Thermodynamics

13–42E A rigid tank contains 1 lbmol of argon gas at 400 Rand 750 psia. A valve is now opened, and 3 lbmol of N 2 gasis allowed to enter the tank at 340 R and 1200 psia. The finalmixture temperature is 360 R. Determine the pressure of themixture, using (a) the ideal-gas equation of state and (b) thecompressibility chart and Dalton’s law. Answers: (a) 2700psia, (b) 2507 psiaProperties of Gas Mixtures13–43C Is the total internal energy of an ideal-gas mixtureequal to the sum of the internal energies of each individual gasin the mixture? Answer the same question for a real-gas mixture.13–44C Is the specific internal energy of a gas mixtureequal to the sum of the specific internal energies of each individualgas in the mixture?13–45C Answer Prob. 13–43C and 13–44C for entropy.13–46C Is the total internal energy change of an ideal-gasmixture equal to the sum of the internal energy changes ofeach individual gas in the mixture? Answer the same questionfor a real-gas mixture.13–47C When evaluating the entropy change of the componentsof an ideal-gas mixture, do we have to use the partialpressure of each component or the total pressure of the mixture?13–48C Suppose we want to determine the enthalpy changeof a real-gas mixture undergoing a process. The enthalpychange of each individual gas is determined by using the generalizedenthalpy chart, and the enthalpy change of the mixtureis determined by summing them. Is this an exact approach?Explain.13–49 A process requires a mixture that is 21 percentoxygen, 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 differenttemperatures. The oxygen enters at 10°C, the nitrogen at60°C, and the argon at 200°C. Determine the total entropychange for the mixing process per unit mass of mixture.13–50 A mixture that is 15 percent carbon dioxide, 5 percentcarbon monoxide, 10 percent oxygen, and 70 percent nitrogenby volume undergoes an adiabatic compression process havinga compression ratio of 8:1. If the initial state of the mixture is300 K and 100 kPa, determine the makeup of the mixture on amass basis and the internal energy change per unit mass ofmixture.13–51 Propane and air are supplied to an internal combustionengine such that the air-fuel ratio is 16:1 when the pressureis 95 kPa and the temperature is 30°C. The compressionratio of the engine is 9.5:1. If the compression process isisentropic, determine the required work input for this compressionprocess, in kJ/kg of mixture.13–52 An insulated rigid tank is divided into two compartmentsby a partition. One compartment contains 2.5 kmol ofChapter 13 | 711CO 2 at 27°C and 200 kPa, and the other compartment contains7.5 kmol of H 2 gas at 40°C and 400 kPa. Now the partitionis removed, and the two gases are allowed to mix.Determine (a) the mixture temperature and (b) the mixturepressure after equilibrium has been established. Assume constantspecific heats at room temperature for both gases.CO 22.5 kmol27°C200 kPaH 27.5 kmol40°C400 kPaFIGURE P13–5213–53 A 0.9-m 3 rigid tank is divided into two equal compartmentsby a partition. One compartment contains Ne at20°C and 100 kPa, and the other compartment contains Ar at50°C and 200 kPa. Now the partition is removed, and the twogases are allowed to mix. Heat is lost to the surrounding airduring this process in the amount of 15 kJ. Determine (a) thefinal mixture temperature and (b) the final mixture pressure.Answers: (a) 16.2°C, (b) 138.9 kPa13–54 Repeat Prob. 13–53 for a heat loss of 8 kJ.13–55 Ethane (C 2 H 6 ) at 20°C and 200 kPa and methane(CH 4 ) at 45°C and 200 kPa enter an adiabaticmixing 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 generationduring this process, in kW/K. Take T 0 25°C.13–56 Reconsider Prob. 13–55. Using EES (or other)software, determine the effect of the mass fractionof methane in the mixture on the mixture temperatureand the rate of exergy destruction. The total mass flow rate ismaintained constant at 13.5 kg/s, and the mass fraction ofmethane is varied from 0 to 1. Plot the mixture temperatureand the rate of exergy destruction against the mass fraction,and discuss the results.13–57 An equimolar mixture of helium and argon gases is tobe used as the working fluid in a closed-loop gas-turbine cycle.2.5 MPa1300 KHe - Arturbine200 kPaFIGURE P13–57