Topic 2615
Real Gases: Liquefaction of Gases
In the nineteenth century a major theme in science concerned the properties of gases
and their liquefaction. The challenge offered by the liquefaction of gases also
prompted the development of thermodynamics and the production of low
temperatures. Michael Faraday is noteworthy in this context. In 1823 Faraday had
liquefied chlorine, ammonia and sulfur dioxide using a combination of pressure and
low temperatures [1].
Based on the observation that the densities of liquids are higher than gases the
expectation was that liquefaction of a given gas would follow application of high
pressure. However this turned out not to be the case. For example, Newton showed
that application of 2790 atmospheres ( ≅ 2.8 x 108 N m-2) did not liquefy air. In 1877
Cailletet and Pictet working independently obtained a mist of oxygen by sudden
expansion of gas compressed at 300 atmospheres (≅ 3 x 107 N m-2) and cooled by
CO2(s). However in developing the background to this subject we turn attention to the
work of Joule.
Experiments by Joule
A gas, chemical substance j, is held in a closed system. The molar thermodynamic
energy Uj is defined by equation (a) where Vj is the molar volume and T, the
temperature.
U j = U j [T , V j ]
(a)
The complete differential of equation (a) describes the change in Uj, dU j , as a
function of temperature and volume.
⎛ ∂U j ⎞
⎛ ∂U j ⎞
⎟ ⋅ dVj
⎟⎟ ⋅ dT + ⎜
dU j = ⎜⎜
⎜ ∂V ⎟
⎝ ∂T ⎠ V
⎝ j ⎠T
(b)
The molar isochoric heat capacity CVj is defined by equation (c).
⎛ ∂U j ⎞
⎟⎟
C V j = ⎜⎜
⎝ ∂T ⎠ V
(c)
The first law of thermodynamics relates the change in Uj to the work done on the
system w and heat q passing from the surroundings into the system.
Thus, dU j = q + w
(d)
⎛ ∂U j ⎞
⎛ ∂U j ⎞
⎟ ⋅ dV j − w
⎟⎟ ⋅ dT + ⎜
Hence, q = ⎜⎜
⎜ ∂V ⎟
⎝ ∂T ⎠ V
⎝ j ⎠T
(e)
The apparatus used by Joule comprised two linked vessels having equal volumes. A
tube joining the two vessels included a tap. In an experiment, one vessel was filled
with gas j at a known pressure whereas the second vessel was evacuated. When the tap
was opened gas flowed into the second vessel, equalising the pressure in the two
vessels. By flowing into an evacuated vessel the gas did no work because there was no
confining pressure; i.e. w = zero. The temperature of the gas in the containing vessel
fell and that in the originally empty vessel rose by an equal amount. In other words dT
for the two vessel system is zero.
⎛ ∂U j ⎞
⎟⎟ = 0
Hence ⎜⎜
⎝ ∂T ⎠ V
(f)
The clear hope was that the temperature would fall dramatically leading to
liquefaction of the gas.
In fact and with the benefit of hindsight the overall change in temperature dT was
⎛ ∂U j ⎞
⎟⎟ ≠ 0
too small to be measured. More sophisticated apparatus would show that ⎜⎜
⎝ ∂T ⎠ V
because as the gas expands work is done against cohesive intermolecular interaction. It
would only be zero for a perfect gas.
Experiments by Joule and Thomson [2,3]
In a series of famous experiments carried out in an English brewery, Joule and
Thomson used an apparatus in which the gas under study passed through a porous plug
from high to low pressures. The plug impeded the flow of the gas such that the
pressure of the gas on the high pressure side and the pressure of gas on the low
pressure side remained constant. It was observed that the temperature of the gas
decreased as a consequence of the work done by the gas against intermolecular
cohesion.
A technological breakthrough was now made. A portion of the cooled gas was
re-cycled to cool the gas on the input side. On passing through the plug the
temperature of the gas fell to a lower temperature. As this process continues a stage
was reached where a fraction of the gas is liquefied.
As noted above, the cooling emerges because work is done on expansion of the
gases against intermolecular interaction. This is a quite general observation. When the
pressure drops the mean intermolecular distance increases with the result that the
temperature decreases. However there are exceptions to this generalisation. If the
pressure is high the dominant intermolecular force is repulsion. Consequently when
the pressure drops, work is done by the repulsive forces increasing the intermolecular
distances thereby raising the temperature.
Footnotes
[1] The account given here is based on that given by N. K. Adam,
Physical Chemistry, Oxford, The Clarendon Press, 1956, chapter III.
[2] Thomson ≡ Lord Kelvin
[3] J. P. Joule and W. Thomson, Proc. Roy. Soc.,1853,143,3457.
[4] G.N. Lewis and M. Randall, Thermodynamics, revised by K. S. Pitzer and
L Brewer, McGraw-Hill, 2nd. edn.,1961, New York, pages 47-49.