Page 111 - Advanced thermodynamics for engineers

96 CHAPTER 4 AVAILABILITY AND EXERGY

Assume
for water : c v ¼ 4:2kJ=kg K;
k ¼ c p c v ¼ 1:0;

for air : c v ¼ 0:7kJ=kg K;

k ¼ c p c v ¼ 1:4:
[2884.2 kJ]
P4.7 An amount of pure substance equal to 1 kmol undergoes an irreversible cycle. Neglecting the
effects of electricity, magnetism and gravity, state whether each of the following relationships
is true or false, giving reasons for your assertion.
H H
(i) dQ ¼ ðdu m þ pdv m Þ;
(ii) H du m þpdv m > 0;
T
(iii) H dW < H pdv m ;
where the suffix m indicates that the quantities are in molar terms.
[False; false; true]
P4.8 A gas turbine operates between an inlet pressure of 15 bar and an exhaust pressure of 1.2 bar.
The inlet temperature to the turbine is 1500 K and the turbine has an isentropic efficiency of
90%. The surroundings are at a pressure of 1 bar and a temperature of 300 K. Calculate, for
the turbine alone:
(i) The specific power output;
(ii) The exhaust gas temperature;
(iii) The exergy change in the gas passing through the turbine and
(iv) The irreversibility or lost work.
Assume the working substance is an ideal gas with a specific heat at constant pressure of
c p ¼ 1.005 kJ/kg K and the specific gas constant, R ¼ 0.287 kJ/kg K.

[697.5 kJ/kg; 806 K; 727.7 kJ/kg; 343.6 kJ/kg]
P4.9 It is proposed to improve the energy utilisation of a steel works by transferring the heat from
the gases leaving the blast furnace at 600 C to those entering the furnace at 50 C (before the

heat exchanger is fitted). The minimum temperature of the flue gases is limited to 150 Cto

avoid condensation of sulfurous acid in the pipework at exit pressure of 1 bar.
Draw a simple schematic diagram of the heat exchanger you would design, showing the hot
and cold gas streams. Explain with the aid of T–s diagrams, why a counterflow heat exchanger
is the most efficient. If the minimum temperature difference between the hot and cold streams
is 10 C, calculate the minimum loss of exergy for both types of heat exchanger, based on dead-

state conditions of 1 bar and 20 C.

[ 72.33 kJ/kg; 45.09 kJ/kg]
P4.10 Find the maximum and maximum useful, specific work (kJ/kg) that could be derived from
combustion products that are (a) stationary and (b) flowing in an environment under the
following conditions.