Thermodynamics

714 | Thermodynamics13–84 A rigid tank contains 2 kmol of N 2 and 6 kmol ofCH 4 gases at 200 K and 12 MPa. Estimate the volume of thetank, using (a) the ideal-gas equation of state, (b) Kay’s rule,and (c) the compressibility chart and Amagat’s law.13–85 A steady stream of equimolar N 2 and CO 2 mixture at100 kPa and 18°C is to be separated into N 2 and CO 2 gases at100 kPa and 18°C. Determine the minimum work requiredper unit mass of mixture to accomplish this separationprocess. Assume T 0 18°C.13–86 A gas mixture consists of O 2 and N 2 . The ratio of themole numbers of N 2 to O 2 is 3:1. This mixture is heated duringa steady-flow process from 180 to 210 K at a constantpressure of 8 MPa. Determine the heat transfer during thisprocess per mole of the mixture, using (a) the ideal-gasapproximation and (b) Kay’s rule.13–87 Reconsider Prob. 13–86. Using EES (or other)software, investigate the effect of the molefraction of oxygen in the mixture on heat transfer using realgasbehavior with EES data. Let the mole fraction of oxygenvary from 0 to 1. Plot the heat transfer against the mole fraction,and discuss the results.13–88 Determine the total entropy change and exergydestruction associated with the process described in Prob.13–86, using (a) the ideal-gas approximation and (b) Kay’srule. Assume constant specific heats and T 0 30°C.13–89 A rigid tank contains a mixture of 4 kg of He and8 kg of O 2 at 170 K and 7 MPa. Heat is now transferred to thetank, and the mixture temperature rises to 220 K. Treating theHe as an ideal gas and the O 2 as a nonideal gas, determine(a) the final pressure of the mixture and (b) the heat transfer.13–90 A mixture of 60 percent carbon dioxide and 40 percentmethane on a mole basis expands through a turbine from1600 K and 800 kPa to 100 kPa. The volume flow rate at theturbine entrance is 10 L/s. Determine the rate of work done bythe mixture using (a) ideal-gas approximation and (b) Kay’srule.13–91 A pipe fitted with a closed valve connects two tanks.One tank contains a 5-kg mixture of 62.5 percent CO 2 and37.5 percent O 2 on a mole basis at 30°C and 125 kPa. Thesecond tank contains 10 kg of N 2 at 15°C and 200 kPa. Thevalve in the pipe is opened and the gases are allowed to mix.During the mixing process 100 kJ of heat energy is suppliedto the combined tanks. Determine the final pressure and temperatureof the mixture and the total volume of the mixture.13–92 Using EES (or other) software, write a programto determine the mole fractions of the componentsof a mixture of three gases with known molar masseswhen the mass fractions are given, and to determine the massfractions of the components when the mole fractions are given.Run the program for a sample case, and give the results.13–93 Using EES (or other) software, write a programto determine the apparent gas constant, constantvolume specific heat, and internal energy of a mixtureof three ideal gases when the mass fractions and other propertiesof the constituent gases are given. Run the program fora sample case, and give the results.13–94 Using EES (or other) software, write a programto determine the entropy change of a mixtureof three ideal gases when the mass fractions and other propertiesof the constituent gases are given. Run the program fora sample case, and give the results.Fundamentals of Engineering (FE) Exam Problems13–95 An ideal-gas mixture whose apparent molar mass is36 kg/kmol consists of N 2 and three other gases. If the molefraction of nitrogen is 0.30, its mass fraction is(a) 0.15 (b) 0.23 (c) 0.30 (d ) 0.39 (e) 0.7013–96 An ideal-gas mixture consists of 2 kmol of N 2 and6 kmol of CO 2 . The mass fraction of CO 2 in the mixture is(a) 0.175 (b) 0.250 (c) 0.500 (d ) 0.750 (e) 0.87513–97 An ideal-gas mixture consists of 2 kmol of N 2 and4 kmol of CO 2 . 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 K13–98 A rigid tank is divided into two compartments by apartition. One compartment contains 3 kmol of N 2 at 600 kPaand the other compartment contains 7 kmol of CO 2 at 200kPa. Now the partition is removed, and the two gases form ahomogeneous mixture at 300 kPa. The partial pressure of N 2in the mixture is(a) 75 kPa (b) 90 kPa (c) 150 kPa (d ) 175 kPa (e) 225 kPa13–99 An 80-L rigid tank contains an ideal-gas mixture of5 g of N 2 and 5 g of CO 2 at a specified pressure and temperature.If N 2 were separated from the mixture and stored atmixture temperature and pressure, its volume would be(a) 32 L (b) 36 L (c) 40 L (d) 49 L (e) 80 L13–100 An ideal-gas mixture consists of 3 kg of Ar and6 kg of CO 2 gases. The mixture is now heated at constantvolume 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 kJ13–101 An ideal-gas mixture consists of 30 percent heliumand 70 percent argon gases by mass. The mixture is nowexpanded isentropically in a turbine from 400°C and 1.2 MPato a pressure of 200 kPa. The mixture temperature at turbineexit is(a) 195°C (b) 56°C (c) 112°C(d ) 130°C (e) 400°C