Page 48 - Advanced thermodynamics for engineers

2.15 PROBLEMS 31

P2.6 Determine the criteria for equilibrium for a thermally isolated system at (a) constant volume;
(b) at constant pressure. Assume that the system is
a. constant, and invariant, in composition;
b. variable in composition.
P2.7 Determine the criteria for isothermal equilibrium of a system at (a) constant volume, and (b)
constant pressure. Assume that the system is:
a. constant, and invariant, in composition;
b. variable in composition.
P2.8 A system at constant pressure consists of 10 kg of air at a temperature of 1000 K. This is
connected to a large reservoir which is maintained at a temperature of 300 K by a reversible
heat engine. Calculate the maximum amount of work which can be obtained from the system.
Take the specific heat at constant pressure of air, c p , as 0.98 kJ/kg K
[3320.3 kJ]
P2.9 A thermally isolated system at constant pressure consists of 10 kg of air at a temperature of
1000 K and 10 kg of water at 300 K, connected together by a heat engine. What would be the
equilibrium temperature of the system if
1. the heat engine has a thermal efficiency of zero;
2. the heat engine is reversible?

[Hint: consider the definition of equilibrium defined by the entropy change of the system.]
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:

[432.4 K; 376.7 K]
P2.10 A thermally isolated system at constant pressure consists of 10 kg of air at a temperature of
1000 K and 10 kg of water at 300 K, connected together by a heat engine. What would be the
equilibrium temperature of the system if the maximum thermal efficiency of the engine is
only 50%?
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:

[385.1 K]