Page 453 - Advanced thermodynamics for engineers

18.4 PROBLEMS 443

Hence, the work required to liquefy the gas is
^
w ¼ w net þ I HE þ I throttle

18.3 CONCLUDING REMARKS
It has been shown that gases can be liquefied in a number of ways. Gases which are liquids at tem-
peratures close to ambient can be liquefied by cooling in a simple refrigeration system. Carbon di-
oxide, which cannot be maintained as a liquid at ambient pressure, is made into dry ice which is not in
equilibrium at room temperature and pressure.
If it is necessary to achieve extremely low temperatures to bring about liquefaction, the
Joule–Thomson effect is employed. It is possible to analyse such liquefaction plant using equilibrium
thermodynamics and suitable equations of state. The efficiency of liquefaction plant has been
calculated and the major influences of irreversibilities in the processes have been illustrated.

18.4 PROBLEMS
P18.1 Show that the Joule–Thomson coefficient, m, is given by

!
1 vv
m ¼ T v :
c p vT
p
Hence or otherwise show that the inversion temperature (T i )is
vT

T i ¼ v:
vv p
The equation of state for air may be represented by
<T 1:368
p ¼
v m 0:0367 v 2
m
3
where p ¼ pressure (bar), T ¼ temperature (K), and v m ¼ molar volume (m /kmol).
Determine the maximum and minimum inversion temperature and the maximum inversion
pressure for air.
[896 K; 99.6 K; 339 bar]
P18.2 The last stage of a liquefaction process is shown in diagrammatic form in Fig. P18.2. Derive
the relationship between p 1 and T 1 for the maximum yield of liquid at conditions p L , T L , h L
for a gas obeying the state equation

1:368
p þ 2 v m 0:0367 ¼<T
v
m
3
where p is pressure (bar), v m is the molar volume (m /kmol), and T is temperature (K).