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18.2 LIQUEFACTION BY EXPANSION – METHOD (II) 429

was a supercritical vapour at ambient conditions, it would be impossible to obtain it in liquid form at
atmospheric pressure.
In the liquefaction process described above, the gas may be expanded from state 3 to state 4 either
by a reciprocating machine or against an expansion turbine. Both these machines suffer the problem
that the work done in the expansion process is a function of the initial temperature because the
temperature drop across the turbine is
k 1
8 9
> >
p 4 k
< =
DT ¼ T 3 h T 1 (18.2)
p 3
> >
: ;
It can be seen from Eqn (18.2) that as T 3 becomes very small the temperature drop achieved by the
expansion gets smaller, which means that pressure ratio to obtain the same temperature drop has to be
increased for very low critical temperatures. Another major problem that occurs at very low tem-
peratures is that lubrication becomes extremely difficult. For this reason, the turbine is a better
alternative than a reciprocating device because it may have air bearings, or gas bearings of the same
substance as that being liquefied, thus reducing contamination.
Fortunately another method of liquefaction is available which overcomes many of the problems
described above. This is known as the Joule–Thomson effect and it can be evaluated analytically. The
Joule–Thomson effect is the result of relationships between the properties of the gas in question.

18.2.1 THE JOULE–THOMSON EFFECT
The Joule–Thomson effect was discovered in the mid-nineteenth century when experiments were
being undertaken to define the First Law of Thermodynamics. Joule had showed that the specific heat
at constant volume was not a function of volume, and a similar experiment was developed to ascertain
the change of enthalpy with pressure. The experiment consisted of forcing a gas through a porous plug
by means of a pressure drop. It was found that, for some gases, at a certain entry temperature, there was
a temperature drop in the gas after it had passed through the plug. This showed that, for these gases, the
enthalpy of the gas was a function of both temperature and pressure (see also Chapter 1).
A suitable apparatus for conducting the experiment is shown in Fig. 18.7.

Insulated walls

Piston maintaining Piston maintaining
high pressure p low pressure
p 1 2
T 1 T 2

Control Porous
surface plug
FIGURE 18.7
Porous plug device for Joule–Thomson experiment.