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The inversion curve separates those gaseous states between which the
transitions lead to the cooling of the gas from those states of the gas in
which the gas heats up. The values of the higher inversion temperatures of
a number of gases are given in Table 3.1.

The Joule-Thomson effect characterized by small ΔT values with small
pressure drops Δp is called the differential Joule-Thomson effect. With
large pressure drops in the throttle, the temperature of the gas can change

appreciably. For example, on throttling from 200 atmospheres to 1
atmosphere at an initial temperature
Table3. 1
17°C, the air cools to 35°C. This
Gas CO Ar N H He Air total effect serves as the basis of
2
2
2
T i,max , °K 1500 723 621 202 50 603 most technical gas liquefaction
processes.

3.4 Liquefaction of Gases

Liquefaction of gases is the transition of a substance from the gaseous
state to the liquid. Liquefaction is accomplished by cooling gases below
the critical temperature T with subsequent condensation as a result of the
c
removal of the heat of vaporization (condensation). Cooling the gas below

T is necessary to reach the range of temperatures in which the gas can
c
condense (when T > T , a liquid cannot exist). Gas (ammonia) was first
c
liquefied in 1792 by the Dutch physicist M. van Ma-rum. Chlorine was

obtained in the liquid state in 1823 by M. Faraday, and oxygen in 1877 by
the Swiss scientist R. Pictet and French scientist L. P. Cailletet. Nitrogen
and carbon dioxide were liquefied in 1883 by Z. F. Wróblewski and
K. Olszewski. Hydrogen was first liquefied in 1898 by J. Dewar, and

helium in 1908 by H. Kamerlingh Onnes.
An ideal process for the liquefaction of gases is illustrated in
Figure 3.4.1 (temperature-entropy diagram for an ideal cycle of gas

liquefaction)
Isobar 1–2 corresponds to the cooling of the gas with the condensation
start , and isotherm 2–0 – to the condensation of the gas. The area below l–

2–0 is equivalent to the amount of heat that must be removed from the gas
during its liquefaction, and the area enclosed by the curve l–2–0–3, where
1–3 is the isothermal compression of the gas and 3–0 the adiabatic

expansion, characterizes the thermodynamically minimum amount of work
L min required for liquefaction of the gas:

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