ME 3320: Thermodynamics II Handout #13

Homework #13: Problems 13-8, 13-10, 13-13, 13-28E, 13-30, 13-33, 13-

39, 13-41E, 13-54, 13-61E

13-39 A mixture of air and methane is formed in the inlet

manifold of a natural gas-fueled internal combustion engine. The

mole fraction of the methane is 15 percent. This engine is

operated at 3000 rpm and has a 5-L displacement. Determine the

mass flow rate of this mixture in the manifold where the pressure

and temperature are 80 kPa and 20°C. Assume that this is a four-

stroke engine (1 cycle = 2 strokes). Answer: 0.1110 kg/s

13-41E A gaseous mixture consists of 75 percent methane and

25 percent ethane by mass. One million cubic feet of this mixture

is trapped in a geological formation as natural gas at 300°F and

2000 psia. Determine the mass of this gas (a) treating it as an

ideal gas mixture, (b) using a compressibility factor based on

Amagat’s law of additive volumes, and (c) using Kay’s

pseudocritical pressure and temperature.

13-50 The volumetic analysis of a mixture of gases is 30

percent oxygen, 40 percent nitrogen, 10 percent carbon dioxide,

and 20 percent methane. This mixture is heated from 20°C to

200°C while flowing through a tube in which the pressure is

maintained at 150 kPa. Determine the heat transfer to the mixture

per unit mass of the mixture. Assume that the component specific

heats are constant over the temperature range.

13-53 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

mass fractions of the components, and determine the enthalpy

change per unit mass of mixture by: (a) Assuming that the

specific heats are constant over this temperature range, (b)

assuming that they are not constant over this temperature range.

13-61E Air enters the compressor of a simple ideal Brayton

cycle. The following heat exchanger represents the combustion

process. The gas that exits the combuston chamber has a

volumetric composition of 20 percent nitrogen, 5 percent oxygen,

40 percent carbon dioxide, and 35 percent water. The combustion

gases then pass through the turbine to generate power. Calculate

the thermal efficiency of this cycle when the air enters the

compressor at 10 psia and 40°F; the pressure ratio is 6; and the

temperature at the turbine inlet is 1400°F. Model the heat-

addition process using constant gas properties that are the average

of the inlet air and the exit combustion product gases.