WOLFRAM NOTEBOOK

Joule-Thomson Expansion

​
diagram
throttle
J-T coeff. vs. temperature
gas
CO
2
N
2
H
2
He
inlet pressure (MPa)
3
outlet pressure (MPa)
0.05
inlet temperature (K)
500
​
When a gas expands through an adiabatic throttle (often a porous plug), the temperature can change as a result of the Joule–Thomson effect. You can select one of four gases, and use sliders to adjust the inlet temperature, inlet pressure and outlet pressure. The intensity of the green color is proportional to the gas density, and the throttle is thicker for a larger pressure drop. Select "J-T coeff. vs. temperature" to see the Joule–Thomson coefficient plotted as a function of temperature.

Details

The energy balance for an adiabatic throttle implies that
H
out
=
H
in
.
The throttle does no work, and because the gas moves so quickly through the throttle, it does not have much time to transfer heat to the surroundings.
The Joule–Thomson coefficient is derived by starting with the exact differential for enthalpy:
dH=
δH
δP
T
dP+
δH
δT
P
dT
.
Since
dH=0
for a throttle, and the derivative of enthalpy
H
with respect to temperature
T
at constant pressure
P
is the heat capacity
C
p
, then:
-
δH
δP
T
dP=
C
p
dT
.
Rearranging, and given that the enthalpy
H
is constant,
-
δH
δP
T
=
C
p
δT
δP
H
,
where
δT
δP
H
=
μ
JT
, and
μ
JT
is the Joule–Thomson coefficient.
Integration then relates the outlet temperature to the inlet temperature and the pressure drop:
T
out
=
T
in
+
μ
JT
(
P
out
-
P
in
)
.
If
μ
JT
>0
, the outlet temperature is lower than the inlet temperature. If
μ
JT
<0
, then the outlet temperature is higher.

References

[1] J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics (2nd ed.), Upper Saddle River, NJ: Prentice Hall, 2012 p. 236.
[2] "Thermophysical Properties of Fluid Systems." (Aug 11, 2016) webbook.nist.gov/chemistry/fluid.

Permanent Citation

Adam J. Johnston, John L. Falconer, Rachael L. Baumann
​
​"Joule-Thomson Expansion"​
​http://demonstrations.wolfram.com/JouleThomsonExpansion/​
​Wolfram Demonstrations Project​
​Published: August 12, 2016
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