Solved: Consider a mixture of two gases. Can the apparent

Problem 3P Somebody claims that the mass and mole fractions for a mixture of CO2 and N2O gases are identical. Is this true? Why?

Problem 2P The sum of the mole fractions for an ideal-gas mixture is equal to 1. Is this also true for a real-gas mixture?

Problem 4P Consider a mixture of two gases. Can the apparent molar mass of this mixture be determined by simply taking the arithmetic average of the molar masses of the individual gases? When will this be the case?

Problem 110P An ideal-gas mixture of helium and argon gases with identical mass fractions enters a turbine at 1500 K and 1 MPa at a rate of 0.12 kg/s, and expands isentropically to 100 kPa. The power output of the turbine is (a) 253 kW ________________ (b) 310kW ________________ (c) 341kW ________________ (d) 463 kW ________________ (e) 550 kW

Problem 1P Consider a mixture of several gases of identical masses. Will all the mass fractions be identical? How about the mole fractions?

Problem 5P What is the apparent molar massfor a gas mixture? Does the mass of every molecule in the mixture equal the apparent molar mass?

Problem 6P Using the definitions of mass and mole fractions, derive a relation between them.

Problem 8P The composition of moist air is given on a molar basis to be 78 percent N2, 20 percent O2, and 2 percent water vapor. Determine the mass fractions of the constituents of air.

Consider a mixture of two gases and . Show that when the mass fractions \(m f_{A} \text { and } m f_{B}\) are known, the mole fractions can be determined from \(y_{A}=\frac{M_{B}}{M_{A}\left(1 / m f_{A}-1\right)+M_{B}} \text { and } y_{B}=1-y_{A}\) where \(M_{A} \text { and } M_{B}\) are the molar masses of and . Equation Transcription: Text Transcription: mfA and mfB yA=MB over MA(1/mfA-1)+MB and yB=1-yA MA and MB

Problem 11P A gas mixture consists of 2 kg of O2, 5 kg of N2, and 7 kg of CO2. Determine (a) the mass fraction of each component, (b) the mole fraction of each component, and (c) the average molar mass and gas constant of the mixture.

Problem 9P A gas mixture has the following composition on a mole basis: 60 percent N2 and 40 percent CO2. Determine the gravimetric analysis of the mixture, its molar mass, and gas constant.

Problem 10P Repeat Prob. 13–9 by replacing N2 by O2. Problem 13–9 A gas mixture has the following composition on a mole basis: 60 percent N2 and 40 percent CO2. Determine the gravimetric analysis of the mixture, its molar mass, and gas constant.

Problem 12P Determine the mole fractions of a gas mixture that consists of 75 percent CH4 and 25 percent CO2 by mass. Also, determine the gas constant of the mixture.

Problem 13P A gas mixture consists of 6 kmol of H2 and 2 kmol of N2. Determine the mass of each gas and the apparent gas constant of the mixture.

Problem 14P Is a mixture of ideal gases also an ideal gas? Give an example.

Problem 16P Express Amagat’s law of additive volumes. Does this law hold exactly for ideal-gas mixtures? How about nonideal-gas mixtures?

Problem 15P Express Dalton’s law of additive pressures. Does this law hold exactly for ideal-gas mixtures? How about nonideal-gas mixtures?

Problem 17P How is the P-v-T behavior of a component in an ideal-gas mixture expressed? How is the P-v-T behavior of a component in a real-gas mixture expressed?

Problem 18P What is the difference between the component pressure and the partial pressurel When are these two equivalent?

Problem 19P What is the difference between the component volume and the partial volumel When are these two equivalent?

Problem 20P In a gas mixture, which component will have the higher partial pressure—the one with the higher mole number or the one with the larger molar mass?

Problem 21P Consider a rigid tank that contains a mixture of two ideal gases. A valve is opened and some gas escapes. As a result, the pressure in the tank drops. Will the partial pressure of each component change? How about the pressure fraction of each component?

Problem 22P Consider a rigid tank that contains a mixture of two ideal gases. The gas mixture is heated, and the pressure and temperature in the tank rise. Will the partial pressure of each component change? How about the pressure fraction of each component?

Problem 24P Is this statement correct? The temperature of an ideal-gas mixture is equal to the sum of the temperatures of each individual gas in the mixture. If not, how would you correct it?

Problem 23P Is this statement correct? The volume of an ideal-gas mixture is equal to the sum of the volumes of each individual gas in the mixture. If not, how would you correct it?

Problem 25P Is this statement correct? The pressure of an ideal-gas mixture is equal to the sum of the partial pressures of each individual gas in the mixture. If not, how would you correct it?

Problem 26P Atmospheric contaminants are often measured in parts per million (by volume). What would the partial pressure of refrigerant-134a be in atmospheric air at 100 kPa and 20°C to form a 100-ppm contaminant?

Problem 27P A mixture of gases consists of 30 percent hydrogen, 40 percent helium, and 30 percent nitrogen by volume. Calculate the mass fractions and apparent molecular weight of this mixture.

Problem 29P A gas mixture at 350 K and 300 kPa has the following volumetric analysis: 65 percent N2, 20 percent O2, and 15 percent CO2. Determine the mass fraction and partial pressure of each gas.

Problem 28P A gas mixture at 600 R and 20 psia consists of 1 lbm of CO2 and 3 lbm of CH4. Determine the partial pressure of each gas and the apparent molar mass of the gas mixture.

In an ideal gas mixture the partial pressures of the component gases are as follows:\(\mathrm{CO}_{2}, 20 \mathrm{kPa} ; \mathrm{O}_{2}, 30 \mathrm{kPa} \text {; and } \mathrm{N}_{2}, 50 \mathrm{kPa}\). Determine the mole fractions and mass fractions of each component. Calculate the apparent molar mass, the apparent gas constant, the constant-volume specific heat, and the specific heat ratio at for the mixture. Equation Transcription: Text Transcription: CO2, 20kPa;O2,30kPa; and N2, 50kPa

Problem 31P An engineer has proposed mixing extra oxygen with normal air in internal combustion engines to control some of the exhaust products. If an additional 5 percent (by volume) of oxygen is mixed with standard atmospheric air, how will this change the mixture’s molecular weight?

A rigid tank that contains \(2 \mathrm{~kg} \text { of } N_{2} \text { at } 25^{\circ} \mathrm{C}\) and is connected to another rigid tank that contains \(4 \mathrm{~kg} \text { of } \mathrm{O}_{2}\) at and . The valve connecting the two tanks is opened, and the two gases are allowed to mix. If the final mixture temperature is , determine the volume of each tank and the final mixture pressure. Equation Transcription: Text Transcription: 2 kg of N2 at 25°C 4 kg of O2 ________________

Problem 34P A mixture of hydrocarbon gases is composed of 60 percent methane, 25 percent propane, and 15 percent butane by weight. Determine the volume occupied by 100 kg of this mixture when its pressure is 3 MPa and its temperature is 37°C.

Problem 33P A mixture of gases consists of 0.4 kg of oxygen, 0.7 kg of carbon dioxide, and 0.2 kg of helium. This mixture is maintained at 100 kPa and 27°C. Determine the apparent molecular weight of this mixture, the volume it occupies, the partial volume of the oxygen, and the partial pressure of the helium.

Problem 36P Repeat Prob. 13–35 for a temperature of 400 K. Problem 13–35 A rigid tank contains 8 kmol of O2 and 10 kmol of CO2 gases at 290 K and 150 kPa. Estimate the volume of the tank.

A 30 percent (by mass) ethane and 70 percent methane mixture is to be blended in a \(100-m^{3}\) tank at and \(25^{\circ} \mathrm{C}\) If the tank is initially evacuated, to what pressure should ethane be added before methane is added? Equation Transcription: Text Transcription: 100-m3 25°C

Problem 38P A mixture is 35 percent by volume liquid water, whose density is 62.4 lbm/ft3, that is mixed with another fluid, whose density is 50.0 lbm/ft3. What is the specific weight, in lbf/ft3, of this mixture at a location where g = 31.9 ft/s2?

Problem 35P A rigid tank contains 8 kmol of O2 and 10 kmol of CO2 gases at 290 K and 150 kPa. Estimate the volume of the tank.

Problem 40P Natural gas (95 percent methane and 5 percent ethane by volume) flows through a 36-in-diameter pipeline with a velocity of 10 ft/s. The pressure in the pipeline is 100 psia, and the temperature is 60°F. Calculate the mass and volumetric flow rates in this pipe.

Problem 39P A mixture of air and methane is formed in the inlet manifold of a natural gas-fueled internal combustion engine. The mole fraction of the methane is 15 percent. This engine is operated at 3000 rpm and has a 5-L displacement. Determine the mass flow rate of this mixture in the manifold where the pressure and temperature are 80 kPa and 20°C.

Problem 41P A gaseous mixtures consists of 75 percent methane and 25 percent ethane by mass. One million cubic feet of this mixture is trapped in a geological formation as natural gas at 300°F and 2000 psia. Determine the mass of this gas (a) treating it as an ideal gas mixture, (b) using a compressibility factor based on Dalton’s law of additive pressures, (c) using a compressibility factor based on the law of additive volumes, and (d) using Kay’s psuedocritical pressure and temperature.

Problem 42P The volumetric analysis of a mixture of gases is 30 percent oxygen, 40 percent nitrogen, 10 percent carbon dioxide, and 20 percent methane. This mixture flows through a 1.6-cm-diameter pipe at 8000 kPa and 15°C with a velocity of 5 m/s. Determine the volumetric and mass flow rates of this mixture (a) treating it as an ideal gas mixture, (b) using a compressibility factor based on Amagad's law of additive volumes, and (c) using Key's psuedocritical pressure and temperature.

Problem 44P Is the total internal energy of an ideal-gas mixture equal to the sum of the internal energies of each individual gas in the mixture? Answer the same question for a real-gas mixture.

Problem 45P Is the specific internal energy of a gas mixture equal to the sum of the specific internal energies of each individual gas in the mixture?

Problem 47P Is the total internal energy change of an ideal-gas mixture equal to the sum of the internal energy changes of each individual gas in the mixture? Answer the same question for a real-gas mixture.

Problem 48P When evaluating the entropy change of the components of an ideal-gas mixture, do we have to use the partial pressure of each component or the total pressure of the mixture?

Problem 46P Answer Prob. 13-47Cand 13-48C for entropy.

Problem 43P A rigid tank contains 1 lbmol of argon gas at 400 R and 750 psia. A valve is now opened, and 3 lbmol of N2 gas is allowed to enter the tank at 340 R and 1200 psia. The final mixture temperature is 360 R. Determine the pressure of the mixture, using (a) the ideal-gas equation of state and (b) the compressibility chart and Dalton's law.

Problem 49P Suppose we want to determine the enthalpy change of a real-gas mixture undergoing a process. The enthalpy change of each individual gas is determined by using the generalized enthalpy chart, and the enthalpy change of the mixture is determined by summing them. Is this an exact approach? Explain.

The volumetric analysis of mixture of gases is 30 percent oxygen, 40 percent nitrogen, 10 percent carbon dioxide, and 20 percent methane. This mixture is heated from \(20^{\circ} \mathrm{C} \text { to } 200^{\circ} \mathrm{C}\) while flowing through a tube in which the pressure is maintained at . Determine the heat transfer to the mixture per unit mass of the mixture. Equation Transcription: Text Transcription: 20°C to 200°C

Problem 51P A process requires a mixture that is 21 percent oxygen, 78 percent nitrogen, and 1 percent argon by volume. All three gases are supplied from separate tanks to an adiabatic, constant-pressure mixing chamber at 200 kPa but at different temperatures. The oxygen enters at 10°C, the nitrogen at 60°C, and the argon at 200°C. Determine the total entropy change for the mixing process per unit mass of mixture.

Problem 55P Repeat Prob. 13–54 for a heat loss of 8 kJ. Problem 13–54 A 0.9-m3 rigid tank is divided into two equal compartments by a partition. One compartment contains Ne at 20°C and 100 kPa, and the other compartment contains Ar at 50°C and 200 kPa. Now the partition is removed, and the two gases are allowed to mix. Heat is lost to the surrounding air during this process in the amount of 15 kJ. Determine (a) the final mixture temperature and (b) the final mixture pressure.

Problem 54P A 0.9-m3 rigid tank is divided into two equal compartments by a partition. One compartment contains Ne at 20°C and 100 kPa, and the other compartment contains Ar at 50°C and 200 kPa. Now the partition is removed, and the two gases are allowed to mix. Heat is lost to the surrounding air during this process in the amount of 15 kJ. Determine (a) the final mixture temperature and (b) the final mixture pressure.

A mixture of helium and nitrogen with a nitrogen mass fraction of 35 percent is contained in a piston-cylinder device arranged to maintain a fixed pressure of 100 psia. Determine the work produced, in , as this device is heated from \(100^{\circ} \mathrm{F} \text { to } 500^{\circ} \mathrm{F}\). Answer: Equation Transcription: Text Transcription: 100°F to 500°F

Problem 53P A mixture that is 20 percent carbon dioxide, 10 percent oxygen, and 70 percent nitrogen by volume undergoes a process from 300 K and 100 kPa to 500 K and 400 kPa. Determine the makeup of the mixture on a mass basis and the enthalpy change per unit mass of mixture.

Problem 56P The mass fractions of a mixture of gases are 15 percent nitrogen, 5 percent helium, 60 percent methane, and 20 percent ethane. This mixture is enclosed in a 4 m3 rigid, well-insulated vessel at 150 kPa and 30°C. A paddle wheel in the vessel is turned until 200 kJ of work have been done on the mixture. Calculate the mixture's final pressure and temperature.

An insulated tank that contains \(1 \mathrm{~kg} of \mathrm{O}_{2}\) at \(15^{\circ} \mathrm{C}\) and is connected to a \(2-m^{3}\) uninsulated tank that contains \(N_{2}\) at \(50^{\circ} \mathrm{C}\) and . The valve connecting the two tanks is opened, and the two gases form a homogeneous mixture at . Determine the final pressure in the tank, (b) the heat transfer, and the entropy generated during this process. Assume \(T_{0}=25^{\circ} \mathrm{C}\) Equation Transcription: Text Transcription: 1 kg of O2 15°C 2-m3 N2 50°C T0=25°C

An equimolar mixture of helium and argon gases is to be used as the working fluid in a closed-loop gas-turbine cycle. The mixture enters the turbine at \(2.5 M P a \text { and } 1300 K\) and expands isentropically to a pressure of \(200 k P a\). Determine the work output of the turbine per unit mass of the mixture. Equation Transcription: Text Transcription: 2.5MPa and 1300 K 200kPa

A mixture of hydrocarbon gases is composed of 60 percent methane, 25 percent propane, and 15 percent butane by weight. This mixture is compressed from and \(20^{\circ} \mathrm{C}\) to in a reversible, isothermal, steady-flow compressor. Calculate the work and heat transfer for this compression per unit mass of the mixture. Equation Transcription: Text Transcription: 20°C

Problem 62P How does the thermal efficiency of the cycle in Prob. 13–60 compare to that predicted by air standard analysis?

Problem 63P A gaseous mixture consists of 75 percent methane and 25 percent ethane by mass. 2 million cubic feet of this mixture is trapped in a geological formation as natural gas at 300°F and 1300 psia. This natural gas is pumped 6000 ft to the surface. At the surface, the gas pressure is 20 psia and its temperature is 200°F. Using Kay's rule and the enthalpy-departure charts, calculate the work required to pump this gas.

Problem 61P The gas passing through the turbine of a simple ideal Brayton cycle has the volumetric composition 20 percent nitrogen, 5 percent oxygen, 40 percent carbon dioxide, and 35 percent water. Calculate the thermal efficiency of this cycle when the air enters the compressor at 10 psia and 40°F; the pressure ratio is 6; and the temperature at the turbine inlet is 1400°F. Model the heat-addition and heat-rejection processes using constant gas properties that are the average of the air and turbine gas properties.

A mixture of 65 percent \(\mathrm{N}_{2}\) and 35 percent (t) \(\mathrm{CO}_{2}\) gases (on a mass basis) enters the nozzle of a turbojet engine at 60 psia and with a low velocity, and it expands to a pressure of 12 psia. If the isentropic efficiency of the nozzle is 88 percent, determine the exit temperature and the exit velocity of the mixture. Assume constant specific heats at room temperature. Equation Transcription: Text Transcription: N2 CO2

Problem 66P A piston-cylinder device contains a mixture of 0.8 kg of H2 and 1.2 kg of N2 at 100 kPa and 300 K. Heat is now transferred to the mixture at constant pressure until the volume is doubled. Assuming constant specific heats at the average temperature, determine (a) the heat transfer and (b) the entropy change of the mixture.

A Ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) at \(15^{\circ} \mathrm{C}\) and and \((\epsilon t)\) methane \(\left(\mathrm{CH}_{4}\right)\) at \(60^{\circ} \mathrm{C}\) and enter an adiabatic mixing chamber. The mass flow rate of ethane is , which is twice the mass flow rate of methane. Determine (a) the mixture temperature and the rate of entropy generation during this process, in . Equation Transcription: Text Transcription: (C2H6) 15°C (\epsilon t) (CH4) 60°C

13-71 Determine the total entropy change and exergy destruction associated with the process described in Prob. 13-70 by treating the mixture as an ideal gas and as a nonideal gas and using Amagat's law. Assume constant specific heats at room temperature and take \(T_{0}=20^{\circ} C\) Equation Transcription: Text Transcription: T0=20°C

Two mass streams of two different ideal gases are mixed in a steady-flow chamber while receiving energy by heat transfer from the surroundings. The mixing process takes place at constant pressure with no work and negligible changes in kinetic and potential energies. Assume the gases have constant specific heats. (a) Determine the expression for the final temperature of the mixture in terms of the rate of heat transfer to the mixing chamber and the mass flow rates, specific heats, and temperatures of the three mass streams. (b) Obtain an expression for the exit volume flow rate in terms of the rate of heat transfer to the mixing chamber, mixturepressure, universal gas constant, and the specific heats and molar masses of the inlet gases and exit mixture. (c) For the special case of adiabatic mixing, show that the exit volume flow rate is a function of the two inlet volume flow rates and the specific heats and molar masses of the inlets and exit. (d) For the special case of adiabatic mixing of the same ideal gases, show that the exit volume flow rate is a function of the two inlet volume flow rates.

In an air-liquefaction plant, it is proposed that the pressure and temperature of air that is initially at 1500 psia and \(40^{\circ} \mathrm{C}\) be adiabatically reduced to 15 psia and - \(100^{\circ} \mathrm{C}\) Using Kay's rule and the departure charts, determine whether this is possible. If so, then how much work per unit mass will this process produce? Equation Transcription: Text Transcription: 40°C 100°C

Problem 73P It is common experience that two gases brought into contact mix by themselves. In the future, could it be possible to invent a process that will enable a mixture to separate into its components by itself without any work (or exergy) input?

A piston-cylinder device contains of \(H_{2}\) and of \(N_{2}\) at and . Heat is now transferred to the device, and the mixture expands at constant pressure until the temperature rises to . Determine the heat transfer during this process by treating the mixture as an ideal gas and as a nonideal gas and using Amagat's law. ________________ Equation Transcription: Text Transcription: H2 N2

Problem 74P A 2-L liquid is mixed with 3 L of another liquid, forming a homogeneous liquid solution at the same temperature and pressure. Can the volume of the solution be more or less than the 5 L? Explain.

Problem 75P A 2-L liquid at 20°C is mixed with 3 L of another liquid at the same temperature and pressure in an adiabatic container, forming a homogeneous liquid solution. Someone claims that the temperature of the mixture rose to 22°C after mixing. Another person refutes the claim, saying that this would be a violation of the first law of thermodynamics. Who do you think is right?

Problem 76P What is an ideal solution? on the volume change, enthalpy change, entropy change, and chemical potential change during the formation of ideal and nonideal solutions.

Problem 78P A river is discharging into the ocean at a rate of 150,000 m3/s. Determine the amount of power that can be generated if the river water mixes with the ocean water reversibly. Take the salinity of the ocean to be 2.5 percent on mass basis, and assume both the river and the ocean are at 15°C.

Problem 82P Fresh water is obtained from seawater at a rate of 1.5 m3/s by a desalination plant that consumes 11.5 MW of power and has a second-law efficiency of 20 percent. Determine the power that can be produced if the fresh water produced is mixed with the seawater reversibly.

Problem 81P A desalination plant produces fresh water from sea-water at 10°C with a salinity of 3.2 percent on mass basis at a rate of 1.4 m3/s while consuming 8.5 MW of power. The salt content of the fresh water is negligible, and the amount of fresh water produced is a small fraction of the seawater used. Determine the second-law efficiency of this plant.

Problem 77P Brackish water at 18°C with total dissolved solid content of TDS = 780 ppm (a salinity of 0.078 percent on mass basis) is to be used to produce fresh water with negligible salt content at a rate of 175 L/s. Determine the minimum power input required. Also, determine the minimum height to which the brackish water must be pumped if fresh water is to be obtained by reverse osmosis using semipermeable membranes.

Problem 80P Fresh water is to be obtained from brackish water at 65°F with a salinity of 0.12 percent on mass basis (or TDS = 1200 ppm). Determine (a) the mole fractions of the water and the salts in the brackish water, (b) the minimum work input required to separate 1 lbm of brackish water completely into pure water and pure salts, and (c) the minimum work input required to obtain 1 lbm of fresh water.

Problem 83P Is it possible for an adiabatic liquid–vapor separator to separate wet steam at 100 psia and 90 percent quality, so that the pressure of the outlet streams is greater than 100 psia?

Problem 85P The products of combustion of a hydrocarbon fuel and air are composed of 8 kmol CO2, 9 kmol H2O, 4 kmol O2, and 94 kmol N2. If the mixture pressure is 101 kPa, determine the partial pressure of the water vapor in the product gas mixture and the temperature at which the water vapor would begin to condense when the products are cooled a constant pressure.

A mixture of ideal gases has a specific heat ratio of \(k=1.35\) and an apparent molecular weight of \(M=32 \mathrm{~kg} / \mathrm{kmol}\). Determine the work, in kJ/kg, required to compress this mixture isentropically in a closed system from 100 kPa and 15oC to 700 kPa. FIGURE P13–92 Equation Transcription: Text Transcription: k=1.35 M=32 kg/kmol

An ideal gas mixture approximation to the makeup of dry air on a percent by volume basis at 100 kPa is as follows: 78 percent \(\mathrm{N}_{2}\), 21 percent \(\mathrm{O}_{2}\), and 1 percent Ar. Determine the mole fractions, mass fractions, and the partial pressure of each component. Calculate the apparent molar mass, the apparent gas constant, and the constant-pressure specific heat at 300 K for the mixture. Compare your answers with those in Table A-1 and A-2a. Equation Transcription: Text Transcription: N2 O2

Problem 88P A mixture of gases consists of 0.1 kg of oxygen, 1 kg of carbon dioxide, and 0.5 kg of helium. This mixture is compressed to 17,500 kPa and 20°G. Determine the mass of this gas contained in a 0.3 m3 tank (a) treating it as an ideal gas mixture, (b) using a compressibility factor based on Dalton’s law of additive pressures, (c) using a compressibility factor based on the law of additive volumes, and (d) Kay’s psuedocritical pressure and temperature.

Problem 91P Determine the total entropy change and exergy destruction associated with the process described in Prob. 13–89, using (a) the ideal-gas approximation and (b) Kay's rule. Assume constant specific heats and T0 = 30°C. Problem 13–89 A gas mixture consists of O2 and N2. The ratio of the mole numbers of N2 to O2 is 3:1. This mixture is heated during a steady-flow process from 180 to 210 K at a constant pressure of 8 MPa. Determine the heat transfer during this process per mole of the mixture, using (a) the ideal-gas approximation and (b) Kay's rule.

A spring-loaded piston–cylinder device contains a mixture of gases whose pressure fractions are 25 percent Ne, 50 percent \(O_{2}\) and 25 percent N2. The piston diameter and spring are selected for this device such that the volume is \(0.1 \mathrm{~m}^{3}\) when the pressure is 200 kPa and \(0.1 \mathrm{~m}^{3}\) when the pressure is 1000 kPa. Initially, the gas is added to this device until the pressure is 200 kPa and the temperature is 108C. The device is now heated until the pressure is 500 kPa. Calculate the total work and heat transfer for this process. Equation Transcription: Text Transcription: O2 N2 0.1 m3 0.1 m3

Problem 89P A gas mixture consists of O2 and N2. The ratio of the mole numbers of N2 to O2 is 3:1. This mixture is heated during a steady-flow process from 180 to 210 K at a constant pressure of 8 MPa. Determine the heat transfer during this process per mole of the mixture, using (a) the ideal-gas approximation and (b) Kay's rule.

Problem 94P The piston-cylinder device of Prob. 13–96 is filled with a mixture whose mass is 55 percent nitrogen and 45 percent carbon dioxide. Initially, this mixture is at 200 kPa and 45°C. The gas is heated until the volume has doubled. Calculate the total work and heat transfer for this process.

The mass fractions of a mixture of gases are 15 percent nitrogen, 5 percent helium, 60 percent methane; and 20 percent ethane. This mixture is expanded from 200 psia and \(400^{\circ} \mathrm{F} \) to 15 psia in an adiabatic, steady-flow turbine of 85 percent isentropic efficiency. Calculate the second law efficiency and the exergy destruction during this expansion process. Take \(T_{0}=77^{\circ} \mathrm{F}\) Equation Transcription: Text Transcription: 400°F T0=77°F

Problem 95P Calculate the total work and heat transfer required to triple the initial pressure of the mixture of Prob. 13–97 as it is heated in the spring-loaded piston-cylinder device.

Using Amagat’s law, show that \(Z_{m}=\sum_{i=1}^{k} y_{i} Z_{i}\) for a real-gas mixture of k gases, where Z is the compressibility factor. Equation Transcription: Text Transcription: Z_{m}=\sum_{i=1}^{k} y_{i} Z_{i}

Using EES (or other) software, write a program to determine the mole fractions of the components of a mixture of three gases with known molar masses when the mass fractions are given, and to determine the mass fractions of the components when the mole fractions are given. Run the program for a sample case, and give the results.

Problem 96P A rigid tank contains a mixture of 4 kg of He and 8 kg of O2 at 170 K and 7 MPa. Heat is now transferred to the tank, and the mixture temperature rises to 220 K. Treating the He as an ideal gas and the O2 as a nonideal gas, determine (a)the final pressure of the mixture and (b) the heat transfer.

Problem 102P An ideal-gas mixture consists of 2 kmol of N2 and 6 kmol of CO2. The mass fraction of CO2 in the mixture is (a) 0.175 ________________ (b) 0.250 ________________ (c) 0.500 ________________ (d) 0.750 ________________ (e) 0.875

Problem 104P A rigid tank is divided into two compartments by a partition. One compartment contains 3 kmol of N2 at 400 kPa and the other compartment contains 7 kmol of CO2 at 200 kPa. Now the partition is removed, and the two gases form a homogeneous mixture at 250 kPa. The partial pressure of N2 in the mixture is (a) 75kPa ________________ (b) 90kPa ________________ (c) 125 kPa ________________ (d) 175 kPa ________________ (e) 250 kPa

Problem 107P An ideal-gas mixture consists of 60 percent helium and 40 percent argon gases by mass. The mixture is now expanded isentropically in a turbine from 400°C and 1.2 MPa to a pressure of 200 kPa. The mixture temperature at turbine exit is (a) 56°C ________________ (b) 195°C ________________ (c) 130°C ________________ (d) 112°C ________________ (e) 400°C

Problem 108P One compartment of an insulated rigid tank contains 2 kmol of CO2 at 20°C and 150 kPa while the other compartment contains 5 kmol of H2 gas at 35°C and 300 kPa. Now the partition between the two gases is removed, and the two gases form a homogeneous ideal-gas mixture. The temperature of the mixture is (a) 25°C ________________ (b) 29°C ________________ (c) 22°C ________________ (d) 32°C ________________ (e) 34°C

Problem 106P An ideal-gas mixture consists of 3 kg of Ar and 6 kg of CO2 gases. The mixture is now heated at constant volume from 250 K to 350 K. The amount of heat transfer is (a) 374 kJ ________________ (b) 436 kJ ________________ (c) 488 kJ ________________ (d) 525 kJ ________________ (e) 664 kJ

Problem 105P An 80-L rigid tank contains an ideal-gas mixture of 5g of N2 and 5 g of CO2 at a specified pressure and temperature. If N2 were separated from the mixture and stored at mixture temperature and pressure, its volume would be (a) 32 L ________________ (b) 36 L ________________ (c) 40 L ________________ (d) 49 L ________________ (e) 80 L

Problem 109P A piston-cylinder device contains an ideal-gas mixture of 3 kmol of He gas and 7 kmol of Ar gas at 50°C and 400 kPa. Now the gas expands at constant pressure until its volume doubles. The amount of heat transfer to the gas mixture is (a) 6.2 MJ ________________ (b) 4.2 MJ ________________ (c) 27 MJ ________________ (d) 10 MJ ________________ (e) 67 MJ

Problem 101P An ideal-gas mixture whose apparent molar mass is 20 kg/kmol consists of N2 and three other gases. If the mole fraction of nitrogen is 0.55, its mass fraction is (a) 0.15 ________________ (b) 0.23 ________________ (c) 0.39 ________________ (d) 0.55 ________________ (e) 0.77

Problem 103P An ideal-gas mixture consists of 2 kmol of N2 and kmol of CO2. The apparent gas constant of the mixture is (a) 0.215 kJ/kg.K ________________ (b) 0.225 kJ/kg.K ________________ (c) 0.243 kJ/kg.K ________________ (d) 0.875 kJ/kg.K ________________ (e) 1.24 kJ/kg.K

Consider a mixture of several gases of identical masses. Will all the mass fractions be identical? How about the mole fractions?

The sum of the mole fractions for an ideal-gas mixture is equal to 1. Is this also true for a real-gas mixture?

Somebody claims that the mass and mole fractions for a mixture of and gases are identical. Is this true? Why?

Consider a mixture of two gases. Can the apparent molar mass of this mixture be determined by simply taking the arithmetic average of the molar masses of the individual gases? When will this be the case?

What is the apparent molar mass for a gas mixture? Does the mass of every molecule in the mixture equal the apparent molar mass?

Using the definitions of mass and mole fractions, derive a relation between them.

Consider a mixture of two gases A and B. Show that when the mass fractions and are known, the mole fractions can be determined from and where and are the molar masses of A and B.

The composition of moist air is given on a molar basis to be 78 percent , 20 percent , and 2 percent water vapor. Determine the mass fractions of the constituents of air.

A gas mixture has the following composition on a mole basis: 60 percent and 40 percent . Determine the gravimetric analysis of the mixture, its molar mass, and gas constant.

13.9 A gas mixture has the following composition on a mole basis: 60 percent and 40 percent . Determine the gravimetric analysis of the mixture, its molar mass, and gas constant. Repeat Prob. 13-9 by replacing by

A gas mixture consists of of , of , and 7 kg of . Determine (a) the mass fraction of each component, (b) the mole fraction of each component, and (c) the average molar mass and gas constant of the mixture.

Determine the mole fractions of a gas mixture that consists of 75 percent and 25 percent by mass. Also, determine the gas constant of the mixture.

A gas mixture consists of of and of . Determine the mass of each gas and the apparent gas constant of the mixture.

Is a mixture of ideal gases also an ideal gas? Give an example.

Express Dalton’s law of additive pressures. Does this law hold exactly for ideal-gas mixtures? How about nonideal-gas mixtures?

Express Amagat’s law of additive volumes. Does this law hold exactly for ideal-gas mixtures? How about non ideal-gas mixtures?

How is the behavior of a component in an ideal-gas mixture expressed? How is the behavior of a component in a real-gas mixture expressed?

What is the difference between the component pressure and the partial pressure? When are these two equivalent?

What is the difference between the component volume and the partial volume? When are these two equivalent?

In a gas mixture, which component will have the higher partial pressure-the one with the higher mole number or the one with the larger molar mass?

Consider a rigid tank that contains a mixture of two ideal gases. A valve is opened and some gas escapes. As a result, the pressure in the tank drops. Will the partial pressure of each component change? How about the pressure fraction of each component?

Consider a rigid tank that contains a mixture of two ideal gases. The gas mixture is heated, and the pressure and temperature in the tank rise. Will the partial pressure of each component change? How about the pressure fraction of each component?

Is this statement correct? The volume of an ideal-gas mixture is equal to the sum of the volumes of each individual gas in the mixture. If not, how would you correct it?

Is this statement correct? The temperature of an ideal-gas mixture is equal to the sum of the temperatures of each individual gas in the mixture. If not, how would you correct it?

Is this statement correct? The pressure of an idealgas mixture is equal to the sum of the partial pressures of each individual gas in the mixture. If not, how would you correct it?

Atmospheric contaminants are often measured in parts per million (by volume). What would the partial pressure of refrigerant-134a be in atmospheric air at 100 kPa and 208C to form a 100-ppm contaminant?

A mixture of gases consists of 30 percent hydrogen, 40 percent helium, and 30 percent nitrogen by volume. Calculate the mass fractions and apparent molecular weight of this mixture.

A gas mixture at 600 R and 20 psia consists of 1 lbm of CO2 and 3 lbm of CH4. Determine the partial pressure of each gas and the apparent molar mass of the gas mixture.

A gas mixture at 350 K and 300 kPa has the following volumetric analysis: 65 percent N2, 20 percent O2, and 15 percent CO2. Determine the mass fraction and partial pressure of each gas.

In an ideal gas mixture the partial pressures of the component gases are as follows: CO2, 20 kPa; O2, 30 kPa; and N2, 50 kPa. Determine the mole fractions and mass fractions of each component. Calculate the apparent molar mass, the apparent gas constant, the constant-volume specific heat, and the specific heat ratio at 300 K for the mixture.

An engineer has proposed mixing extra oxygen with normal air in internal combustion engines to control some of the exhaust products. If an additional 5 percent (by volume) of oxygen is mixed with standard atmospheric air, how will this change the mixtures molecular weight?

A rigid tank that contains 2 kg of N2 at 258C and 550 kPa is connected to another rigid tank that contains 4 kg of O2 at 258C and 150 kPa. The valve connecting the two tanks is opened, and the two gases are allowed to mix. If the final mixture temperature is 258C, determine the volume of each tank and the final mixture pressure. A

A mixture of gases consists of 0.4 kg of oxygen, 0.7 kg of carbon dioxide, and 0.2 kg of helium. This mixture is maintained at 100 kPa and 278C. Determine the apparent molecular weight of this mixture, the volume it occupies, the partial volume of the oxygen, and the partial pressure of the helium.

A mixture of hydrocarbon gases is composed of 60 percent methane, 25 percent propane, and 15 percent butane by weight. Determine the volume occupied by 100 kg of this mixture when its pressure is 3 MPa and its temperature is 378C.

A rigid tank contains 8 kmol of O2 and 10 kmol of CO2 gases at 290 K and 150 kPa. Estimate the volume of the tank.

Repeat Prob. 1335 for a temperature of 400 K.

A 30 percent (by mass) ethane and 70 percent methane mixture is to be blended in a 100-m3 tank at 130 kPa and 258C. If the tank is initially evacuated, to what pressure should ethane be added before methane is added?

A mixture is 35 percent by volume liquid water, whose density is 62.4 lbm/ft3 , that is mixed with another fluid, whose density is 50.0 lbm/ft3 . What is the specific weight, in lbf/ft3 , of this mixture at a location where g 5 31.9 ft/s2 ?

A mixture of air and methane is formed in the inlet manifold of a natural gas-fueled internal combustion engine. The mole fraction of the methane is 15 percent. This engine is operated at 3000 rpm and has a 5-L displacement. Determine the mass flow rate of this mixture in the manifold where the pressure and temperature are 80 kPa and 208C.

Natural gas (95 percent methane and 5 percent ethane by volume) flows through a 36-in-diameter pipeline with a velocity of 10 ft/s. The pressure in the pipeline is 100 psia, and the temperature is 608F. Calculate the mass and volumetric flow rates in this pipe.

A gaseous mixtures consists of 75 percent methane and 25 percent ethane by mass. One million cubic feet of this mixture is trapped in a geological formation as natural gas at 3008F and 2000 psia. Determine the mass of this gas (a) treating it as an ideal gas mixture, (b) using a compressibility factor based on Daltons law of additive pressures, (c) using a compressibility factor based on the law of additive volumes, and (d) using Kays psuedocritical pressure and temperature.

The volumetric analysis of a mixture of gases is 30 percent oxygen, 40 percent nitrogen, 10 percent carbon dioxide, and 20 percent methane. This mixture flows through a 1.6-cm-diameter pipe at 8000 kPa and 158C with a velocity of 5 m/s. Determine the volumetric and mass flow rates of this mixture (a) treating it as an ideal gas mixture, (b) using a compressibility factor based on Amagads law of additive volumes, and (c) using Keys psuedocritical pressure and temperature.

A rigid tank contains 1 lbmol of argon gas at 400 R and 750 psia. A valve is now opened, and 3 lbmol of N2 gas is allowed to enter the tank at 340 R and 1200 psia. The final mixture temperature is 360 R. Determine the pressure of the mixture, using (a) the ideal-gas equation of state and (b) the compressibility chart and Daltons law.

Is the total internal energy of an ideal-gas mixture equal to the sum of the internal energies of each individual gas in the mixture? Answer the same question for a real-gas mixture.

Is the specific internal energy of a gas mixture equal to the sum of the specific internal energies of each individual gas in the mixture?

Answer Prob. 1344C and 1345C for entropy.

Is the total internal energy change of an ideal-gas mixture equal to the sum of the internal energy changes of each individual gas in the mixture? Answer the same question for a real-gas mixture.

When evaluating the entropy change of the components of an ideal-gas mixture, do we have to use the partial pressure of each component or the total pressure of the mixture?

Suppose we want to determine the enthalpy change of a real-gas mixture undergoing a process. The enthalpy change of each individual gas is determined by using the generalized enthalpy chart, and the enthalpy change of the mixture is determined by summing them. Is this an exact approach? Explain.

The volumetric analysis of mixture of gases is 30 percent oxygen, 40 percent nitrogen, 10 percent carbon dioxide, and 20 percent methane. This mixture is heated from 208C to 2008C while flowing through a tube in which the pressure is maintained at 150 kPa. Determine the heat transfer to the mixture per unit mass of the mixture.

A process requires a mixture that is 21 percent oxygen, 78 percent nitrogen, and 1 percent argon by volume. All three gases are supplied from separate tanks to an adiabatic, constant-pressure mixing chamber at 200 kPa but at different temperatures. The oxygen enters at 108C, the nitrogen at 608C, and the argon at 2008C. Determine the total entropy change for the mixing process per unit mass of mixture.

A mixture of helium and nitrogen with a nitrogen mass fraction of 35 percent is contained in a pistoncylinder device arranged to maintain a fixed pressure of 100 psia. Determine the work produced, in Btu/lbm, as this device is heated from 1008F to 5008F.

A mixture that is 20 percent carbon dioxide, 10 percent oxygen, and 70 percent nitrogen by volume undergoes a process from 300 K and 100 kPa to 500 K and 400 kPa. Determine the makeup of the mixture on a mass basis and the enthalpy change per unit mass of mixture.

A 0.9-m3 rigid tank is divided into two equal compartments by a partition. One compartment contains Ne at 208C and 100 kPa, and the other compartment contains Ar at 508C and 200 kPa. Now the partition is removed, and the two gases are allowed to mix. Heat is lost to the surrounding air during this process in the amount of 15 kJ. Determine (a) the final mixture temperature and (b) the final mixture pressure.

Repeat Prob. 1354 for a heat loss of 8 kJ.

The mass fractions of a mixture of gases are 15 percent nitrogen, 5 percent helium, 60 percent methane, and 20 percent ethane. This mixture is enclosed in a 4 m3 rigid, well-insulated vessel at 150 kPa and 308C. A paddle wheel in the vessel is turned until 200 kJ of work have been done on the mixture. Calculate the mixtures final pressure and temperature.

An insulated tank that contains 1 kg of O2 at 158C and 300 kPa is connected to a 2-m3 uninsulated tank that contains N2 at 508C and 500 kPa. The valve connecting the two tanks is opened, and the two gases form a homogeneous mixture at 258C. Determine (a) the final pressure in the tank, (b) the heat transfer, and (c) the entropy generated during this process. Assume T0 5 258C.

Reconsider Prob. 1357. Using EES (or other) software, compare the results obtained assuming ideal-gas behavior with constant specific heats at the average temperature, and using real-gas data obtained from EES by assuming variable specific heats over the temperature range.

A mixture of hydrocarbon gases is composed of 60 percent methane, 25 percent propane, and 15 percent butane by weight. This mixture is compressed from 100 kPa and 208C to 1000 kPa in a reversible, isothermal, steady-flow compressor. Calculate the work and heat transfer for this compression per unit mass of the mixture.

An equimolar mixture of helium and argon gases is to be used as the working fluid in a closed-loop gas-turbine cycle. The mixture enters the turbine at 2.5 MPa and 1300 K and expands isentropically to a pressure of 200 kPa. Determine the work output of the turbine per unit mass of the mixture.

The gas passing through the turbine of a simple ideal Brayton cycle has the volumetric composition 20 percent nitrogen, 5 percent oxygen, 40 percent carbon dioxide, and 35 percent water. Calculate the thermal efficiency of this cycle when the air enters the compressor at 10 psia and 408F; the pressure ratio is 6; and the temperature at the turbine inlet is 14008F. Model the heat-addition and heat-rejection processes using constant gas properties that are the average of the air and turbine gas properties.

How does the thermal efficiency of the cycle in Prob. 1361E compare to that predicted by air standard analysis?

A gaseous mixture consists of 75 percent methane and 25 percent ethane by mass. 2 million cubic feet of this mixture is trapped in a geological formation as natural gas at 3008F and 1300 psia. This natural gas is pumped 6000 ft to the surface. At the surface, the gas pressure is 20 psia and its temperature is 2008F. Using Kays rule and the enthalpy-departure charts, calculate the work required to pump this gas. A

A mixture of 65 percent N2 and 35 percent CO2 gases (on a mass basis) enters the nozzle of a turbojet engine at 60 psia and 1400 R with a low velocity, and it expands to a pressure of 12 psia. If the isentropic efficiency of the nozzle is 88 percent, determine (a) the exit temperature and (b) the exit velocity of the mixture. Assume constant specific heats at room temperature.

Reconsider Prob. 1364E. Using EES (or other) software, first solve the stated problem and then, for all other conditions being the same, resolve the problem to determine the composition of the nitrogen and carbon dioxide that is required to have an exit velocity of 2200 ft/s at the nozzle exit.

A pistoncylinder device contains a mixture of 0.8 kg of H2 and 1.2 kg of N2 at 100 kPa and 300 K. Heat is now transferred to the mixture at constant pressure until the volume is doubled. Assuming constant specific heats at the average temperature, determine (a) the heat transfer and (b) the entropy change of the mixture.

Ethane (C2H6) at 158C and 300 kPa and methane (CH4) at 608C and 300 kPa enter an adiabatic mixing chamber. The mass flow rate of ethane is 6 kg/s, which is twice the mass flow rate of methane. Determine (a) the mixture temperature and (b) the rate of entropy generation during this process, in kW/K.

Reconsider Prob. 1367. Using EES (or other) software, determine the effect of the mass fraction of methane in the mixture on the mixture temperature and the rate of exergy destruction. The total mass flow rate is maintained constant at 9 kg/s, and the mass fraction of methane is varied from 0 to 1. Plot the mixture temperature and the rate of exergy destruction against the mass fraction, and discuss the results. Take T0 5 258C.

In an air-liquefaction plant, it is proposed that the pressure and temperature of air that is initially at 1500 psia and 408F be adiabatically reduced to 15 psia and 21008F. Using Kays rule and the departure charts, determine whether this is possible. If so, then how much work per unit mass will this process produce?

A pistoncylinder device contains 6 kg of H2 and 21 kg of N2 at 160 K and 5 MPa. Heat is now transferred to the device, and the mixture expands at constant pressure until the temperature rises to 200 K. Determine the heat transfer during this process by treating the mixture (a) as an ideal gas and (b) as a nonideal gas and using Amagats law.

Determine the total entropy change and exergy destruction associated with the process described in Prob. 1370 by treating the mixture (a) as an ideal gas and (b) as a nonideal gas and using Amagats law. Assume constant specific heats at room temperature and take T0 5 208C.

Two mass streams of two different ideal gases are mixed in a steady-flow chamber while receiving energy by heat transfer from the surroundings. The mixing process takes place at constant pressure with no work and negligible changes in kinetic and potential energies. Assume the gases have constant specific heats. (a) Determine the expression for the final temperature of the mixture in terms of the rate of heat transfer to the mixing chamber and the mass flow rates, specific heats, and temperatures of the three mass streams. (b) Obtain an expression for the exit volume flow rate in terms of the rate of heat transfer to the mixing chamber, mixture pressure, universal gas constant, and the specific heats and molar masses of the inlet gases and exit mixture. (c) For the special case of adiabatic mixing, show that the exit volume flow rate is a function of the two inlet volume flow rates and the specific heats and molar masses of the inlets and exit. (d) For the special case of adiabatic mixing of the same ideal gases, show that the exit volume flow rate is a function of the two inlet volume flow rates.

It is common experience that two gases brought into contact mix by themselves. In the future, could it be possible to invent a process that will enable a mixture to separate into its components by itself without any work (or exergy) input?

A 2-L liquid is mixed with 3 L of another liquid, forming a homogeneous liquid solution at the same temperature and pressure. Can the volume of the solution be more or less than the 5 L? Explain.

A 2-L liquid at 208C is mixed with 3 L of another liquid at the same temperature and pressure in an adiabatic container, forming a homogeneous liquid solution. Someone claims that the temperature of the mixture rose to 228C after mixing. Another person refutes the claim, saying that this would be a violation of the first law of thermodynamics. Who do you think is right?

What is an ideal solution? Comment on the volume change, enthalpy change, entropy change, and chemical potential change during the formation of ideal and nonideal solutions.

Brackish water at 188C with total dissolved solid content of TDS 5 780 ppm (a salinity of 0.078 percent on mass basis) is to be used to produce fresh water with negligible salt content at a rate of 175 L/s. Determine the minimum power input required. Also, determine the minimum height to which the brackish water must be pumped if fresh water is to be obtained by reverse osmosis using semipermeable membranes.

A river is discharging into the ocean at a rate of 150,000 m3 /s. Determine the amount of power that can be generated if the river water mixes with the ocean water reversibly. Take the salinity of the ocean to be 2.5 percent on mass basis, and assume both the river and the ocean are at 158C.

Reconsider Prob. 1378. Using EES (or other) software, investigate the effect of the salinity of the ocean on the maximum power generated. Let the salinity vary from 0 to 5 percent. Plot the power produced versus the salinity of the ocean, and discuss the results.

Fresh water is to be obtained from brackish water at 658F with a salinity of 0.12 percent on mass basis (or TDS 5 1200 ppm). Determine (a) the mole fractions of the water and the salts in the brackish water, (b) the minimum work input required to separate 1 lbm of brackish water completely into pure water and pure salts, and (c) the minimum work input required to obtain 1 lbm of fresh water.

A desalination plant produces fresh water from seawater at 108C with a salinity of 3.2 percent on mass basis at a rate of 1.4 m3 /s while consuming 8.5 MW of power. The salt content of the fresh water is negligible, and the amount of fresh water produced is a small fraction of the seawater used. Determine the second-law efficiency of this plant.

Fresh water is obtained from seawater at a rate of 1.5 m3 /s by a desalination plant that consumes 11.5 MW of power and has a second-law efficiency of 20 percent. Determine the power that can be produced if the fresh water produced is mixed with the seawater reversibly.

Is it possible for an adiabatic liquid-vapor separator to separate wet steam at 100 psia and 90 percent quality, so that the pressure of the outlet streams is greater than 100 psia?

An ideal gas mixture approximation to the makeup of dry air on a percent by volume basis at 100 kPa is as follows: 78 percent N2, 21 percent O2, and 1 percent Ar. Determine the mole fractions, mass fractions, and the partial pressure of each component. Calculate the apparent molar mass, the apparent gas constant, and the constant-pressure specific heat at 300 K for the mixture. Compare your answers with those in Table A-1 and A-2a.

The products of combustion of a hydrocarbon fuel and air are composed of 8 kmol CO2, 9 kmol H2O, 4 kmol O2, and 94 kmol N2. If the mixture pressure is 101 kPa, determine the partial pressure of the water vapor in the product gas mixture and the temperature at which the water vapor would begin to condense when the products are cooled a constant pressure.

A pipe fitted with a closed valve connects two tanks. One tank contains a 5-kg mixture of 62.5 percent CO2 and 37.5 percent O2 on a mole basis at 308C and 125 kPa. The second tank contains 10 kg of N2 at 158C and 200 kPa. The valve in the pipe is opened and the gases are allowed to mix. During the mixing process 100 kJ of heat energy is supplied to the combined tanks. Determine the final pressure and temperature of the mixture and the total volume of the mixture.

A pistoncylinder device contains products of combustion from the combustion of a hydrocarbon fuel with air. The combustion process results in a mixture that has the composition on a volume basis as follows: 4.89 percent carbon dioxide, 6.50 percent water vapor, 12.20 percent oxygen, and 76.41 percent nitrogen. This mixture is initially at 1800 K and 1 MPa and expands in an adiabatic, reversible process to 200 kPa. Determine the work done on the piston by the gas, in kJ/kg of mixture. Treat the water vapor as an ideal gas.

A mixture of gases consists of 0.1 kg of oxygen, 1 kg of carbon dioxide, and 0.5 kg of helium. This mixture is compressed to 17,500 kPa and 208C. Determine the mass of this gas contained in a 0.3 m3 tank (a) treating it as an ideal gas mixture, (b) using a compressibility factor based on Daltons law of additive pressures, (c) using a compressibility factor based on the law of additive volumes, and (d ) Kays psuedocritical pressure and temperature.

A gas mixture consists of O2 and N2. The ratio of the mole numbers of N2 to O2 is 3:1. This mixture is heated during a steady-flow process from 180 to 210 K at a constant pressure of 8 MPa. Determine the heat transfer during this process per mole of the mixture, using (a) the ideal-gas approximation and (b) Kays rule.

Reconsider Prob. 1389. Using EES (or other) software, investigate the effect of the mole fraction of oxygen in the mixture on heat transfer using real-gas behavior with EES data. Let the mole fraction of oxygen vary from 0 to 1. Plot the heat transfer against the mole fraction, and discuss the results.

Determine the total entropy change and exergy destruction associated with the process described in Prob. 1389, using (a) the ideal-gas approximation and (b) Kays rule. Assume constant specific heats and T0 5 308C.

A mixture of ideal gases has a specific heat ratio of k 5 1.35 and an apparent molecular weight of M 5 32 kg/ kmol. Determine the work, in kJ/kg, required to compress this mixture isentropically in a closed system from 100 kPa and 158C to 700 kPa.

A spring-loaded pistoncylinder device contains a mixture of gases whose pressure fractions are 25 percent Ne, 50 percent O2, and 25 percent N2. The piston diameter and spring are selected for this device such that the volume is 0.1 m3 when the pressure is 200 kPa and 1.0 m3 when the pressure is 1000 kPa. Initially, the gas is added to this device until the pressure is 200 kPa and the temperature is 108C. The device is now heated until the pressure is 500 kPa. Calculate the total work and heat transfer for this process.

The pistoncylinder device of Prob. 1393 is filled with a mixture whose mass is 55 percent nitrogen and 45 percent carbon dioxide. Initially, this mixture is at 200 kPa and 458C. The gas is heated until the volume has doubled. Calculate the total work and heat transfer for this process.

Calculate the total work and heat transfer required to triple the initial pressure of the mixture of Prob. 1394 as it is heated in the spring-loaded piston-cylinder device.

A rigid tank contains a mixture of 4 kg of He and 8 kg of O2 at 170 K and 7 MPa. Heat is now transferred to the tank, and the mixture temperature rises to 220 K. Treating the He as an ideal gas and the O2 as a nonideal gas, determine (a) the final pressure of the mixture and (b) the heat transfer.

The mass fractions of a mixture of gases are 15 percent nitrogen, 5 percent helium, 60 percent methane; and 20 percent ethane. This mixture is expanded from 200 psia and 4008F to 15 psia in an adiabatic, steady-flow turbine of 85 percent isentropic efficiency. Calculate the second law efficiency and the exergy destruction during this expansion process. Take T0 5 778F.

Using EES (or other) software, write a program to determine the mole fractions of the components of a mixture of three gases with known molar masses when the mass fractions are given, and to determine the mass fractions of the components when the mole fractions are given. Run the program for a sample case, and give the results.

Using EES (or other) software, write a program to determine the apparent gas constant, constant volume specific heat, and internal energy of a mixture of three ideal gases when the mass fractions and other properties of the constituent gases are given. Run the program for a sample case, and give the results.

Using Amagats law, show that Zm 5 a k i51 yi Zi for a real-gas mixture of k gases, where Z is the compressibility factor.

An ideal-gas mixture whose apparent molar mass is 20 kg/kmol consists of N2 and three other gases. If the mole fraction of nitrogen is 0.55, its mass fraction is (a) 0.15 (b) 0.23 (c) 0.39 (d) 0.55 (e) 0.77

An ideal-gas mixture consists of 2 kmol of N2 and 6 kmol of CO2. The mass fraction of CO2 in the mixture is (a) 0.175 (b) 0.250 (c) 0.500 (d) 0.750 (e) 0.875

An ideal-gas mixture consists of 2 kmol of N2 and 4 kmol of CO2. The apparent gas constant of the mixture is (a) 0.215 kJ/kg?K (b) 0.225 kJ/kg?K (c) 0.243 kJ/kg?K (d) 0.875 kJ/kg?K (e) 1.24 kJ/kg?K

A rigid tank is divided into two compartments by a partition. One compartment contains 3 kmol of N2 at 400 kPa and the other compartment contains 7 kmol of CO2 at 200 kPa. Now the partition is removed, and the two gases form a homogeneous mixture at 250 kPa. The partial pressure of N2 in the mixture is (a) 75 kPa (b) 90 kPa (c) 125 kPa (d) 175 kPa (e) 250 kPa

An 80-L rigid tank contains an ideal-gas mixture of 5 g of N2 and 5 g of CO2 at a specified pressure and temperature. If N2 were separated from the mixture and stored at mixture temperature and pressure, its volume would be (a) 32 L (b) 36 L (c) 40 L (d) 49 L (e) 80 L

An ideal-gas mixture consists of 3 kg of Ar and 6 kg of CO2 gases. The mixture is now heated at constant volume from 250 K to 350 K. The amount of heat transfer is (a) 374 kJ (b) 436 kJ (c) 488 kJ (d) 525 kJ (e) 664 kJ

An ideal-gas mixture consists of 60 percent helium and 40 percent argon gases by mass. The mixture is now expanded isentropically in a turbine from 4008C and 1.2 MPa to a pressure of 200 kPa. The mixture temperature at turbine exit is (a) 568C (b) 1958C (c) 1308C (d ) 1128C (e) 4008C

One compartment of an insulated rigid tank contains 2 kmol of CO2 at 208C and 150 kPa while the other compartment contains 5 kmol of H2 gas at 358C and 300 kPa. Now the partition between the two gases is removed, and the two gases form a homogeneous ideal-gas mixture. The temperature of the mixture is (a) 258C (b) 298C (c) 228C (d ) 328C (e) 348C

A pistoncylinder device contains an ideal-gas mixture of 3 kmol of He gas and 7 kmol of Ar gas at 508C and 400 kPa. Now the gas expands at constant pressure until its volume doubles. The amount of heat transfer to the gas mixture is (a) 6.2 MJ (b) 4.2 MJ (c) 27 MJ (d) 10 MJ (e) 67 MJ

An ideal-gas mixture of helium and argon gases with identical mass fractions enters a turbine at 1500 K and 1 MPa at a rate of 0.12 kg/s, and expands isentropically to 100 kPa. The power output of the turbine is (a) 253 kW (b) 310 kW (c) 341 kW (d) 463 kW (e) 550 kW

The simple additive rule may not be appropriate for the volume of binary mixtures of gases, Prove this for a pair of gases of your choice at several different temperatures and pressures using Kays rule and the principle of corresponding states.

You have a rigid tank equipped with a pressure gauge. Describe a procedure by which you could use this tank to blend ideal gases in prescribed mole-fraction portions.

Prolonged exposure to mercury even at relatively low but toxic concentrations in the air is known to cause permanent mental disorders, insomnia, and pain and numbness in the hands and the feet, among other things. Therefore, the maximum allowable concentration of mercury vapor in the air at work places is regulated by federal agencies. These regulations require that the average level of mercury concentration in the air does not exceed 0.1 mg/m3 . Consider a mercury spill that occurs in an airtight storage room at 208C in San Francisco during an earthquake. Calculate the highest level of mercury concentration in the air that can occur in the storage room, in mg/m3 , and determine if it is within the safe level. The vapor pressure of mercury at 208C is 0.173 Pa. Propose some guidelines to safeguard against the formation of toxic concentrations of mercury vapor in air in storage rooms and laboratories.