text { Btu } /{ }^{\circ} \mathrm{R}\).

Air is compressed adiabatically in a piston–cylinder assembly from 1 bar, 300 K to 10 bar, 600 K. The air can be modeled as an ideal gas and kinetic and potential energy effects are negligible. Determine the amount of entropy produced, in kJ/K per kg of air, for the compression. What is the minimum theoretical work input, in kJ per kg of air, for an adiabatic compression from the given initial state to a final pressure of 10 bar?

Five kg of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) gas undergoes a process in a well-insulated piston–cylinder assembly from 2 bar, 280 K to 20 bar, 520 K. If the carbon dioxide behaves as an ideal gas, determine the amount of entropy produced, in kJ/K, assuming (a) constant specific heats with \(c_{\mathrm{p}}=0.939 \mathrm{\ kJ} / \mathrm{kg} \cdot \mathrm{K}\). (b) variable specific heats. Compare the results of parts (a) and (b).

Steam undergoes an adiabatic expansion in a piston– cylinder assembly from 100 bar, \(360^{\circ} \mathrm{C}\) to 1 bar, \(160^{\circ} \mathrm{C}\). What is work in kJ per kg of steam for the process? Calculate the amount of entropy produced, in kJ/K per kg of steam. What is the maximum theoretical work that could be obtained from the given initial state to the same final pressure? Show both processes on a properly labeled sketch of the T–s diagram.

Two kg of air contained in a piston–cylinder assembly are initially at 1.5 bar and 400 K. Can a final state at 6 bar and 500 K be attained in an adiabatic process?

One lb of Refrigerant 134a contained within a piston–cylinder assembly undergoes a process from a state where the temperature is \(60^{\circ} \mathrm{F}\) and the refrigerant is saturated liquid to a state where the pressure is \(140 \mathrm{\ lbf} / \mathrm{in} .^{2}\) and quality is 50%. Determine the change in specific entropy of the refrigerant, in \(\mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\). Can this process be accomplished adiabatically?

Refrigerant 134a contained in a piston–cylinder assembly rapidly expands from an initial state where \(T_{1}=140^{\circ} \mathrm{F}, \ p_{1}=200 \mathrm{\ lbf} / \mathrm{in}^{2}\) to a final state where \(p_{2}=5 \mathrm{\ lbf} / \mathrm{in} .^{2}\) and the quality, \(x_{2}\), is (a) 99%, (b) 95%. In each case, determine if the process can occur adiabatically. If yes, determine the work, in Btu/lb, for an adiabatic expansion between these states. If no, determine the direction of the heat transfer

One kg of air contained in a piston–cylinder assembly undergoes a process from an initial state where \(T_{1}=300 \mathrm{\ K},\ v_{1}=0.8 \mathrm{\ m}^{3} / \mathrm{kg}\) to a final state where \(T_{2}=420 \mathrm{\ K}, \ v_{2}=0.2 \mathrm{\ m}^{3} / \mathrm{kg}\). Can this process occur adiabatically? If yes, determine the work, in kJ, for an adiabatic process between these states. If no, determine the direction of the heat transfer. Assume the ideal gas model for air.

Air as an ideal gas contained within a piston–cylinder assembly is compressed between two specified states. In each of the following cases, can the process occur adiabatically? If yes, determine the work in appropriate units for an adiabatic process between these states. If no, determine the direction of the heat transfer. (a) State 1: \(p_{1}=0.1 \mathrm{\ MPa}, \ T_{1}=27^{\circ} \mathrm{C}\). State 2: \(p_{2}=0.5 \mathrm{\ MPa},\ T_{2}=207^{\circ} \mathrm{C}\). Use Table A-22 data. (b) State 1: \(p_{1}=3\) atm, \(T_{1}=80^{\circ} \mathrm{F}\) State 2: \(p_{2}=10\) atm, \(T_{2}=240^{\circ} \mathrm{F}\). Assume \(c_{\mathrm{p}}=0.241 \mathrm{\ Btu} / \mathrm{lb}^{\circ} \mathrm{R}\).

One kg of propane initially at 8 bar and 50\(^{\circ}\)C undergoes a process to 3 bar, 20\(^{\circ}\)C while being rapidly expanded in a piston–cylinder assembly. Heat transfer between the propane and its surroundings occurs at an average temperature of 35\(^{\circ}\)C. The work done by the propane is measured as 42.4 kJ. Kinetic and potential energy effects can be ignored. Determine whether it is possible for the work measurement to be correct.

Figure P6.52 shows a piston–cylinder assembly containing 20 lb of water, initially a saturated liquid at 20 lbf/in.\(^{2}\) in contact with a hot plate. Heat transfer occurs slowly from the hot plate to the contents of the cylinder, and the pressure of the water remains nearly constant as phase change occurs. The process continues until the quality is 80%. There is no significant heat transfer across the vertical surface of the cylinder or to the piston, and kinetic and potential energy effects are negligible. (a) For the water as the system, determine the work and heat transfer, each in Btu. (b) Consider an enlarged system that includes the bottom of the piston–cylinder assembly wall in contact with the hot plate such that the boundary temperature is 240\(^{\circ}\)F. Neglecting any change of state of the cylinder wall material, calculate the entropy production for the enlarged system, in Btu/\(^{\circ}\)R.

A system consisting of 10 lb of air contained within a closed, rigid tank is initially at 1 atm and 600\(^{\circ}\)R. Energy is transferred to the system by heat transfer from a thermal reservoir at 900\(^{\circ}\)R until the temperature of the air is 800\(^{\circ}\)R. During the process, the temperature of the system boundary where the heat transfer occurs is 900\(^{\circ}\)R. Using the ideal gas model, determine the amount of energy transfer by heat, in Btu, and the amount of entropy produced, in Btu/\(^{\circ}\)R.

An inventor claims that the device shown in Fig. P6.54 generates electricity while receiving a heat transfer at the rate of 250 Btu/s at a temperature of 500\(^{\circ}\)R, a second heat transfer at the rate of 350 Btu/s at 700\(^{\circ}\)R, and a third at the rate of 500 Btu/s at 1000\(^{\circ}\)R. For operation at steady state, evaluate this claim.

For the silicon chip of Example 2.5, determine the rate of entropy production, in kW/K. What is the cause of entropy production in this case?

Data are provided for steady-state operation of an electric motor in Fig. P6.56. Determine for the motor the rate of entropy production, in kW/K. Repeat for an enlarged system boundary such that the heat transfer occurs in the nearby surroundings at \(T_{f}\)= 21\(^{\circ}\)F

A power plant has a turbogenerator, shown in Fig. P6.57, operating at steady state with an input shaft rotating at 1800 RPM with a torque of 16,700 N \(\cdot\) m. The turbogenerator produces current at 230 amp with a voltage of 13,000 V. The rate of heat transfer between the turbogenerator and its surroundings is related to the surface temperature \(T_{b}\) and the lower ambient temperature \(T_{01}\) and is given by \(Q=-\mathrm{hA}\left(T_{\mathrm{b}}-T_{0}\right), \text { where } \mathrm{h}=110 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}, \mathrm{A}=32 \mathrm{~m}^{2}\) and \(T_{0}\) = 298 K (a) Determine the temperature \(T_{b}\), in K. (b) For the turbogenerator as the system, determine the rate of entropy production, in kW/K (c) If the system boundary is located to take in enough of the nearby surroundings for heat transfer to take place at temperature \(T_{0}\), determine the rate of entropy production, in kW/K, for the enlarged system.

A 33.8-lb aluminum bar, initially at 200\(^{\circ}\)F, is placed in a tank together with 249 lb of liquid water, initially at 70\(^{\circ}\)F, and allowed to achieve thermal equilibrium. The aluminum bar and water can be modeled as incompressible with specific heats 0.216 Btu/lb \(\cdot \) \(^{\circ}\)R and 0.998 Btu/lb \(\cdot \) \(^{\circ}\)R, respectively. For the aluminum bar and water as the system, determine (a) the final temperature, in \(^{\circ}\)F, and (b) the amount of entropy produced within the tank, in Btu/\(^{\circ}\)R. Ignore heat transfer between the system and its surroundings.

In a heat-treating process, a 1-kg metal part, initially at 1075 K, is quenched in a tank containing 100 kg of water, initially at 295 K. There is negligible heat transfer between the contents of the tank and their surroundings. The metal part and water can be modeled as incompressible with specific heats 0.5 kJ/kg \(\cdot \) K and 4.2 kJ/kg \(\cdot \) K, respectively. Determine (a) the final equilibrium temperature after quenching, in K, and (b) the amount of entropy produced within the tank, in kJ/K.

A 50-lb iron casting, initially at 700\(^{\circ}\)F, is quenched in a tank filled with 2121 lb of oil, initially at 80\(^{\circ}\)F. The iron casting and oil can be modeled as incompressible with specific heats 0.10 Btu/lb \(\cdot \) \(^{\circ}\)R, and 0.45 Btu/lb \(\cdot \) \(^{\circ}\)R, respectively. For the iron casting and oil as the system, determine (a) the final equilibrium temperature, in \(^{\circ}\)F, and (b) the amount of entropy produced within the tank, in Btu/\(^{\circ}\)R. Ignore heat transfer between the system and its surroundings.

A 2.64-kg copper part, initially at 400 K, is plunged into a tank containing 4 kg of liquid water, initially at 300 K. The copper part and water can be modeled as incompressible with specific heats 0.385 kJ/kg \(\cdot \) K and 4.2 kJ/kg \(\cdot \) K, respectively. For the copper part and water as the system, determine (a) the final equilibrium temperature, in K, and (b) the amount of entropy produced within the tank, in kJ/K. Ignore heat transfer between the system and its surroundings.

A rigid, insulated vessel is divided into two compartments connected by a valve. Initially, one compartment, occupying one-third of the total volume, contains air at 500\(^{\circ}\)R, and the other is evacuated. The valve is opened and the air is allowed to fill the entire volume. Assuming the ideal gas model, determine the final temperature of the air, in \(^{\circ}\)R, and the amount of entropy produced, in Btu/\(^{\circ}\)R per lb of air.

A rigid, well-insulated tank contains air. A partition in the tank separates 12 ft\(^{3}\) of air at 14.7 lbf/in.\(^{2}\) , 40\(^{\circ}\)F from 10 ft\(^{3}\) of air at 50 lbf/in.\(^{2}\) , 200\(^{\circ}\)F, as illustrated in Fig. P6.63. The partition is removed and air from the two sides mix until a final equilibrium state is attained. The air can be modeled as an ideal gas, and kinetic and potential energy effects can be neglected. Determine the final temperature, in \(^{\circ}\)F, and pressure, in lbf/in.\(^{2}\) Calculate the amount of entropy produced, in Btu/\(^{\circ}\)R.

As shown in Fig. P6.64, an insulated box is initially divided into halves by a frictionless, thermally conducting piston. On one side of the piston is 1.5 m\(^{3}\) of air at 400 K, 4 bar. On the other side is 1.5 m\(^{3}\) of air at 400 K, 2 bar. The piston is released and equilibrium is attained, with the piston experiencing no change of state. Employing the ideal gas model for the air, determine (a) the final temperature, in K. (b) the final pressure, in bar. (c) the amount of entropy produced, in kJ/K.

A rigid, insulated vessel is divided into two equal-volume compartments connected by a valve. Initially, one compartment contains 1 m\(^{3}\) of water at 20\(^{\circ}\)C, x = 50%, and the other is evacuated. The valve is opened and the water is allowed to fill the entire volume. For the water, determine the final temperature, in \(^{\circ}\)C, and the amount of entropy produced, in kJ/K.

An insulated vessel is divided into two equal-sized compartments connected by a valve. Initially, one compartment contains steam at 50 lbf/in.\(^{2}\) and 700\(^{\circ}\)F, and the other is evacuated. The valve is opened and the steam is allowed to fill the entire volume. Determine (a) the final temperature, in \(^{\circ}\)F. (b) the amount of entropy produced, in Btu/lb ? \(^{\circ}\)R.

An insulated, rigid tank is divided into two compartments by a frictionless, thermally conducting piston. One compartment initially contains 1 m\(^{3}\) of saturated water vapor at 4 MPa and the other compartment contains 1 m\(^{3}\) of water vapor at 20 MPa, 800\(^{\circ}\)C. The piston is released and equilibrium is attained, with the piston experiencing no change of state. For the water as the system, determine (a) the final pressure, in MPa. (b) the final temperature, in \(^{\circ}\)C. (c) the amount of entropy produced, in kJ/K

A system consisting of air initially at 300 K and 1 bar experiences the following two different types of interactions. In each case, the system is brought from the initial state to a state where the temperature is 500 K, while volume remains constant. (a) The temperature rise is brought about adiabatically by stirring the air with a paddle wheel. Determine the amount of entropy produced, in kJ/kg \(\cdot \) K. (b) The temperature rise is brought about by heat transfer from a reservoir at temperature T. The temperature at the system boundary where heat transfer occurs is also T. Plot the amount of entropy produced, in kJ/kg \(\cdot \) K, versus T for T \(\geq\) 500 K. Compare with the result of (a) and discuss

Consider the solid rod at steady state shown in Fig. P6.69. The rod is insulated on its lateral surfaces, but energy transfer occurs at the rate \(\dot{Q}_{1}\) into the rod at location 1, and energy transfer occurs at the rate \(\dot{Q}_{2}\) out of the rod at location 2. Applying the energy and entropy rate balances to the rod as a system, determine which temperature, \(T_{1}\) or \(T_{2}\), is greater

A cylindrical copper rod of base area A and length L is insulated on its lateral surface. One end of the rod is in contact with a wall at temperature TH. The other end is in contact with a wall at a lower temperature TC. At steady state, the rate at which energy is conducted into the rod from the hot wall is \(\dot{Q}_{\mathrm{H}}=\frac{\kappa \mathrm{A}\left(T_{\mathrm{H}}-T_{\mathrm{C}}\right)}{L}\) where \(\kappa\) is the thermal conductivity of the copper rod. (a) For the rod as the system, obtain an expression for the time rate of entropy production in terms of \(\mathrm{A}, L, T_{\mathrm{H}}, T_{\mathrm{C}} \text {, and } \kappa\). (b) If \(T_{\mathrm{H}}=327^{\circ} \mathrm{C}, T_{\mathrm{C}}=77^{\circ} \mathrm{C}, \kappa=0.4 \mathrm{~kW} / \mathrm{m} \cdot \mathrm{K}, \mathrm{A}=0.1 \mathrm{~m}^{2}\), plot the heat transfer rate \(Q_{H}\), in kW, and the time rate of entropy production, in kW/K, each versus L ranging from 0.01 to 1.0 m. Discuss.

A closed, rigid tank contains 5 kg of air initially at 300 K, 1 bar. As illustrated in Fig. P6.71, the tank is in contact with a thermal reservoir at 600 K and heat transfer occurs at the boundary where the temperature is 600 K. A stirring rod transfers 600 kJ of energy to the air. The final temperature is 600 K. The air can be modeled as an ideal gas with \(c_{v}\) = 0.733 kJ/kg \(\cdot \) K and kinetic and potential energy effects are negligible. Determine the amount of entropy transferred into the air and the amount of entropy produced, each in kJ/K.

An isolated system of total mass m is formed by mixing two equal masses of the same liquid initially at the temperatures \(T_{1}\) and \(T_{2}\). Eventually, the system attains an equilibrium state. Each mass is incompressible with constant specific heat c. (a) Show that the amount of entropy produced is \(\sigma=m c \ln \left[\frac{T_{1}+T_{2}}{2\left(T_{1} T_{2}\right)^{1 / 2}}\right]\) (b) Demonstrate that\(\sigma\) must be positive.

A cylindrical rod of length L insulated on its lateral surface is initially in contact at one end with a wall at temperature \(T_{H}\) and at the other end with a wall at a lower temperature \(T_{C}\). The temperature within the rod initially varies linearly with position z according to \(T(z)=T_{\mathrm{H}}-\left(\frac{T_{\mathrm{H}}-T_{\mathrm{C}}}{L}\right) z\) The rod is then insulated on its ends and eventually comes to a final equilibrium state where the temperature is \(T_{f}\). Evaluate \(T_{f}\) in terms of \(T_{H}\) and \(T_{C}\) and show that the amount of entropy produced is \(\sigma=m c\left(1+\ln T_{\mathrm{f}}+\frac{T_{C}}{T_{\mathrm{H}}-T_{\mathrm{C}}} \ln T_{\mathrm{C}}-\frac{T_{\mathrm{H}}}{T_{\mathrm{H}}-T_{\mathrm{C}}} \ln T_{\mathrm{H}}\right)\) where c is the specific heat of the rod.

A system undergoing a thermodynamic cycle receives \(Q_{H}\) at temperature \(T’_{H}\) and discharges \(Q_{C}\) at temperature \(T’_{C}\). There are no other heat transfers. (a) Show that the net work developed per cycle is given by \(W_{\text {cycle }}=Q_{\mathrm{H}}\left(1-\frac{T_{\mathrm{C}}^{\prime}}{T_{\mathrm{H}}^{\prime}}\right)-T_{\mathrm{C}}^{\prime} \sigma\) where s is the amount of entropy produced per cycle owing to irreversibilities within the system. (b) If the heat transfers \(Q_{H}\) and \(Q_{C}\) are with hot and cold reservoirs, respectively, what is the relationship of \(T’_{H}\) to the temperature of the hot reservoir \(T_{H}\) and the relationship of \(T’_{C}\) to the temperature of the cold reservoir \(T_{C}\)? (c) Obtain an expression for \(W_{cycle}\) if there are (i) no internal irreversibilities, (ii) no internal or external irreversibilities

A thermodynamic power cycle receives energy by heat transfer from an incompressible body of mass m and specific heat c initially at temperature \(T_{H}\). The cycle discharges energy by heat transfer to another incompressible body of mass m and specific heat c initially at a lower temperature \(T_{C}\). There are no other heat transfers. Work is developed by the cycle until the temperature of each of the two bodies is the same. Develop an expression for the maximum theoretical amount of work that can be developed, \(W_{max}\), in terms of m, c, \(T_{H}\), and \(T_{C}\)

The temperature of an incompressible substance of mass m and specific heat c is reduced from \(T_{0}\) to T (< \(T_{0}\)) by a refrigeration cycle. The cycle receives energy by heat transfer at T from the substance and discharges energy by heat transfer at \(T_{0}\) to the surroundings. There are no other heat transfers. Plot (\(W_{min}\)/mc\(T_{0}\)) versus T/\(T_{0}\) ranging from 0.8 to 1.0, where \(W_{min}\) is the minimum theoretical work input required.

The heat pump cycle shown in Fig. P6.77 operates at steady state and provides energy by heat transfer at a rate of 15 kW to maintain a dwelling at 22\(^{\circ}\)C when the outside temperature is -22\(^{\circ}\)C. The manufacturer claims that the power input required for this operating condition is 3.2 kW. Applying energy and entropy rate balances evaluate this claim

As shown in Fig. P6.78, a turbine is located between two tanks. Initially, the smaller tank contains steam at 3.0 MPa, 280\(^{\circ}\)C and the larger tank is evacuated. Steam is allowed to flow from the smaller tank, through the turbine, and into the larger tank until equilibrium is attained. If heat transfer with the surroundings is negligible, determine the maximum theoretical work that can be developed, in kJ.

Air enters a turbine operating at steady state at 8 bar, 1400 K and expands to 0.8 bar. The turbine is well insulated, and kinetic and potential energy effects can be neglected. Assuming ideal gas behavior for the air, what is the maximum theoretical work that could be developed by the turbine in kJ per kg of air flow?

Water at 20 bar, 400\(^{\circ}\)C enters a turbine operating at steady state and exits at 1.5 bar. Stray heat transfer and kinetic and potential energy effects are negligible. A hard-to-read data sheet indicates that the quality at the turbine exit is 98%. Can this quality value be correct? If no, explain. If yes, determine the power developed by the turbine, in kJ per kg of water flowing.

Air enters a compressor operating at steady state at 15 lbf/in.\(^{2}\) , 80\(^{\circ}\)F and exits at 400\(^{\circ}\)F. Stray heat transfer and kinetic and potential energy effects are negligible. Assuming the ideal gas model for the air, determine the maximum theoretical pressure at the exit, in lbf/in.\(^{2}\)

Propane at 0.1 MPa, 20\(^{\circ}\)C enters an insulated compressor operating at steady state and exits at 0.4 MPa, 90\(^{\circ}\)C. Neglecting kinetic and potential energy effects, determine (a) the power required by the compressor, in kJ per kg of propane flowing. (b) the rate of entropy production within the compressor, in kJ/K per kg of propane flowing

By injecting liquid water into superheated steam, the desuperheater shown in Fig. P6.83 has a saturated vapor stream at its exit. Steady-state operating data are provided in the accompanying table. Stray heat transfer and all kinetic and potential energy effects are negligible. (a) Locate states 1, 2, and 3 on a sketch of the T–s diagram. (b) Determine the rate of entropy production within the desuperheater, in kW/K.

An inventor claims that at steady state the device shown in Fig. P6.84 develops power from entering and exiting streams of water at a rate of 1174.9 kW. The accompanying table provides data for inlet 1 and exits 3 and 4. The pressure at inlet 2 is 1 bar. Stray heat transfer and kinetic and potential energy effects are negligible. Evaluate the inventor’s claim.

An inventor claims to have developed a device requiring no work or heat transfer input yet able to produce hot and cold air streams at steady state. Data claimed by the inventor are shown on the control volume in Fig. P6.85. The ideal gas model can be used for the air, and kinetic and potential energy effects can be neglected. Evaluate this claim

Steam enters a well-insulated nozzle operating at steady state at 1000\(^{\circ}\)F, 500 lbf/in.\(^{2}\) and a velocity of 10 ft/s. At the nozzle exit, the pressure is 14.7 lbf/in.\(^{2}\) and the velocity is 4055 ft/s. Determine the rate of entropy production, in Btu/\(^{\circ}\)R per lb of steam flowing.

Air at 400 kPa, 970 K enters a turbine operating at steady state and exits at 100 kPa, 670 K. Heat transfer from the turbine occurs at an average outer surface temperature of 315 K at the rate of 30 kJ per kg of air flowing. Kinetic and potential energy effects are negligible. For air as an ideal gas with \(c_{p}\) = 1.1 kJ/ kg \(\cdot \) K, determine (a) the rate power is developed, in kJ per kg of air flowing, and (b) the rate of entropy production within the turbine, in kJ/K per kg of air flowing.

An open feedwater heater is a direct-contact heat exchanger used in vapor power plants. Shown in Fig. P6.88 are operating data for an open feedwater heater with \(H_{2}\)O as the working fluid operating at steady state. Ignoring stray heat transfer from the outside of the heat exchanger to its surroundings and kinetic and potential energy effects, determine the rate of entropy production, in kW/K.

By injecting liquid water into superheated vapor, the de-superheater shown in Fig. P6.89 has a saturated vapor stream at its exit. Steady-state operating data are shown on the figure. Ignoring stray heat transfer and kinetic and potential energy effects, determine (a) the mass flow rate of the superheated vapor stream, in kg/min, and (b) the rate of entropy production within the desuperheater, in kW/K.

Air at 600 kPa, 330 K enters a well-insulated, horizontal pipe having a diameter of 1.2 cm and exits at 120 kPa, 300 K. Applying the ideal gas model for air, determine at steady state (a) the inlet and exit velocities, each in m/s, (b) the mass flow rate, in kg/s, and (c) the rate of entropy production, in kW/K.

Air at 200 kPa, 52\(^{\circ}\)C, and a velocity of 355 m/s enters an insulated duct of varying cross-sectional area. The air exits at 100 kPa, 82\(^{\circ}\)C. At the inlet, the cross-sectional area is 6.57 cm\(^{2}\) . Assuming the ideal gas model for the air, determine (a) the exit velocity, in m/s. (b) the rate of entropy production within the duct, in kW/K.

For the computer of Example 4.8, determine the rate of entropy production, in W/K, when air exits at 32\(^{\circ}\)C. Ignore the change in pressure between the inlet and exit.

Electronic components are mounted on the inner surface of a horizontal cylindrical duct whose inner diameter is 0.2 m, as shown in Fig. P6.93. To prevent overheating of the electronics, the cylinder is cooled by a stream of air flowing through it and by convection from its outer surface. Air enters the duct at 25\(^{\circ}\)C, 1 bar and a velocity of 0.3 m/s and exits at 40\(^{\circ}\)C with negligible changes in kinetic energy and pressure. Convective cooling occurs on the outer surface to the surroundings, which are at 25\(^{\circ}\)C, in accord with hA 5 3.4 W/K, where h is the heat transfer coefficient and A is the surface area. The electronic components require 0.20 kW of electric power. For a control volume enclosing the cylinder, determine at steady state (a) the mass flow rate of the air, in kg/s, (b) the temperature on the outer surface of the duct, in \(^{\circ}\)C, and (c) the rate of entropy production, in W/K. Assume the ideal gas model for air.

Air enters a turbine operating at steady state at 500 kPa, 860 K and exits at 100 kPa. A temperature sensor indicates that the exit air temperature is 460 K. Stray heat transfer and kinetic and potential energy effects are negligible, and the air can be modeled as an ideal gas. Determine if the exit temperature reading can be correct. It yes, determine the power developed by the turbine for an expansion between these states, in kJ per kg of air flowing. If no, provide an explanation with supporting calculations.

Figure P6.95 provides steady-state test data for a control volume in which two entering streams of air mix to form a single exiting stream. Stray heat transfer and kinetic and potential energy effects are negligible. A hard-to-read photocopy of the data sheet indicates that the pressure of the exiting stream is either 1.0 MPa or 1.8 MPa. Assuming the ideal gas model for air with \(c_{p}\) = 1.02 kJ/kg \(\cdot \) K, determine if either or both of these pressure values can be correct.

Students in a laboratory are studying air flowing at steady state through a horizontal insulated duct. One student group reports the measured pressure, temperature, and velocity at one location in the duct as 0.95 bar, 67\(^{\circ}\)C, and 75 m/s, respectively. The group reports the following values at another location in the duct: 0.8 bar, 22\(^{\circ}\)C, and 310 m/s. The group neglected to note the direction of flow on the data sheet, however. Using the data provided, determine the direction of flow.

An inventor has provided the steady-state operating data shown in Fig. P6.97 for a cogeneration system producing power and increasing the temperature of a stream of air. The system receives and discharges energy by heat transfer at the rates and temperatures indicated on the figure. All heat transfers are in the directions of the accompanying arrows. The ideal gas model applies to the air. Kinetic and potential energy effects are negligible. Using energy and entropy rate balances, evaluate the thermodynamic performance of the system.

Steam at 550 lbf/in.\(^{2}\) , 700\(^{\circ}\)F enters a turbine operating at steady state and exits at 1 lbf/in.\(^{2}\) The turbine produces 500 hp. For the turbine, heat transfer is negligible as are kinetic and potential energy effects. (a) Determine the quality of the steam at the turbine exit, the mass flow rate, in lb/s, and the entropy production rate, in Btu/s \(\cdot \) \(^{\circ}\)R, if the turbine operates without internal irreversibilities. (b) Plot the mass flow rate, in lb/s, and the entropy production rate, in Btu/s \(\cdot \) \(^{\circ}\)R, for exit qualities ranging from the value calculated in part (a) to 1.

Ammonia enters the compressor of an industrial refrigeration plant at 2 bar, -10\(^{\circ}\)C with a mass flow rate of 15 kg/min and is compressed to 12 bar, 140\(^{\circ}\)C. Heat transfer occurs from the compressor to its surroundings at a rate of 6 kW. For steady-state operation with negligible kinetic and potential energy effects, determine (a) the power input to the compressor, in kW, and (b) the rate of entropy production, in kW/K, for a control volume enclosing the compressor and its immediate surroundings such that the heat transfer occurs at 300 K.

Refrigerant 22 in a refrigeration system enters one side of a counterflow heat exchanger at 12 bar, 28\(^{\circ}\)C. The refrigerant exits at 12 bar, 20\(^{\circ}\)C. A separate stream of R-22 enters the other side of the heat exchanger as saturated vapor at 2 bar and exits as superheated vapor at 2 bar. The mass flow rates of the two streams are equal. Stray heat transfer from the heat exchanger to its surroundings and kinetic and potential energy effects are negligible. Determine the entropy production in the heat exchanger, in kJ/K per kg of refrigerant flowing. What gives rise to the entropy production in this application?

Air at 500 kPa, 500 K and a mass flow of 600 kg/h enters a pipe passing overhead in a factory space. At the pipe exit, the pressure and temperature of the air are 475 kPa and 450 K, respectively. Air can be modeled as an ideal gas with k 5 1.39. Kinetic and potential energy effects can be ignored. Determine at steady state, (a) the rate of heat transfer, in kW, for a control volume comprising the pipe and its contents, and (b) the rate of entropy production, in kW/K, for an enlarged control volume that includes the pipe and enough of its surroundings that heat transfer occurs at the ambient temperature, 300 K.

Steam enters a turbine operating at steady state at 6 MPa, 600\(^{\circ}\)C with a mass flow rate of 125 kg/min and exits as saturated vapor at 20 kPa, producing power at a rate of 2 MW. Kinetic and potential energy effects can be ignored. Determine (a) the rate of heat transfer, in kW, for a control volume including the turbine and its contents, and (b) the rate of entropy production, in kW/K, for an enlarged control volume that includes the turbine and enough of its surroundings that heat transfer occurs at the ambient temperature, 27\(^{\circ}\)C.

Refrigerant 134a is compressed from 2 bar, saturated vapor, to 10 bar, 90\(^{\circ}\)C in a compressor operating at steady state. The mass flow rate of refrigerant entering the compressor is 7 kg/min, and the power input is 10.85 kW. Kinetic and potential energy effects can be neglected. (a) Determine the rate of heat transfer, in kW. (b) If the heat transfer occurs at an average surface temperature of 50\(^{\circ}\)C, determine the rate of entropy production, in kW/K. (c) Determine the rate of entropy production, in kW/K, for an enlarged control volume that includes the compressor and its immediate surroundings such that the heat transfer occurs at 300 K. Compare the results of parts (b) and (c) and discuss

Nitrogen (\(N_{2}\)) enters a well-insulated diffuser operating at steady state at 0.656 bar, 300 K with a velocity of 282 m/s. The inlet area is 4.8 X 10\(^{-3}\) m\(^{2}\) . At the diffuser exit, the pressure is 0.9 bar and the velocity is 130 m/s. The nitrogen behaves as an ideal gas with k 5 1.4. Determine the exit temperature, in K, and the exit area, in m\(^{2}\) . For a control volume enclosing the diffuser, determine the rate of entropy production, in kJ/K per kg of nitrogen flowing.

Refrigerant 22 enters the heat exchanger of an airconditioning system at 80 lbf/in.\(^{2}\) with a quality of 0.2. The refrigerant stream exits at 80 lbf/in.\(^{2}\) , 60\(^{\circ}\)F. Air flows in counterflow through the heat exchanger, entering at 14.9 lbf/ in.\(^{2}\) , 808F, with a volumetric flow rate of 100,000 ft\(^{3}\) /min and exiting at 14.5 lbf/in.\(^{2}\) , 65\(^{\circ}\)F. Operation is at steady state, stray heat transfer from the outside of the heat exchanger to the surroundings can be neglected, and kinetic and potential energy effects are negligible. Assuming ideal gas behavior for the air, determine the rate of entropy production in the heat exchanger, in Btu/min \(\cdot \) \(^{\circ}\)R.

Saturated water vapor at 100 kPa enters a counterflow heat exchanger operating at steady state and exits at 20\(^{\circ}\)C with a negligible change in pressure. Ambient air at 275 K, 1 atm enters in a separate stream and exits at 290 K, 1 atm. The air mass flow rate is 170 times that of the water. The air can be modeled as an ideal gas with \(c_{p}\) = 1.005 kJ/kg \(\cdot \) K. Kinetic and potential energy effects can be ignored. (a) For a control volume enclosing the heat exchanger, evaluate the rate of heat transfer, in kJ per kg of water flowing. (b) For an enlarged control volume that includes the heat exchanger and enough of its immediate surroundings that heat transfer from the control volume occurs at the ambient temperature, 275 K, determine the rate of entropy production, in kJ/K per kg of water flowing

Figure P6.107 shows data for a portion of the ducting in a ventilation system operating at steady state. The ducts are well insulated and the pressure is very nearly 1 atm throughout. Assuming the ideal gas model for air with \(c_{p}\) = 0.24 Btu/lb \(\cdot \) \(^{\circ}\)R, and ignoring kinetic and potential energy effects, determine (a) the temperature of the air at the exit, in \(^{\circ}\)F, (b) the exit diameter, in ft, and (c) the rate of entropy production within the duct, in Btu/min \(\cdot \) \(^{\circ}\)R

Air flows through an insulated circular duct having a diameter of 2 cm. Steady-state pressure and temperature data obtained by measurements at two locations, denoted as 1 and 2, are given in the accompanying table. Modeling air as an ideal gas with \(c_{p}\) = 1.005 kJ/kg \(\cdot \) K, determine (a) the direction of the flow, (b) the velocity of the air, in m/s, at each of the two locations, and (c) the mass flow rate of the air, in kg/s.

Determine the rates of entropy production, in Btu/min \(\cdot \) \(^{\circ}\)R, for the steam generator and turbine of Example 4.10. Identify the component that contributes more to inefficient operation of the overall system.

Figure P6.110 shows an air compressor and regenerative heat exchanger in a gas turbine system operating at steady state. Air flows from the compressor through the regenerator, and a separate stream of air passes though the regenerator in counterflow. Operating data are provided on the figure. Stray heat transfer to the surroundings and kinetic and potential energy effects can be neglected. The compressor power input is 6700 kW. Determine the mass flow rate of air entering the compressor, in kg/s, the temperature of the air exiting the regenerator at state 5, in K, and the rates of entropy production in the compressor and regenerator, in kW/K.

Figure P6.111 shows several components in series, all operating at steady state. Liquid water enters the boiler at 60 bar. Steam exits the boiler at 60 bar, 540\(^{\circ}\)C and undergoes a throttling process to 40 bar before entering the turbine. Steam expands adiabatically through the turbine to 5 bar, 240\(^{\circ}\)C, and then undergoes a throttling process to 1 bar before entering the condenser. Kinetic and potential energy effects can be ignored. (a) Locate each of the states 2–5 on a sketch of the T–s diagram. (b) Determine the power developed by the turbine, in kJ per kg of steam flowing. (c) For the valves and the turbine, evaluate the rate of entropy production, each in kJ/K per kg of steam flowing. (d) Using the result of part (c), place the components in rank order, beginning with the component contributing the most to inefficient operation of the overall system. (e) If the goal is to increase the power developed per kg of steam flowing, which of the components (if any) might be eliminated? Explain

Air as an ideal gas flows through the turbine and heat exchanger arrangement shown in Fig. P6.112. Steady-state data are given on the figure. Stray heat transfer and kinetic and potential energy effects can be ignored. Determine (a) temperature \(T_{3}\), in K. (b) the power output of the second turbine, in kW. (c) the rates of entropy production, each in kW/K, for the turbines and heat exchanger. (d) Using the result of part (c), place the components in rank order, beginning with the component contributing most to inefficient operation of the overall system.

A rigid, insulated tank whose volume is 10 L is initially evacuated. A pinhole leak develops and air from the surroundings at 1 bar, 25\(^{\circ}\)C enters the tank until the pressure in the tank becomes 1 bar. Assuming the ideal gas model with k = 1.4 for the air, determine (a) the final temperature in the tank, in \(^{\circ}\)C, (b) the amount of air that leaks into the tank, in g, and (c) the amount entropy produced, in J/K.

An insulated, rigid tank whose volume is 0.5 m\(^{3}\) is connected by a valve to a large vessel holding steam at 40 bar, 500\(^{\circ}\)C. The tank is initially evacuated. The valve is opened only as long as required to fill the tank with steam to a pressure of 20 bar. Determine (a) the final temperature of the steam in the tank, in \(^{\circ}\)C, (b) the final mass of the steam in the tank, in kg, and (c) the amount of entropy produced, in kJ/K.

A tank of volume 1 m\(^{3}\) initially contains steam at 60 bar, 320\(^{\circ}\)C. Steam is withdrawn slowly from the tank until the pressure drops to 15 bar. An electric resistor in the tank transfers energy to the steam maintaining the temperature constant at 320\(^{\circ}\)C during the process. Neglecting kinetic and potential energy effects, determine the amount of entropy produced, in kJ/K

A two-phase liquid–vapor mixture of Refrigerant 134a is held in a large storage tank at 100 lbf/in.\(^{2}\) , 50\(^{\circ}\)F, as illustrated in Fig. P6.114. A technician fills a 3.5-ft\(^{3}\) cylinder that is initially evacuated to take on a service call. The technician opens a valve and lets refrigerant from the storage tank flow into the cylinder until the pressure gage on the cylinder reads 25.5 lbf/in.\(^{2}\) (gage). The surrounding atmospheric pressure is 14.5 lbf/in.\(^{2}\) Assuming no heat transfer and neglecting kinetic and potential energy effects, determine the final mass of refrigerant in the cylinder, in lb, and the amount of entropy produced, in Btu/\(^{\circ}\)R.

A 180-ft\(^{3}\) tank initially filled with air at 1 atm and 70\(^{\circ}\)F is evacuated by a device known as a vacuum pump, while the tank contents are maintained at 70\(^{\circ}\)F by heat transfer through the tank walls. The vacuum pump discharges air to the surroundings at the temperature and pressure of the surroundings, which are 1 atm and 70\(^{\circ}\)F, respectively. Determine the minimum theoretical work required, in Btu.

Air in a piston–cylinder assembly expands isentropically from \(T_{1}\) = 1800\(^{\circ}\)R, \(p_{1}\) = 20 lbf/in.\(^{2}\) , to \(p_{2}\) = 2000 lbf/in.\(^{2}\) Assuming the ideal gas model, determine the temperature at state 2, in \(^{\circ}\)R, using (a) data from Table A-22E, and (b) a constant specific heat ratio, k = 1.4. Compare the values obtained in parts (a) and (b) and comment.

Air in a piston–cylinder assembly is compressed isentropically from state 1, where \(T_{1}\) = 35\(^{\circ}\)C, to state 2, where the specific volume is one-tenth of the specific volume at state 1. Applying the ideal gas model with k = 1.4, determine (a) \(T_{2}\), in \(^{\circ}\)C and (b) the work, in kJ/kg

Steam undergoes an isentropic compression in an insulated piston–cylinder assembly from an initial state where \(T_{1}\) = 120\(^{\circ}\)C, \(p_{1}\) = 1 bar to a final state where the pressure \(p_{2}\) = 100 bar. Determine the final temperature, in \(^{\circ}\)C, and the work, in kJ per kg of steam

Propane undergoes an isentropic expansion from an initial state where \(T_{1}\) = 40\(^{\circ}\)C, \(p_{1}\) = 1 MPa to a final state where the temperature and pressure are \(T_{2}\), \(p_{2}\), respectively. Determine (a) \(p_{2}\), in kPa, when \(T_{2}\) = 240\(^{\circ}\)C. (b) \(T_{2}\), in \(^{\circ}\)C, when \(p_{2}\) = 0.8 MPa.

Argon in a piston–cylinder assembly is compressed isentropically from state 1, where \(p_{1}=150 \mathrm{kPa}, T_{1}=35^{\circ} \mathrm{C}\), to state 2, where \(p_{2}\) = 300 kPa. Assuming the ideal gas model with k = 1.67, determine (a) \(T_{2}\), in \(^{\circ}\)C, and (b) the work, in kJ per kg of argon.

Air within a piston–cylinder assembly, initially at 12 bar, 620 K, undergoes an isentropic expansion to 1.4 bar. Assuming the ideal gas model for the air, determine the final temperature, in K, and the work, in kJ/kg. Solve two ways: using (a) data from Table A-22 and (b) k = 1.4

Air within a piston–cylinder assembly, initially at 30 lbf/ in.\(^{2}\) , 510\(^{\circ}\)R, and a volume of 6 ft\(^{3}\) , is compressed isentropically to a final volume of 1.2 ft\(^{3}\) . Assuming the ideal gas model with k = 1.4 for the air, determine the (a) mass, in lb, (b) final pressure, in lbf/in.\(^{2}\) , (c) final temperature, in \(^{\circ}\)R, and (d) work, in Btu.

Air contained in a piston–cylinder assembly, initially at 4 bar, 600 K and a volume of 0.43 m\(^{3}\) , expands isentropically to a pressure of 1.5 bar. Assuming the ideal gas model for the air, determine the (a) mass, in kg, (b) final temperature, in K, and (c) work, in kJ.

Carbon dioxide (CO2) expands isentropically in a piston–cylinder assembly from \(p_{1}\) = 200 lbf/in.\(^{2}\) , \(T_{1}\) = 800\(^{\circ}\)R to a final specific volume of \(y_{2}\) = 1.8 ft\(^{3}\) /lb. Determine the work, in Btu per lb of carbon dioxide, assuming the ideal gas model with (a) constant specific heat evaluated at 600\(^{\circ}\)R. (b) variable specific heat using data from IT: Interactive Thermodynamics.

Air in a piston–cylinder assembly is compressed isentropically from an initial state where \(T_{1}\) = 340 K to a final state where the pressure is 90% greater than at state 1. Assuming the ideal gas model, determine (a) \(T_{2}\), in K, and (b) the work, in kJ/kg

A rigid, insulated tank with a volume of 20 m\(^{3}\) is filled initially with air at 10 bar, 500 K. A leak develops, and air slowly escapes until the pressure of the air remaining in the tank is 5 bar. Employing the ideal gas model with k = 1.4 for the air, determine the amount of mass remaining in the tank, in kg, and its temperature, in K.

A rigid, insulated tank with a volume of 21.61 ft\(^{3}\) is filled initially with air at 110 lbf/in.\(^{2}\) , 535\(^{\circ}\)R. A leak develops, and air slowly escapes until the pressure of the air remaining in the tank is 15 lbf/in.\(^{2}\) Employing the ideal gas model with k = 1.4 for the air, determine the amount of mass remaining in the tank, in lb, and its temperature, in \(^{\circ}\)R.

The accompanying table provides steady-state data for an isentropic expansion of steam through a turbine. For a mass flow rate of 2.55 kg/s, determine the power developed by the turbine, in MW. Ignore the effects of potential energy.

Water vapor enters a turbine operating at steady state at 1000\(^{\circ}\)F, 140 lbf/in.\(^{2}\) , with a volumetric flow rate of 21.6 ft\(^{3}\)/s, and expands isentropically to 2 lbf/in.\(^{2}\) Determine the power developed by the turbine, in hp. Ignore kinetic and potential energy effects.

Refrigerant 22 enters a compressor operating at steady state as saturated vapor at 10 bar and is compressed adiabatically in an internally reversible process to 16 bar. Ignoring kinetic and potential energy effects, determine the required mass flow rate of refrigerant, in kg/s, if the compressor power input is 6 kW

Figure P6.133 shows a simple vapor power cycle operating at steady state with water as the working fluid. Data at key locations are given on the figure. Flow through the turbine and pump occurs isentropically. Flow through the steam generator and condenser occurs at constant pressure. Stray heat transfer and kinetic and potential energy effects are negligible. Sketch the four processes of this cycle in series on a T–s diagram. Determine the thermal efficiency.

The accompanying table provides steady-state data for steam expanding adiabatically though a turbine. The states are numbered as in Fig. 6.11. Kinetic and potential energy effects can be ignored. Determine for the turbine (a) the work developed per unit mass of steam flowing, in kJ/kg, (b) the amount of entropy produced per unit mass of steam flowing, in kJ/kg \(\cdot \) K, and (c) the isentropic turbine efficiency.

The accompanying table provides steady-state data for steam expanding adiabatically with a mass flow rate of 4 lb/s through a turbine. Kinetic and potential energy effects can be ignored. Determine for the turbine (a) the power developed, in hp, (b) the rate of entropy production, in hp/\(^{\circ}\)R, and (c) the isentropic turbine efficiency

Water vapor at 800 lbf/in.\(^{2}\) , 1000\(^{\circ}\)F enters a turbine operating at steady state and expands adiabatically to 2 lbf/ in.\(^{2}\) , developing work at a rate of 490 Btu per lb of vapor flowing. Determine the condition at the turbine exit: twophase liquid–vapor or superheated vapor? Also, evaluate the isentropic turbine efficiency. Kinetic and potential energy effects are negligible.

Air at 1600 K, 30 bar enters a turbine operating at steady state and expands adiabatically to the exit, where the temperature is 830 K. If the isentropic turbine efficiency is 90%, determine (a) the pressure at the exit, in bar, and (b) the work developed, in kJ per kg of air flowing. Assume ideal gas behavior for the air and ignore kinetic and potential energy effects.

Water vapor at 5 bar, 320\(^{\circ}\)C enters a turbine operating at steady state with a volumetric flow rate of 0.65 m\(^{3}\)/s and expands adiabatically to an exit state of 1 bar, 160\(^{\circ}\)C. Kinetic and potential energy effects are negligible. Determine for the turbine (a) the power developed, in kW, (b) the rate of entropy production, in kW/K, and (c) the isentropic turbine efficiency

Air at 1175 K, 8 bar enters a turbine operating at steady state and expands adiabatically to 1 bar. The isentropic turbine efficiency is 92%. Employing the ideal gas model with k = 1.4 for the air, determine (a) the work developed by the turbine, in kJ per kg of air flowing, and (b) the temperature at the exit, in K. Ignore kinetic and potential energy effects.

Water vapor at 10 MPa, 600\(^{\circ}\)C enters a turbine operating at steady state with a volumetric flow rate of 0.36 m3 /s and exits at 0.1 bar and a quality of 92%. Stray heat transfer and kinetic and potential energy effects are negligible. Determine for the turbine (a) the mass flow rate, in kg/s, (b) the power developed by the turbine, in MW, (c) the rate at which entropy is produced, in kW/K, and (d) the isentropic turbine efficiency

Air modeled as an ideal gas enters a turbine operating at steady state at 1040 K, 278 kPa and exits at 120 kPa. The mass flow rate is 5.5 kg/s, and the power developed is 1120 kW. Stray heat transfer and kinetic and potential energy effects are negligible. Assuming k = 1.4, determine (a) the temperature of the air at the turbine exit, in K, and (b) the isentropic turbine efficiency

Water vapor at 10008F, 140 lbf/in.\(^{2}\) enters a turbine operating at steady state and expands to 2 lbf/in.\(^{2}\) , 150\(^{\circ}\)F. Stray heat transfer and kinetic and potential energy effects are negligible. Determine the actual work and the maximum theoretical work that could be developed for a turbine with the same inlet state and exit pressure, in Btu per lb of water vapor flowing

Water vapor at 6 MPa, 600\(^{\circ}\)C enters a turbine operating at steady state and expands to 10 kPa. The mass flow rate is 2 kg/s, and the power developed is 2626 kW. Stray heat transfer and kinetic and potential energy effects are negligible. Determine (a) the isentropic turbine efficiency and (b) the rate of entropy production within the turbine, in kW/K.

Water vapor at 5MPa, 320\(^{\circ}\)C enters a turbine operating at steady state and expands to 0.1 bar.\(^{2}\) The mass flow rate is 2.52 kg/s, and the isentropic turbine efficiency is 92%. Stray heat transfer and kinetic and potential energy effects are negligible. Determine the power developed by the turbine, in kW

Air enters the compressor of a gas turbine power plant operating at steady state at 290 K, 100 kPa and exits at 330 kPa. Stray heat transfer and kinetic and potential energy effects are negligible. The isentropic compressor efficiency is 90.3%. Using the ideal gas model for air, determine the work input, in kJ per kg of air flowing.

Oxygen (\(O_{2}\)) at 25\(^{\circ}\)C, 100 kPa enters a compressor operating at steady state and exits at 260\(^{\circ}\)C, 650 kPa. Stray heat transfer and kinetic and potential energy effects are negligible. Modeling the oxygen as an ideal gas with k = 1.379, determine the isentropic compressor efficiency and the work in kJ per kg of oxygen flowing.

Air at 290 K, 100 kPa enters a compressor operating at steady state and is compressed adiabatically to an exit state of 420 K, 330 kPa. The air is modeled as an ideal gas, and kinetic and potential energy effects are negligible. For the compressor, (a) determine the rate of entropy production, in kJ/K per kg of air flowing, and (b) the isentropic compressor efficiency.

Carbon dioxide (C\(O_{2}\)) at 1 bar, 300 K enters a compressor operating at steady state and is compressed adiabatically to an exit state of 10 bar, 520 K. The C\(O_{2}\) is modeled as an ideal gas, and kinetic and potential energy effects are negligible. For the compressor, determine (a) the work input, in kJ per kg of C\(O_{2}\) flowing, (b) the rate of entropy production, in kJ/K per kg of C\(O_{2}\) flowing, and (c) the isentropic compressor efficiency

Air at 300 K, 1 bar enters a compressor operating at steady state and is compressed adiabatically to 1.5 bar. The power input is 42 kJ per kg of air flowing. Employing the ideal gas model with k = 1.4 for the air, determine for the compressor (a) the rate of entropy production, in kJ/K per kg of air flowing, and (b) the isentropic compressor efficiency. Ignore kinetic and potential energy effects.

Air at 1 atm, 520\(^{\circ}\)R enters a compressor operating at steady state and is compressed adiabatically to 3 atm. The isentropic compressor efficiency is 80%. Employing the ideal gas model with k = 1.4 for the air, determine for the compressor (a) the power input, in Btu per lb of air flowing, and (b) the amount of entropy produced, in Btu/\(^{\circ}\)R per lb of air flowing. Ignore kinetic and potential energy effects

Nitrogen (\(N_{2}\)) enters an insulated compressor operating at steady state at 1 bar, 37\(^{\circ}\)C with a mass flow rate of 1000 kg/h and exits at 10 bar. Kinetic and potential energy effects are negligible. The nitrogen can be modeled as an ideal gas with k = 1.391. (a) Determine the minimum theoretical power input required, in kW, and the corresponding exit temperature, in \(^{\circ}\)C. (b) If the exit temperature is 397\(^{\circ}\)C, determine the power input, in kW, and the isentropic compressor efficiency.

Saturated water vapor at 300\(^{\circ}\)F enters a compressor operating at steady state with a mass flow rate of 5 lb/s and is compressed adiabatically to 800 lbf/in.\(^{2}\) If the power input is 2150 hp, determine for the compressor (a) the isentropic compressor efficiency and (b) the rate of entropy production, in hp/\(^{\circ}\)R. Ignore kinetic and potential energy effects

Refrigerant 134a at a rate of 0.8 lb/s enters a compressor operating at steady state as saturated vapor at 30 psia and exits at a pressure of 160 psia. There is no significant heat transfer with the surroundings, and kinetic and potential energy effects can be ignored. (a) Determine the minimum theoretical power input required, in Btu/s, and the corresponding exit temperature, in \(^{\circ}\)F. (b) If the refrigerant exits at a temperature of 130\(^{\circ}\)F, determine the actual power, in Btu/s, and the isentropic compressor efficiency.

Air at 1.3 bar, 423 K and a velocity of 40 m/s enters a nozzle operating at steady state and expands adiabatically to the exit, where the pressure is 0.85 bar and velocity is 307 m/s. For air modeled as an ideal gas with k = 1.4, determine for the nozzle (a) the temperature at the exit, in K, and (b) the isentropic nozzle efficiency

Water vapor at 100 lbf/in.\(^{2}\) , 500\(^{\circ}\)F and a velocity of 100 ft/s enters a nozzle operating at steady state and expands adiabatically to the exit, where the pressure is 40 lbf/in.\(^{2}\) If the isentropic nozzle efficiency is 95%, determine for the nozzle (a) the velocity of the steam at the exit, in ft/s, and (b) the amount of entropy produced, in Btu/\(^{\circ}\)R per lb of steam flowing.

Helium gas at 810\(^{\circ}\)R, 45 lbf/in.\(^{2}\) , and a velocity of 10 ft/s enters an insulated nozzle operating at steady state and exits at 670\(^{\circ}\)R, 25 lbf/in.\(^{2}\) Modeling helium as an ideal gas with k = 1.67, determine (a) the velocity at the nozzle exit, in ft/s, (b) the isentropic nozzle efficiency, and (c) the rate of entropy production within the nozzle, in Btu/\(^{\circ}\)R per lb of helium flowing.

Air modeled as an ideal gas enters a one-inlet, one-exit control volume operating at steady state at 100 lbf/in.\(^{2}\) , 900\(^{\circ}\)R and expands adiabatically to 25 lbf/in.\(^{2}\) Kinetic and potential energy effects are negligible. Determine the rate of entropy production, in Btu/\(^{\circ}\)R per lb of air flowing, (a) if the control volume encloses a turbine having an isentropic turbine efficiency of 89.1%. (b) if the control volume encloses a throttling valve.

As part of an industrial process, air as an ideal gas at 10 bar, 400 K expands at steady state through a valve to a pressure of 4 bar. The mass flow rate of air is 0.5 kg/s. The air then passes through a heat exchanger where it is cooled to a temperature of 295 K with negligible change in pressure. The valve can be modeled as a throttling process, and kinetic and potential energy effects can be neglected. (a) For a control volume enclosing the valve and heat exchanger and enough of the local surroundings that the heat transfer occurs at the ambient temperature of 295 K, determine the rate of entropy production, in kW/K. (b) If the expansion valve were replaced by an adiabatic turbine operating isentropically, what would be the entropy production, in kW/K? Compare the results of parts (a) and (b) and discuss.

Figure P6.159 provides the schematic of a heat pump using Refrigerant 134a as the working fluid, together with steady-state data at key points. The mass flow rate of the refrigerant is 7 kg/min, and the power input to the compressor is 5.17 kW. (a) Determine the coefficient of performance for the heat pump. (b) If the valve were replaced by a turbine, power could be produced, thereby reducing the power requirement of the heat pump system. Would you recommend this power-saving measure? Explain.

Air as an ideal gas enters a diffuser operating at steady state at 4 bar, 290 K with a velocity of 512 m/s. The exit velocity is 110 m/s. For adiabatic operation with no internal irreversibilities, determine the exit temperature, in K, and the exit pressure, in bar, (a) for k = 1.4. (b) using data from Table A-22.

As shown in Fig. P6.161, air enters the diffuser of a jet engine at 18 kPa, 216 K with a velocity of 265 m/s, all data corresponding to high-altitude flight. The air flows adiabatically through the diffuser, decelerating to a velocity of 50 m/s at the diffuser exit. Assume steady-state operation, the ideal gas model for air, and negligible potential energy effects. (a) Determine the temperature of the air at the exit of the diffuser, in K. (b) If the air would undergo an isentropic process as it flows through the diffuser, determine the pressure of the air at the diffuser exit, in kPa. (c) If friction were present, would the pressure of the air at the diffuser exit be greater than, less than, or equal to the value found in part (b)? Explain.

As shown in Fig. P6.162, a steam turbine having an isentropic turbine efficiency of 90% drives an air compressor having an isentropic compressor efficiency of 85%. Steadystate operating data are provided on the figure. Assume the ideal gas model for air, and ignore stray heat transfer and kinetic and potential energy effects. (a) Determine the mass flow rate of the steam entering the turbine, in kg of steam per kg of air exiting the compressor. (b) Repeat part (a) if \(\eta_{\mathrm{t}}=\eta_{\mathrm{c}}=100 \%\)

Figure P6.163 shows a simple vapor power plant operating at steady state with water as the working fluid. Data at key locations are given on the figure. The mass flow rate of the water circulating through the components is 109 kg/s. Stray heat transfer and kinetic and potential energy effects can be ignored. Determine (a) the net power developed, in MW. (b) the thermal efficiency. (c) the isentropic turbine efficiency. (d) the isentropic pump efficiency. (e) the mass flow rate of the cooling water, in kg/s. (f) the rates of entropy production, each in kW/K, for the turbine, condenser, and pump.

Figure P6.164 shows a power system operating at steady state consisting of three components in series: an air compressor having an isentropic compressor efficiency of 80%, a heat exchanger, and a turbine having an isentropic turbine efficiency of 90%. Air enters the compressor at 1 bar, 300 K with a mass flow rate of 5.8 kg/s and exits at a pressure of 10 bar. Air enters the turbine at 10 bar, 1400 K and exits at a pressure of 1 bar. Air can be modeled as an ideal gas. Stray heat transfer and kinetic and potential energy effects are negligible. Determine, in kW, (a) the power required by the compressor, (b) the power developed by the turbine, and (c) the net power output of the overall power system.

Steam enters a two-stage turbine with reheat operating at steady state as shown in Fig. P6.165. The steam enters turbine 1 with a mass flow rate of 120,000 lb/h at 1000 lbf/in.\(^{2}\), 800\(^{\circ}\)F and expands to a pressure of 60 lbf/in.\(^{2}\) From there, the steam enters the reheater where it is heated at constant pressure to 350\(^{\circ}\)C before entering turbine 2 and expanding to a final pressure of 1 lbf/in.\(^{2}\) The turbines operate adiabatically with isentropic efficiencies of 88% and 85%, respectively. Kinetic and potential energy effects can be neglected. Determine the net power developed by the two turbines and the rate of heat transfer in the reheater, each in Btu/h.

A rigid tank is filled initially with 5.0 kg of air at a pressure of 0.5 MPa and a temperature of 500 K. The air is allowed to discharge through a turbine into the atmosphere, developing work until the pressure in the tank has fallen to the atmospheric level of 0.1 MPa. Employing the ideal gas model for the air, determine the maximum theoretical amount of work that could be developed, in kJ. Ignore heat transfer with the atmosphere and changes in kinetic and potential energy

A tank initially containing air at 30 atm and 10008R is connected to a small turbine. Air discharges from the tank through the turbine, which produces work in the amount of 100 Btu. The pressure in the tank falls to 3 atm during the process and the turbine exhausts to the atmosphere at 1 atm. Employing the ideal gas model for the air with k = 14 and ignoring irreversibilities within the tank and the turbine, determine the volume of the tank, in ft\(^{3}\). Heat transfer with the atmosphere and changes in kinetic and potential energy are negligible.

Air enters the turbine of a jet engine at 1190 K, 10.8 bar and expands to 5.2 bar. The air then flows through a nozzle and exits at 0.8 bar. Operation is at steady state, and the flow is adiabatic. The nozzle operates with no internal irreversibilities, and the isentropic turbine efficiency is 85%. The air velocities at the turbine inlet and exit are negligible. Assuming the ideal gas model for the air, determine the velocity of the air exiting the nozzle, in m/s

A Carnot power cycle operates at steady state as shown in Fig. 5.15 with water as the working fluid. The boiler pressure is 200 lbf/in.\(^{2}\) , with saturated liquid entering and saturated vapor exiting. The condenser pressure is 20 lbf/in.\(^{2}\) (a) Sketch the cycle on T–s coordinates. (b) Determine the heat transfer and work for each process, in Btu per lb of water flowing. (c) Evaluate the thermal efficiency

Figure P6.169 shows a Carnot heat pump cycle operating at steady state with ammonia as the working fluid. The condenser temperature is 120\(^{\circ}\)F, with saturated vapor entering and saturated liquid exiting. The evaporator temperature is 10\(^{\circ}\)F. (a) Determine the heat transfer and work for each process, in Btu per lb of ammonia flowing. (b) Evaluate the coefficient of performance for the heat pump. (c) Evaluate the coefficient of performance for a Carnot refrigeration cycle operating as shown in the figure

Carbon dioxide (CO2) expands isothermally at steady state with no irreversibilities through a turbine from 10 bar, 500 K to 2 bar. Assuming the ideal gas model and neglecting kinetic and potential energy effects, determine the heat transfer and work, each in kJ per kg of carbon dioxide flowing.

Steam at 12.0 MPa, 480\(^{\circ}\)C expands through a turbine operating at steady state to 10 bar, saturated vapor. The process follows p\(v^{n}\) = constant and occurs with negligible effects of kinetic or potential energy. The mass flow rate of steam is 5 kg/s. Determine the power developed and the rate of heat transfer, each in kW.

An air compressor operates at steady state with air entering at \(p_{1}=15 \mathrm{lbf} / \mathrm{in} .^{2}, T_{1}=60^{\circ} \mathrm{F} .\). The air undergoes a polytropic process, and exits at \(p_{2}=75 \mathrm{lbf} / \mathrm{in} .^{2}, T_{2}=294^{\circ} \mathrm{F}\). (a) Evaluate the work and heat transfer, each in Btu per lb of air flowing. (b) Sketch the process on p– and T–s diagrams and associate areas on the diagrams with work and heat transfer, respectively. Assume the ideal gas model for air and neglect changes in kinetic and potential energy.

An air compressor operates at steady state with air entering at \(p_{1}=1 \mathrm{bar}, T_{1}=17^{\circ} \mathrm{C} \text { and exiting at } p_{2}=5\) bar. The air undergoes a polytropic process for which the compressor work input is 162.2 kJ per kg of air flowing. Determine (a) the temperature of the air at the compressor exit, in \(^{\circ}\)C, and (b) the heat transfer, in kJ per kg of air flowing. (c) Sketch the process on p–v and T–s diagrams and associate areas on the diagrams with work and heat transfer, respectively. Assume the ideal gas model for air and neglect changes in kinetic and potential energy

Water as saturated liquid at 1 bar enters a pump operating at steady state and is pumped isentropically to a pressure of 50 bar. Kinetic and potential energy effects are negligible. Determine the pump work input, in kJ per kg of water flowing, using (a) Eq. 6.51c, (b) an energy balance. Obtain data from Tables A-3 and A-5, as appropriate. Compare the results of parts (a) and (b), and comment

Fig. P6.176 shows a vapor power plant operating at steady state. Data at key locations are given on the figure. The turbine and pump operate adiabatically, and kinetic and potential energy effects can be neglected. The isentropic pump efficiency is 90%. For such a vapor power cycle, the back work ratio is the ratio of the pump work input to the turbine work output. Determine the back work ratio (a) using data interpolated from Table A-5 to obtain the specific enthalpy at state 4 (b) using the approximation of Eq. 6.51c to obtain the specific enthalpy at state 4. Compare the results of parts (a) and (b) and discuss

A pump operating at steady state receives saturated liquid water at 50\(^{\circ}\)C with a mass flow rate of 20 kg/s. The pressure of the water at the pump exit is 1 MPa. If the pump operates with negligible internal irreversibilities and negligible changes in kinetic and potential energy, determine the power required in kW.

A pump operating at steady state receives liquid water at 20\(^{\circ}\)C 100 kPa with a mass flow rate of 53 kg/min. The pressure of the water at the pump exit is 5 MPa. The isentropic pump efficiency is 70%. Stray heat transfer and changes in kinetic and potential energy are negligible. Determine the power required by the pump, in kW

A pump operating at steady state receives liquid water at 50\(^{\circ}\)C, 1.5 MPa. The pressure of the water at the pump exit is 15 MPa. The magnitude of the work required by the pump is 18 kJ per kg of water flowing. Stray heat transfer and changes in kinetic and potential energy are negligible. Determine the isentropic pump efficiency

Liquid water at 70\(^{\circ}\)F, 14.7 lbf/in.\(^{2}\) , and a velocity of 30 ft/s enters a system at steady state consisting of a pump and attached piping and exits at a point 30 ft above the inlet at 250 lbf/in.\(^{2}\) , a velocity of 15 ft/s, and no significant change in temperature. (a) In the absence of internal irreversibilities, determine the power input required by the system, in Btu per lb of liquid water flowing. (b) For the same inlet and exit states, in the presence of friction would the power input be greater or less than determined in part (a)? Explain. Let g = 32.2 ft/s\(^{2}\).

A 3-hp pump operating at steady state draws in liquid water at 1 atm, 60\(^{\circ}\)F and delivers it at 5 atm at an elevation 20 ft above the inlet. There is no significant change in velocity between the inlet and exit, and the local acceleration of gravity is 32.2 ft/s\(^{2}\). Would it be possible to pump 1000 gal in 10 min or less? Explain

An electrically driven pump operating at steady state draws water from a pond at a pressure of 1 bar and a rate of 50 kg/s and delivers the water at a pressure of 4 bar. There is no significant heat transfer with the surroundings, and changes in kinetic and potential energy can be neglected. The isentropic pump efficiency is 75%. Evaluating electricity at 8.5 cents per kW \(\cdot \) h, estimate the hourly cost of running the pump

As shown in Fig. P6.183, water behind a dam enters an intake pipe at a pressure of 24 psia and velocity of 5 ft/s, flows through a hydraulic turbine-generator, and exits at a point 200 ft below the intake at 19 psia, 45 ft/s, and a specific volume of 0.01602 ft\(^{3}\)/lb. The diameter of the exit pipe is 5 ft and the local acceleration of gravity is 32.2 ft/s\(^{2}\). Evaluating the electricity generated at 8.5 cents per kW \(\cdot \) h, determine the value of the power produced, in $/day, for operation at steady state and in the absence of internal irreversibilities.

As shown in Figure P6.184, water flows from an elevated reservoir through a hydraulic turbine operating at steady state. Determine the maximum power output, in MW, associated with a mass flow rate of 950 kg/s. The inlet and exit diameters are equal. The water can be modeled as incompressible with 5 10\(^{-3}\) m\(^{3}\)/kg. The local acceleration of gravity is 9.8 m/s\(^{2}\)

Nitrogen (\(N_{2}\)) enters a nozzle operating at steady state at 0.2 MPa, 550 K with a velocity of 1 m/s and undergoes a polytropic expansion with n = 1.3 to 0.15 MPa. Using the ideal gas model with k = 1.4, and ignoring potential energy effects, determine (a) the exit velocity, in m/s, and (b) the rate of heat transfer, in kJ per kg of gas flowing

Carbon monoxide enters a nozzle operating at steady state at 5 bar, 200\(^{\circ}\)C with a velocity of 1 m/s and undergoes a polytropic expansion to 1 bar and an exit velocity of 630 m/s. Using the ideal gas model and ignoring potential energy effects, determine (a) the exit temperature, in \(^{\circ}\)C. (b) the rate of heat transfer, in kJ per kg of gas flowing

In 1996, Professor Adrian Bejan proposed a new theory about the way systems evolve over time called the constructal law. Dr. Bejan asserts that this is a fundamental principle that describes mechanical as well as biological systems, particularly flow systems. The theory has led to significant discussion and debate in the scientific and engineering communities. Prepare a report that explains the basics of the theory and discusses the issues being debated about the viability of the theory

Both electricity and heat transfer are needed for processes within manufacturing settings. Combined heat and power (CHP) systems are designed to provide both from a single fuel source such as natural gas (see Sec. 8.5.2). Investigate CHP system designs and prepare a report explaining the types of technology in use in the U.S. manufacturing sector. Discuss the potential for increased use of such technologies and the associated economic considerations. Include at least three references

The U.S. Energy Information Administration estimates that as much as 30–40% of residential energy use is for appliances, electronics, and lighting. Manufacturers of these devices have made significant strides in improving the energy efficiency of their products in recent years. Prepare a report that summarizes improvements in energy efficiency that have been incorporated into home appliances, electronics, and lighting in the last five years. Identify further improvements that are presently under development. Include at least three references.

For a compressor or pump located at your campus or workplace, take data sufficient for evaluating the isentropic compressor or pump efficiency. Compare the experimentally determined isentropic efficiency with data provided by the manufacturer. Rationalize any significant discrepancy between experimental and manufacturer values. Prepare a technical report including a full description of instrumentation, recorded data, results and conclusions, and at least three references

Classical economics was developed largely in analogy to the notion of mechanical equilibrium. Some observers are now saying that a macroeconomic system is more like a thermodynamic system than a mechanical one. Further, they say the failure of traditional economic theories to account for recent economic behavior may be partially due to not recognizing the role of entropy in controlling economic change and equilibrium, similar to the role of entropy in thermodynamics. Write a report, including at least three references, on how the second law and entropy are used in economics

Design and execute an experiment to obtain measured property data required to evaluate the change in entropy of a common gas, liquid, or solid undergoing a process of your choice. Compare the experimentally determined entropy change with a value obtained from published engineering data, including property software. Rationalize any significant discrepancy between values. Prepare a technical report including a full description of the experimental set-up and instrumentation, recorded data, sample calculations, results and conclusions, and at least three references.

The Kelvin temperature scale is absolute, and 0 K is the coldest temperature on this scale. Negative absolute temperatures have been reported in the literature on statistical thermodynamics. According to the macroscopic development of the second law of thermodynamics in Chapters 5 and 6, this is not possible. Investigate the use of the term temperature in these two contexts and explain the apparent paradox. Present your findings in a slide show and include at least three references.

The performance of turbines, compressors, and pumps decreases with use, reducing isentropic efficiency. Select one of these three types of components and develop a detailed understanding of how the component functions. Contact a manufacturer’s representative to learn what measurements are typically recorded during operation, causes of degraded performance with use, and maintenance actions that can be taken to extend service life. Visit an industrial site where the selected component can be observed in operation and discuss the same points with personnel there. Prepare a poster presentation of your findings suitable for classroom use

Elementary thermodynamic modeling, including the use of the temperature–entropy diagram for water and a form of the Bernoulli equation has been employed to study certain types of volcanic eruptions. (See L. G. Mastin, “Thermodynamics of Gas and Steam-Blast Eruptions,” Bull. Volcanol., 57, 85–98, 1995.) Write a report critically evaluating the underlying assumptions and application of thermodynamic principles, as reported in the article. Include at least three references.

In recent decades, many have written about the relationship between life in the biosphere and the second law of thermodynamics. Among these are Nobel Prize winners Erwin Schrodinger (Physics, 1933) and Ilya Prigogine (Chemistry, 1977). Contemporary observers such as Eric Schneider also have weighed in. Survey and critically evaluate such contributions to the literature. Summarize your conclusions in a report having at least three references.

Figure P6.11D shows an air compressor fitted with a water jacket fed from an existing water line accessible at a location 50 ft horizontally and 10 ft below the connection port on the water jacket. The compressor is a single-stage, double-acting, horizontal reciprocating compressor with a discharge pressure of 50 psig when compressing ambient air. Water at 45\(^{\circ}\)F experiences a 10\(^{\circ}\)F temperature rise as it flows through the jacket at a flow rate of 300 gal per hour. Design a cooling water piping system to meet these needs. Use standard pipe sizes and fittings and an appropriate off-the-shelf pump with a single-phase electric motor. Prepare a technical report including a diagram of the piping system, a full parts list, the pump specifications, an estimate of installed cost, and sample calculations.