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3.7 THE JOULE-THOMSON EXPERIMENT 61

Pressure gauges FIGURE 3.5
In the Joule-Thomson experiment, a gas is
forced through a porous plug using a pis-
ton and cylinder mechanism. The pistons
move to maintain a constant pressure in
each region. There is an appreciable pres-
sure drop across the plug, and the temper-
P V T ature change of the gas is measured. The
1 1 1
upper and lower figures show the initial
and final states, respectively. As shown in
the text, if the piston and cylinder assem-
bly forms an adiabatic wall between the
Porous plug system (the gases on both sides of the
plug) and the surroundings, the expansion
is isenthalpic.

P V T
2 2 2

The Joule-Thomson experiment shown in Figure 3.5 can be viewed as an improved
version of the Joule experiment because it allows (0U>0V) T to be measured with a
much higher sensitivity than in the Joule experiment. In this experiment, gas flows
from the high-pressure cylinder on the left to the low-pressure cylinder on the right
through a porous plug in an insulated pipe. The pistons move to keep the pressure
unchanged in each region until all the gas has been transferred to the region to the right
of the porous plug. If N 2 is used in the expansion process (P 7 P ) , it is found that
1
2
T 6 T 1 ; in other words, the gas is cooled as it expands. What is the origin of this
2
effect? Consider an amount of gas equal to the initial volume V as it passes through the
1
apparatus from left to right. The total work in this expansion process is the sum of the
work performed on each side of the plug separately by the moving pistons:
0 V 2
w = w left + w right =- P dV - P dV = P V - P V (3.48)
2 2
2
1 1
1
3 3
V 1 0
Because the pipe is insulated, q = 0 , and
¢U = U - U = w = P V - P V (3.49)
2 2
2
1 1
1
This equation can be rearranged to
U + P V = U + P V or H = H 1 (3.50)
2
1
1 1
2
2 2
Note that the enthalpy is constant in the expansion; the expansion is isenthalpic. For
the conditions of the experiment using N 2 , both dT and dP are negative, so
(0T>0P) H 7 0 . The experimentally determined limiting ratio of ¢T to ¢P at constant
enthalpy is known as the Joule-Thomson coefficient:
¢T 0T
m J-T = lim a b = a b (3.51)
¢P:0 ¢P H 0P H
If m J-T is positive, the conditions are such that the attractive part of the potential dom-
inates, and if m J-T is negative, the repulsive part of the potential dominates. Using
experimentally determined values of m J-T , (0H>0P) T can be calculated. For an isen-
thalpic process,
0H
dH = C dT + a b dP = 0 (3.52)
P
0P T