Page 92 - Advanced thermodynamics for engineers

4.7 AVAILABILITY BALANCE FOR A CLOSED SYSTEM 77

ii. Change of entropy of casting
T
T
Z f Z f
dQ R m c c c dT T f 296:12
dS c ¼ ¼ ¼ m c c c ln ¼ 20 0:42 ln ¼ 10:815 kJ=K
T T T c 1073
T s T s
iii. Change of entropy of water

T
T
Z f Z f
dQ R m w c w dT T f 296:12
dS w ¼ ¼ ¼ m w c w ln ¼ 500 4:18 ln ¼ 22:154 kJ=K
T T T w 293
T w T w
iv. Change of entropy of system (and universe)
dS ¼ dS c þ dS w ¼ 10:815 þ 22:154 ¼ 11:339 kJ=K

v. Change of availability
A 2 A 1 ¼ T 0 s ¼ 293 11:34 ¼ 3323 kJ
This solution indicates that the universe is less able to do work after the quenching of the casting
than it was before the casting was quenched. The loss of availability was analysed above by
considering the irreversibility associated with the transfer of energy between the casting and the water.
It could have been analysed in a different manner by taking explicit note of the work which could be
achieved from each part of the composite system before and after the heat transfer had taken place.
This will now be done.
i. Work available by transferring energy from the casting to the environment through a reversible
heat engine before the process
T T
Z 0 Z 0
T 0
T 0 T 0
W c ¼ 1 dQ ¼ 1 m c c c dT ¼ m c c c T T 0 ln T
T T
T c
T s T s
293

¼ 20 0:42 ð293 1073Þ 293 ln ¼ 3357:3kJ
1073
ii. Work available by transferring energy from the water bath to the environment through a reversible
heat engine after the process

T T
Z 0 Z 0 T 0
T 0 T 0
W w ¼ 1 dQ ¼ 1 m w c w dT ¼ m w c w T f T 0 ln T
T T
T f
T f T f
293

¼ 500 4:18 ð293 296:12Þ 293 ln ¼ 34:47 kJ
296:12