Page 48 - Advanced Thermodynamics for Engineers, Second Edition

32 CHAPTER 2 THE SECOND LAW AND EQUILIBRIUM

P2.11 Show that if a liquid is in equilibrium with its own vapour and an inert gas in a closed vessel,
then

dp v r v
¼
dp r l

where p v is the partial pressure of the vapour, p is the total pressure, r v is the density of the
vapour, r l is the density of the liquid.
P2.12 An incompressible liquid of specific volume v l , is in equilibrium with its own vapour and an
inert gas in a closed vessel. The vapour obeys the law
pðv bÞ¼<T
Show that

p v 1
ln ¼ ðp p 0 Þv [ ðp v p 0 Þb
p 0 <T
where p 0 is the vapour pressure when no inert gas is present, and p is the total pressure.
P2.13 a. Describe the meaning of the term thermodynamic equilibrium. Explain how entropy can
be used as a measure of equilibrium and also how other properties can be developed which
can be used to assess the equilibrium of a system.
If two phases of a component coexist in equilibrium (e.g. liquid and vapour phase H 2 O) show
that

dp l
T ¼
dT v fg
where
T ¼ temperature;
p ¼ pressure;
l ¼ latent heat
and v fg ¼ difference between liquid and vapour phases

Show the significance of this on a phase diagram.
b. The melting point of tin at a pressure of 1 bar is 505 K, but increases to 508.4 K at
1000 bar. Evaluate
– the change of density between these pressures and
– the change in entropy during melting.
The latent heat of fusion of tin is 58.6 kJ/kg.
3
[254,100 kg/m ; 0.1157 kJ/kg K]
P2.14 Show that when different phases are in equilibrium the specific Gibbs energy of each phase is
equal.