Page 217 - Advanced thermodynamics for engineers

9.7 PROBLEMS 203

n
The expansion follows the law pV ¼ C and there is 60% excess air. The specific heats at
constant volume in kJ/kmol K between 600 C and 2400 C are:

O 2 32 þ 0.0025T N 2 29 þ 0.0025T
H 2 O 34 þ 0.08T CO 2 50 þ 0.0067T

The water vapour (H 2 O) may be considered to act as a perfect gas.
[(a) 22.1 þ 0.0184T; (b) 11.42 kJ/kmol K]
P9.5 The exhaust gases of a compression-ignition engine are to be used to drive an exhaust gas
turbo-supercharger. Estimate the mean pressure ratio of expansion and the isentropic
enthalpy drop per kmol of gas in the turbine if the mean exhaust temperature is 600 C and

the isentropic temperature drop is 100 C. The composition of the exhaust gas by volume is

CO 2 , 8%; H 2 O, 9.1%; O 2 , 7.5%; N 2 , 75.4%.
The specific heats at constant volume in kJ/kmol K are

O 2 32 þ 0.0025T N 2 29 þ 0.0025T
H 2 O 34 þ 0.08T CO 2 50 þ 0.0067T

The water vapour (H 2 O) may be considered to act as a perfect gas.
[1.946; 4547.1 kJ/kmol]
P9.6 (a) An amount of substance equal to 2 kmols of an ideal gas at temperature Tand pressure p is
contained in a compartment. In an adjacent compartment is an amount of substance equal to
1 kmol of an ideal gas at temperature 2T and pressure p. The gases mix adiabatically but do
not react chemically when a partition separating the compartments is withdrawn. Show that,
as a result of the mixing process, the entropy increases by

27 k 32

< ln þ ln
4 k 1 27
provided that the gases are different and that k, the ratio of specific heats, is the same for both
gases and remains a constant in the temperature range T to 2T.
(b) What would be the entropy change if the gases being mixed were of the same species?

k< 32
ln
k 1 27
P9.7 The exhaust gas from a two-stroke cycle compression-ignition engine is exhausted at an
elevated pressure into a large chamber. The gas from the chamber is subsequently expanded
in a turbine. If the mean temperature in the chamber is 811 K and the pressure ratio of
expansion in the turbine is 4:1, calculate the isentropic enthalpy drop in the turbine per unit
mass of gas.
[256.68 kJ/kg]