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Modern Engineering Thermodynamics

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442 CHAPTER 12: Mixtures of Gases and Vapors<br />

1.00 kg/min of nitrogen at 30.0°C and 1.00 atm. The mixture<br />

leaves the mixing chamber at 60.0°C and 0.800 atm. Find<br />

the heat transfer rate and indicate whether it is into or out of<br />

the mixture.<br />

18. On planet 3M4G6 in the subsystem Zeta-12, the atmosphere<br />

consists of a binary mixture of sewer gas (methane) and an<br />

unknown gas, called Esh-nugim Marookee Moo by the local<br />

mushfoot natives. An extremely accurate spectral scan reveals<br />

that the mass fraction to mole fraction ratio for methane<br />

is 0.9341875 and the mole fraction of methane is<br />

0.4281378. Determine the name of the unknown gas (in<br />

English).<br />

19. Methane, ethane, and propane, all ideal gases, are mixed<br />

together in equal parts by mass to create a new “super” fuel gas.<br />

Then, it is adiabatically compressed from 40.0°F to 1.75 ft 3 at<br />

300. psia, 80.0°F. Determine the work required.<br />

20.* A chemical processing facility produces exhaust gases (46.0%<br />

N 2 , 43.0% CO 2 , and 11.0% SO 2 by volume) at a total pressure<br />

of 0.320 MPa at 1000.°C. It is proposed that energy be<br />

recovered from this gas by expanding it through a turbine to<br />

atmospheric pressure. Assuming ideal gas behavior, determine<br />

the maximum possible power output per unit mass flow rate for<br />

this system.<br />

21.* Two parts of molecular hydrogen gas are mixed with one part of<br />

molecular oxygen gas (on a molar basis) at 2.00 MPa, 0.00°C<br />

and expanded through a reversible nozzle from a negligible<br />

inlet velocity to 292 m/s at the entrance to the combustion<br />

zone of a rocket engine. Through a preheating process in the<br />

nozzle, the gas mixture receives 1325.5 kJ per kg of mixture<br />

of heat at 500.°C. Determine the exit pressure of the gas<br />

mixture. Assume ideal gas behavior.<br />

22. A diving experiment is to be performed with a mixture of<br />

helium and air at a total pressure of 50.0 psia. The composition<br />

must be such that the partial pressure of oxygen in the<br />

compressed mixture is the same as that in air at standard<br />

pressure and temperature (14.7 psia and 70.0°F). Assuming a<br />

closed system and ideal gas behavior, determine<br />

a. The work required to isentropically compress 2.70 lbm of<br />

the mixture from 14.7 psia, 70.0°F to 50.0 psia.<br />

b. The heat transfer required to aergonically cool the<br />

compressed mixture back to 70.0°F again.<br />

23.* Acetylene and oxygen are drawn from pressurized storage tanks<br />

and mixed together in an oxyacetylene torch in a ratio of 5.00<br />

parts of oxygen per 1 part acetylene on a volume basis. This<br />

mixture flows reversibly through the torch from 0.140 MPa,<br />

20.0°C, to atmospheric pressure at 173°C, at which point it is<br />

ignited by the flame. The mean surface temperature of the<br />

torch is 30.0°C, and it uses 0.100 m 3 /s of oxygen at STP<br />

(0.101325 MPa, 20.0°C). Assuming ideal gas behavior,<br />

determine the work and heat transfer rates.<br />

24.* 18.0 m 3 /s of methane are mixed with 10.0 m 3 /s of isobutane<br />

in a test of a new furnace gas. The mixture is preheated before<br />

being ignited by passing it through an adiabatic, isobaric heat<br />

exchanger. The second fluid in the heat exchanger is condensing<br />

steam at 200.°C flowing at 8.30 kg/s. The steam enters as a<br />

saturated vapor and exits with a quality of 21.0%. The gas<br />

mixture enters at 20.0°C and exits at 150.°C (Figure 12.13).<br />

Determine the entropy production rate of the heat<br />

exchanger.<br />

Steam at 200.°C<br />

(x in = 1.00)<br />

Methane<br />

(20.0°C)<br />

Isobutane<br />

(20.0°C)<br />

FIGURE 12.13<br />

Problem 24.<br />

Q internal<br />

Steam at 200.°C<br />

x out = 0.210<br />

p out = p in<br />

Mixture at 150.°C<br />

p out = p in<br />

25.* Air at 0.101 MPa and 50.0°C is saturated with water vapor. It is<br />

to be aergonically heated to 80.0°C in a steady flow, isobaric<br />

process by putting it in contact with an isothermal reservoir at<br />

100.°C. Determine the heat transfer and entropy production<br />

rates per unit mass flow rate if<br />

a. The presence of the water vapor is ignored.<br />

b. The presence of the water vapor is considered (as an ideal<br />

gas).<br />

c. Determine the percent error in the answer a due to the effect<br />

of the water vapor.<br />

26.* The combustion of 1.00 mole of octane, C 8 H 18 , yields 8 moles<br />

of CO 2 , 9.00 moles of H 2 O, and 47.0 moles of N 2 . The exhaust<br />

gases at 811 K, 0.172 MPa from a spark ignition engine are to<br />

be expanded through a turbocharger used to compress the<br />

incoming air charge to the engine. The incoming air is at 20.0°C<br />

and atmospheric pressure, and the turbocharger turbine exhausts<br />

to the atmosphere (Figure 12.14). Find the compressor’s<br />

isentropic outlet temperature T 2 and its isentropic power input<br />

per unit mass flow rate _W C / _m s :<br />

Dry air<br />

1<br />

FIGURE 12.14<br />

Problem 26.<br />

Compressor<br />

Turbocharger<br />

2 3<br />

Engine<br />

Turbine<br />

4<br />

Exhaust<br />

27. A pneumatic motor in a highly explosive environment uses a<br />

mixture of the ideal gases argon and helium in equal parts on a<br />

mass basis. The motor has inlet conditions of 150. psia at 500. R<br />

and an exit pressure of 14.7 psia. If the motor must produce<br />

3.00 hp of output power while operating in a steady state,<br />

steady flow, reversible, and adiabatic manner, then<br />

a. What is the exit temperature of the gas mixture?<br />

b. What mass flow rate of the mixture is required?<br />

28.* An insulated gas turbine is attached to the exhaust stack of an<br />

oil-fired boiler in a power plant. The pressure and temperature<br />

at the inlet to the turbine are 0.500 MPa absolute, 1000.°C and<br />

the exit pressure is atmospheric. The exhaust gas analysis by<br />

volume is 12.0% CO 2 , 2.00% CO, 4.00% O 2 , and 82.0% N 2 .<br />

What is the maximum possible power output from this turbine<br />

per kg of exhaust gas flowing through it? Assume that the

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