Page 176 - Advanced thermodynamics for engineers

162 CHAPTER 7 GENERAL THERMODYNAMIC RELATIONSHIPS

The following table gives values of the specific volume of water, in cubic metres per kilogram. A
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quantity of water is initially at 30 C, 20 bar and occupies a volume of 0.2 m . It is heated at

constant volume to 50 C and then cooled at constant pressure to 30 C. Calculate the net heat

transfer to the water.
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Specific Volume (m /kg)
Pressure (bar) 20 200
Temperature ( C)

30 0.0010034 0.0009956
50 0.0010112 0.0010034

[438 kJ]
P7.7 Assuming that entropy is a continuous function, s ¼ s(T,v), derive the expression for entropy
change

dT vp
ds ¼ c v þ dv
T vT
v
and similarly, for s ¼ s(T,p) derive

dT vv
ds ¼ c p dp:
T vT
p
Apply these relationships to a gas obeying van der Waals equation

RT a
p ¼ 2
v b v
and derive an equation for the change of entropy during a process in terms of the basic properties
and gas parameters. Also derive an expression for the change of internal energy as such a gas
undergoes a process.
2 3
Z 2
p 2 þ a 2 2aðv bÞ 3
!
T 2 v v
4s 2 s 1 ¼ c p ln R ln ; u 2 u 1 ¼ c v dT a v 1 v 2 7
6
5
T 1 p 1 þ a = v 2 2aðv bÞ = v 3 v 1 v 2
1