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mechanical engineering

Thermodynamics An Engineering Approach 8th edition Yunus A. Cengel, Michael A. Boles - Solutions

Express Dalton’s law of additive pressures. Does this law hold exactly for ideal-gas mixtures? How about non-ideal gas mixtures?
Express Amagat’s law of additive volumes. Does this law hold exactly for ideal-gas mixtures? How about non-ideal as mixtures?
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?
What is the difference between the component pressure and the partial pressure? When are these two equivalents?
What is the difference between the component volume and the partial volume? When are these two equivalents?
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?
Explain how a real-gas mixture can be treated as a pseudo pure substance using Kay’s rule.
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. 13–31 for a temperature of 400 K.
A gas mixture at 300 K and 200 kPa consists of 1 kg of CO2 and 3 kg of CH4. Determine the partial pressure of each gas and the apparent molar mass of the gas mixture.
A rigid tank contains 0.5 kmol of Ar and 2 kmol of N2 at 250 kPa and 280 K. The mixture is now heated to 400 K. Determine the volume of the tank and the final pressure of the 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 0.3-m3 rigid tank contains 0.6 kg of N2 and 0.4 kg of O2 at 300 K. Determine the partial pressure of each gas and the total pressure of the 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.
A rigid tank that contains 1 kg of N2 at 25°C and 300 kPa is connected to another rigid tank that contains 3 kg of O2 at 25°C and 500 kPa. The valve connecting the two tanks is opened, and the two gases are allowed to mix. If the final mixture temperature is 25°C, determine the volume
A volume of 0.3 m3 of O2 at 200 K and 8 MPa is mixed with 0.5 m3 of N2 at the same temperature and pressure, forming a mixture at 200 K and 8 MPa. Determine the volume of the mixture, using (a) The ideal-gas equation of state, (b) Kay’s rule, and (c) The compressibility chart and Amagat’s
A rigid tank contains 1 kmol of Ar gas at 220 K and 5 MPa. A valve is now opened and 3 kmol of N2 gas is allowed to enter the tank at 190 K and 8 MPa. The final mixture temperature is 200 K. Determine the pressure of the mixture, using(a) The ideal-gas equation of state and(b) The compressibility
Reconsider Prob. 13–40. Using EES (or other) software, study the effect of varying the moles of nitrogen supplied to the tank over the range of 1 to 10 kmol of N2. Plot the final pressure of the mixture as a function of the amount of nitrogen supplied using the ideal-gas equation of state and the
A rigid tank contains 1 lb mol of argon gas at 400 R and 750 psia. A valve is now opened, and 3 lb mol 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)
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.
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,
A mixture that is 15 percent carbon dioxide, 5 percent carbon monoxide, 10 percent oxygen, and 70 percent nitrogen by volume undergoes an adiabatic compression process having a compression ratio of 8:1. If the initial state of the mixture is 300 K and 100 kPa, determine the makeup of the mixture on
Propane and air are supplied to an internal combustion engine such that the air-fuel ratio is 16:1 when the pressure is 95 kPa and the temperature is 30°C. The compression ratio of the engine is 9.5:1. If the compression process is isentropic, determine the required work input for this compression
An insulated rigid tank is divided into two compartments by a partition. One compartment contains 2.5 kmol of CO2 at 27°C and 200 kPa, and the other compartment contains 7.5 kmol of H2 gas at 40°C and 400 kPa. Now the partition is removed, and the two gases are allowed to mix. Determine(a)
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
Repeat Prob. 13–53 for a heat loss of 8 kJ.
Ethane (C2H6) at 20°C and 200 kPa and methane (CH4) at 45°C and 200 kPa enter an adiabatic mixing chamber. The mass flow rate of ethane is 9 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
Reconsider Prob. 13–55. 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 energy destruction. The total mass flow rate is maintained constant at 13.5 kg/s, and the mass fraction of methane is varied from 0
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.
A mixture of 80 percent N2 and 20 percent CO2 gases (on a mass basis) enters the nozzle of a turbojet engine at 90 psia and 1800 R with a low velocity and it expands to a pressure of 12 psia. If the isentropic efficiency of the nozzle is 92 percent, determine (a) The exit temperature and (b)
Reconsider Prob. 13–58E 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 2600 ft /s at the nozzle exit.
A piston–cylinder device contains a mixture of 0.5 kg of H2 and 1.6 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
An insulated tank that contains 1 kg of O2 at 15°C and 300 kPa is connected to a 2-m3 uninsulated tank that contains N2 at 50°C and 500 kPa. The valve connecting the two tanks is opened, and the two gases form a homogeneous mixture at 25°C. Determine(a) The final pressure in the
Reconsider Prob. 13–61. 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 piston€“cylinder 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
Determine the total entropy change and energy destruction associated with the process described in Prob.13–63 by treating the mixture (a) As an ideal gas and (b) As anon-ideal gas and using Amagat’s law. Assume constant specific heats at room temperature and take T0 = 30°C.
Air, which may be considered as a mixture of 79 percent N2 and 21 percent O2 by mole numbers, is compressed isothermally at 200 K from 4 to 8 MPa in a steady-flow device. The compression process is internally reversible, and the mass flow rate of air is 2.9 kg/s. Determine the power input to the
Reconsider Prob. 13–65. Using EES (or other) software, compare the results obtained by assuming ideal behavior, real gas behavior with Amagat’s law, and real gas behavior with EES data.
The combustion of a hydrocarbon fuel with air results in a mixture of products of combustion having 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. Determine the average molar mass of the mixture,
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.
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 energy) 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 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
What is an ideal solution? Comment on the volume change, enthalpy change, entropy change, and chemical potential change during the formation of ideal and non-ideal solutions.
Brackish water at 12°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 280 L/s. Determine the minimum power input required. Also, determine the minimum height to which the
A river is discharging into the ocean at a rate of 400,000 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 3.5 percent on mass basis, and assume both the river and the ocean are at 15°C.
Reconsider Prob. 13–74. 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 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
A desalination plant produces fresh water from seawater 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.
Fresh water is obtained from seawater at a rate of 0.5 m3/s by a desalination plant that consumes 3.3 MW of power and has a second-law efficiency of 18 percent. Determine the power that can be produced if the fresh water produced is mixed with the seawater reversibly.
Air has the following composition on a mole basis: 21 percent O2, 78 percent N2, and 1 percent Ar. Determine the gravimetric analysis of air and its molar mass
Using Amagat’s law, show that for a real-gas mixture of k gases, where Z is the compressibility factor.
Using Dalton€™s law, show that for a real-gas mixture of k gases, where Z is the compressibility factor.
A mixture of carbon dioxide and nitrogen flows through a converging nozzle. The mixture leaves the nozzle at a temperature of 500 K with a velocity of 360 m/s. If the velocity is equal to the speed of sound at the exit temperature, determine the required makeup of the mixture on a mass basis.
A piston–cylinder 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
A rigid tank contains 2 kmol of N2 and 6 kmol of CH4 gases at 200 K and 12 MPa. Estimate the volume of the tank, using (a) The ideal-gas equation of state, (b) Kay’s rule, and (c) The compressibility chart and Amagat’s law.
A steady stream of equimolar N2 and CO2 mixture at 100 kPa and 18°C is to be separated into N2 and CO2 gases at 100 kPa and 18°C. Determine the minimum work required per unit mass of mixture to accomplish this separation process. Assume T0 = 18°C.
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
Reconsider Prob. 13–86. 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
Determine the total entropy change and energy destruction associated with the process described in Prob. 13–86, using (a) the ideal-gas approximation and (b) Kay’s rule. Assume constant specific heats and T0 = 30°C.
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 non-ideal gas, determine (a) The final pressure of the mixture and (b) The heat
A mixture of 60 percent carbon dioxide and 40 percent methane on a mole basis expands through a turbine from 1600 K and 800 kPa to 100 kPa. The volume flow rate at the turbine entrance is 10 L/s. Determine the rate of work done by the mixture using (a) ideal-gas approximation and (b) Kay’s rule.
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 30°C and 125 kPa. The second tank contains 10 kg of N2 at 15°C and 200 kPa. The valve in the pipe is opened and the gases are allowed to mix. During
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
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
Using EES (or other) software, write a program to determine the entropy change 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.
An ideal-gas mixture whose apparent molar mass is 36 kg/kmol consists of N2 and three other gases, if the mole fraction of nitrogen is 0.30, its mass fraction is (a) 0.15 (b) 0.23 (c) 0.30 (d ) 0.39 (e) 0.70
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 600 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 300 kPa. The partial pressure of N2 in the
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 30 percent helium and 70 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) 195°C (b) 56°C (c) 112°C (d) 130°C (e) 400°C
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
A piston–cylinder device contains an ideal-gas mixture of 3 kmol of His 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
An ideal-gas mixture of helium and argon gases with identical mass fractions enters a turbine at 1200 K and 1 MPa at a rate of 0.3 kg/s, and expands isentropically to 100 kPa. The power output of the turbine is (a) 478 kW (b) 619 kW (c) 926 KW (d) 729 kW (e) 564 kW
How would you compare the enthalpy of water vapor at 20°C and 2 kPa with the enthalpy of water vapor at 20°C and 0.5 kPa?
How would you compare the enthalpy of water vapor at 20°C and 2 kPa with the enthalpy of water vapor at 20°C and 0.5 kPa? Discuss.
How will (a) the specific humidity and (b) the relative humidity of the air contained in a well-sealed room change as it is heated?
How will (a) the specific humidity and (b) the relative humidity of the air contained in a well-sealed room change as it is cooled?
Consider a tank that contains moist air at 3 atm and whose walls are permeable to water vapor. The surrounding air at 1 atm pressure also contains some moisture. Is it possible for the water vapor to flow into the tank from surroundings? Explain.
Why the chilled water lines are always wrapped with vapor barrier jackets?
Explain how vapor pressure of the ambient air is determined when the temperature, total pressure, and the relative humidity of air are given.
An 8 m3-tank contains saturated air at 30°C, 105 kPa. Determine (a) The mass of dry air, (b) The specific humidity, and (c) The enthalpy of the air per unit mass of the dry air.
A tank contains 21 kg of dry air and 0.3 kg of water vapor at 30°C and 100 kPa total pressures. Determine (a) the specific humidity, (b) The relative humidity, and (c) The volume of the tank.
Repeat Prob. 14–15 for a temperature of 24°C.
A room contains air at 20°C and 98 kPa at a relative humidity of 85 percent. Determine (a) The partial pressure of dry air, (b) The specific humidity of the air, and (c) The enthalpy per unit mass of dry air.
Repeat Prob. 14–17 for a pressure of 85 kPa.
A room contains air at 70°F and 14.6 psia at a relative humidity of 85 percent. Determine (a) The partial pressure of dry air, (b) The specific humidity, and (c) The enthalpy per unit mass of dry air.
Determine the masses of dry air and the water vapor contained in a 240-m3 room at 98 kPa, 23°C, and 50 percent relative humidity.
What is the dew-point temperature?
Andy and Wendy both wear glasses. On a cold winter day, Andy comes from the cold outside and enters the warm house while Wendy leaves the house and goes outside. Whose glasses are more likely to be fogged? Explain.
In summer, the outer surface of a glass filled with iced water frequently “sweats.” How can you explain this sweating?
In some climates, cleaning the ice off the windshield of a car is a common chore on winter mornings. Explain how ice forms on the windshield during some nights even when there is no rain or snow.
A house contains air at 25°C and 65 percent relative humidity. Will any moisture condense on the inner surfaces of the windows when the temperature of the window drops to 10°C?
After a long walk in the 8°C outdoors, a person wearing glasses enters a room at 25°C and 40 percent relative humidity. Determine whether the glasses will become fogged.
Repeat Prob. 14–28 for a relative humidity of 30 percent
A thirsty woman opens the refrigerator and picks up a cool canned drink at 40°F. Do you think the can will “sweat” as she enjoys the drink in a room at 80°F and 50 percent relative humidity?
The dry- and wet-bulb temperatures of atmospheric air at 95 kPa are 25 and 17°C, respectively. Determine (a) The specific humidity, (b) The relative humidity, and (c) The enthalpy of the air, in kJ/kg dry air.

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