Page 47 - Advanced thermodynamics for engineers

30 CHAPTER 2 THE SECOND LAW AND EQUILIBRIUM

P2.1 A mass of 10 kg of water at 0 C is brought into contact with a large heat reservoir at 100 C.
a. When the water has reached 100 C what has been

– the change of entropy of the water;
– the change of entropy of the reservoir;
– the change of entropy of the universe?
b. If the water had been heated from 0 to 100 C by first bringing it into contact with a

reservoir at 30 C and then a reservoir of 100 C, what would have been the change in the

entropy of the universe?
c. Explain how the water could have been heated to give no change in the entropy of the
universe.
[13.11 kJ/kg K; 11.26 kJ/kg K; 1.85 kJ/kg K; 1.070 kJ/kg K; infinite number of reservoirs]
P2.2 A system contains a fluid at a temperature of 70 C and 1 bar. It undergoes a reversible process

during which the temperature of the system remains constant. Given that the heat transfer to the
fluid during the process is 100 kJ, evaluate
a. the increase in entropy.
b. if the system has a mass of 2.31 kg. Evaluate the increase in specific entropy of the system.
c. If a second fluid system, identical to the first one undergoes an irreversible isothermal
process from the same initial state to the same final state as above; and the heat transfer
to the fluid in this irreversible process is 180 kJ; evaluate the increase in entropy of the
fluid.
[0.2915 kJ/K; 0.1262 kJ/kg K; 0.2915 kJ/kg K]
P2.3 Calculate the gain in entropy when 1 kg of water at 30 C is converted into steam at 150 C and

then superheated to 300 C, with the process taking place at constant pressure.
Take c p (water) ¼ 4.2 kJ/kg K, c p (steam) ¼ 2.1 kJ/kg K, h fg ¼ 2600 1.5t, where
t ¼ temperature in C.

[7.6533kJ/kgK]
P2.4 A mass of a liquid, m, at temperature, T 1 , is mixed with an equal mass of the same liquid at
temperature, T 2 . The system is thermally insulated. Show that the change of entropy of the
Universe is

ðT 1 þ T 2 Þ=2

2mc p ln p ffiffiffiffiffiffiffiffiffiffi
T 1 T 2
and prove that this is necessarily positive.
[Hint: Do not specifically consider the mixing of the fluids.]
P2.5 A substance has the following physical properties at a certain pressure:
Saturation temperature, t s ¼ 76 C; h fg ¼ 61.1 kJ/kg

c p(liquid) ¼ 0.21 kJ/kg K; c p(vapour) ¼ 0.14 þ 0.00036T kJ/kg K, where T ¼ temperature in K
Determine the enthalpy and entropy of superheated vapour at 150 C assuming these properties

are zero for the fluid in liquid state at 40 C.

[106.10 kJ/kg; 0.31348 kJ/kg K]