Page 217 - Advanced Thermodynamics for Engineers, Second Edition

204 CHAPTER 9 THERMODYNAMIC PROPERTIES OF IDEAL GASES

P9.8 The following data refer to an analysis of a dual combustion cycle with a gas having specific
heats varying linearly with temperature:
The pressure and temperature of the gas at the end of compression are 31 bar and 227 C

respectively; the maximum pressure achieved during the cycle is 62 bar, while the maximum

temperature achieved is 1700 C. The temperature at the end of the expansion stroke is 1240 C.
The increases in entropy during constant volume and constant pressure combustion are 0.882
and 1.450 kJ/kg K respectively. Assuming that the fluid behaves as an ideal gas of molecular
weight, m w ¼ 30.5 calculate the equations for the specific heats, and also the expansion ratio if
that process is isentropic.
[0.6747 þ 0.000829T; 0.94735 þ 0.000829T; 7.814]
P9.9 Distinguish between an ideal and a perfect gas and show that in both cases the specific
entropy, s, is given by

Z T
dh p
s ¼ s 0 þ < ln
T p 0
T 0
Two streams of perfect gases, A and B, mix adiabatically at constant pressure and without
chemical change to form a third stream. The molar specific heat at constant pressure c p,m of
the gas in stream A is equal to that in stream B. Stream A flows at M kmol/s and is at a
temperature T 1 , while stream B flows at 1 kmol/s and is at a temperature nT 1 . Assuming that
the gases A and B are different, show that the rate of entropy increase is

" Mþ1 # " Mþ1 #
1 M þ n 1 M
c p ln < ln
n M þ 1 M M þ 1
How is the above expression modified if the gases A and B are the same?
For the case n ¼ 1, evaluate the rate of entropy increase
(a) when different gases mix, and
(b) when the gas in each stream is the same.
Mþ1 Mþ1
1 M þ n 1 M
c p;m ln ; < ln
n M þ 1 M M þ 1
P9.10 A jet engine burns a weak mixture of octane (C 8 H 18 ) and air, with an equivalence ratio, f ¼ 2.
The products of combustion, in which dissociation may be neglected, enter the nozzle with
negligible velocity at a temperature of 1000 K. The gases, which may be considered to be
ideal, leave the nozzle at atmospheric pressure of 1.013 bar with an exit velocity of 500 m/s.
The nozzle may be considered to be adiabatic and frictionless.
Determine:
(a) the specific heat at constant pressure c p , of the products as a function of temperature;
(b) the molecular weight, m w , of the products;
(c) the temperature of the products at the nozzle exit;
(d) the pressure of the products at the nozzle inlet.