13–84 A rigid tank contains 2 kmol of N 2 and 6 kmol of
CH 4 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.
13–85 A steady stream of equimolar N 2 and CO 2 mixture at
100 kPa and 18°C is to be separated into N 2 and CO 2 gases at
100 kPa and 18°C. Determine the minimum work required
per unit mass of mixture to accomplish this separation
process. Assume T 0 18°C.
13–86 A gas mixture consists of O 2 and N 2. The ratio of the
mole numbers of N 2 to O 2 is 3:1. This mixture is heated dur-
ing 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.
13–87 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 frac-
tion, and discuss the results.
13–88 Determine the total entropy change and exergy
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 T 0 30°C.
13–89 A rigid tank contains a mixture of 4 kg of He and
8 kg of O 2 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 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 per-
cent 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.
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 and
37.5 percent O 2 on a mole basis at 30°C and 125 kPa. The
second tank contains 10 kg of N 2 at 15°C 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 tem-
perature of the mixture and the total volume of the mixture.
13–92 Using EES (or other) software, write a program
to determine the mole fractions of the compo-
nents 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.
714 | Thermodynamics
13–93 Using EES (or other) software, write a program
to determine the apparent gas constant, con-
stant volume specific heat, and internal energy of a mixture
of three ideal gases when the mass fractions and other prop-
erties of the constituent gases are given. Run the program for
a sample case, and give the results.
13–94 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 prop-
erties of the constituent gases are given. Run the program for
a sample case, and give the results.Fundamentals of Engineering (FE) Exam Problems
13–95 An ideal-gas mixture whose apparent molar mass is
36 kg/kmol consists of N 2 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
13–96 An ideal-gas mixture consists of 2 kmol of N 2 and
6 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) 0.875
13–97 An ideal-gas mixture consists of 2 kmol of N 2 and
4 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 K
13–98 A rigid tank is divided into two compartments by a
partition. One compartment contains 3 kmol of N 2 at 600 kPa
and the other compartment contains 7 kmol of CO 2 at 200
kPa. Now the partition is removed, and the two gases form a
homogeneous mixture at 300 kPa. The partial pressure of N 2
in the mixture is
(a) 75 kPa (b) 90 kPa (c) 150 kPa (d) 175 kPa (e) 225 kPa
13–99 An 80-L rigid tank contains an ideal-gas mixture of
5 g of N 2 and 5 g of CO 2 at a specified pressure and temper-
ature. If N 2 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
13–100 An ideal-gas mixture consists of 3 kg of Ar and
6 kg of CO 2 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
13–101 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