Page 215 - Advanced Thermodynamics for Engineers, Second Edition

202 CHAPTER 9 THERMODYNAMIC PROPERTIES OF IDEAL GASES

9.7 PROBLEMS

Assume that air consists of 79% N 2 and 21% O 2 by volume

3
P9.1 A closed vessel of 0.15 m capacity contains a mixture of methane (CH 4 )and air, theair
being 20% in excess of that required for chemically correct combustion. The pressure
and temperature in the vessel before combustion are respectively 3 bar and 100 C.

Determine:
a. the individual partial pressures and the weights of methane, nitrogen and oxygen present
before combustion;
b. the individual partial pressures of the burnt products, on the assumption that these are
cooled to 100 C without change of volume and that all the vapour produced by

combustion is condensed.
[(a) 0.2415, 2.179, 0.579 bar; 0.01868, 0.2951, 0.08969 kg. (b) 2.179, 0.2415, 0.0966 bar]
P9.2 An engine runs on a rich mixture of methyl and ethyl alcohol and air. At a pressure of 1 bar

and 10 C the fuel is completely vapourised. Calculate the air–fuel ratio by volume under
these conditions, and the percentage of ethyl alcohol in the fuel by weight. If the total
pressure of the exhaust gas is 1 bar, calculate the dew point of the water vapour in the exhaust
and the percentage by volume of carbon monoxide in the dry exhaust gas assuming all the
hydrogen in the fuel forms water vapour.

Vapour pressures at 10 C: methyl alcohol (CH 3 OH), 0.0745 bar; and ethyl alcohol
(C 2 H 5 OH), 0.310 bar.

[63 C; 4.15%]
P9.3 An engine working on the constant volume (Otto) cycle has a compression ratio of 6.5 to 1,
and the compression follows the law pV 1.3 ¼ C, the initial pressure and temperature being

1 bar and 40 C. The specific heats at constant pressure and constant volume throughout
compression and combustion are 0.96 þ 0.00002T kJ/kg K and 0.67 þ 0.00002T kJ/kg K
respectively, where T is in K.
Find:
(a) the change in entropy during compression;
(b) the heat rejected per unit mass during compression;
(c) the heat rejected per unit mass during combustion if the maximum pressure is 43 bar and
the energy liberated by the combustion is 2150 kJ/kg of air.
[(a) 0.1621 kJ/kg K; (b) 67.8 kJ/kg; (c) 1090.6 kJ/kg]
P9.4 A compression-ignition engine runs on a fuel of the following analysis by weight: carbon
84%, hydrogen 16%. If the pressure at the end of combustion is 55 bar, the volume ratio of
expansion is 15:1, the pressure and temperature at the end of expansion are 1.75 bar and

600 C respectively, calculate:
a. the variable specific heat at constant volume for the products of combustion; and
b. the change in entropy during the expansion stroke per kg molecule.