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In [[physics]], the '''Joule-Thomson effect''' or '''Joule-Kelvin effect''' describes the increase or decrease in the [[temperature]] of a real gas (as differentiated from an [[Ideal gas law|ideal gas]]) when it is allowed to expand freely at constant [[enthalpy]] (which means that no [[heat]] is transferred to or from the gas, and no external [[Mechanical work|work]] is extracted from the gas).<ref name=Roy>{{cite book|author=Bimalendu Narayan Roy|title=Fundamentals of Classical and Statistical Thermodynamics|edition=|publisher=Wiley|year=2002|id=ISBN 0-470-84313-6}}</ref><ref name=Edmister>{{cite book|author=Wayne C. Edmister and Byunk Ik Lee|title=Applied Hydrocarbon Thermodynamics|edition= 2nd edition (Volume 1)|publisher=Gulf Publishing|year=1984|id=ISBN 0-87201-855-5}}</ref><ref name=Ott>{{cite book|author=J. Bevan Ott and Juliana Boerio-Goates |title=Chemical Thermodynamics: Principles and Applications|edition=1st Edition|publisher=Academic Press|year=2000|id=ISBN 0-12-530990-2}}</ref><ref name=Perry>{{cite book | author=Perry, R.H. and Green, D.W. | title=[[Perry's Chemical Engineers' Handbook]] | publisher=McGraw-Hill Book Co. | year=1984 | id=ISBN 0-07-049479-7}}</ref>


It's named for [[James Prescott Joule]] and [[William Thomson, 1st Baron Kelvin]] who established the effect in [[1852]] following earlier work by Joule on '''Joule expansion''' in which a gas expands at constant [[internal energy]].
==Joule-Thomson inversion temperature==
[[Isentropic|Isentropic expansion]], in which a gas does positive work in the process of expansion, always causes a decrease in the gas temperature. For example, when gas is expanded through an [[expansion turbine]] (also known as a ''turboexpander''), the temperature of the gas always decreases.
However, when a real gas (as differentiated from an ideal gas) expands freely at constant enthalpy, the temperature may either decrease or increase, depending on the initial temperature and pressure.  For any given pressure, a real gas has a '''Joule-Thomson inversion temperature'''<ref name=Roy/><ref name=Ott/> above which expansion at constant enthalpy causes the temperature to rise, and below which expansion at constant enthalpy causes cooling. For most gases at [[atmospheric pressure]], the inversion temperature is fairly high (above room temperature), and so most gases at those temperature and pressure conditions are cooled by [[isenthalpic]] expansion.
==The Joule-Thomson coefficient==
The change of temperature with respect to a change of pressure in a Joule-Thomson process is the '''Joule-Thomson coefficient''':<ref name=Edmister/><ref name=Ott/><ref name=Perry/><ref>[http://www.chem.arizona.edu/~salzmanr/480a/480ants/jadjte/jadjte.html Joule Expansion] (by W.R. Salzman, Department of Chemistry, [[University of Arizona]])</ref>
:<math>\mu_{JT} = \left( {\partial T \over \partial P} \right)_H</math>
The value of <math>\mu_{JT}</math> is typically expressed in °C/bar (SI units: K/Pa) and depends on the specific gas, as well as the temperature and pressure of the gas before expansion.
For all real gases, it will equal zero at some point called the '''inversion point''' and, as explained above, the '''Joule-Thomson inversion temperature''' is the temperature where the coefficient changes sign (i.e., where the coefficient equals zero).  The Joule-Thomson inversion temperature depends on the pressure of the gas before expansion.
In any gas expansion, the gas pressure decreases and thus the sign of <math>\partial P</math> is always negative. With that in mind, the following table explains when the Joule-Thomson effect cools or heats a real gas:
{| class="wikitable"
!If the gas temperature is!!then <math>\mu_{JT}</math> is!!since <math>\partial P</math> is!!thus <math>\partial T</math> must be!!so the gas
|-
|align=center|below the inversion temperature||align=center|positive||always negative||align=center|negative||align=center|cools
|-
|align=center|above the inversion temperature||align=center|negative||always negative||align=center|positive||align=center|heats
|}
[[Helium]] and [[hydrogen]] are two gases whose Joule-Thomson inversion temperatures at one [[atmosphere (unit)|atmosphere]] are very low (e.g., about −222 °C for helium).  Thus, helium and hydrogen will warm when expanded at constant enthalpy at typical room temperatures.  On the other hand [[nitrogen]] has an inversion temperature of 621 K (348 °C) and [[oxygen]] has an inversion temperature of 764 K (491 °C): the two most abundant gases in air can be cooled by the Joule-Thomson effect at typical room temperatures.<ref name=Perry/>
It should be noted that <math>\mu_{JT}</math> is always equal to zero for ideal gases. In other words, they will neither heat nor cool upon being freely expanded at constant enthalpy.
==Physical mechanism==
As a gas expands, the average distance between molecules grows.  Because of intermolecular attractive forces, expansion causes an increase in the [[potential energy]] of the gas.  If no external work is extracted in the process (i.e., free expansion) and no heat is transferred, the total energy of the gas remains the same because of the [[conservation of energy]].  The increase in potential energy thus means a decrease in [[kinetic energy]] and therefore in temperature. 
A second mechanism has the opposite effect. During gas molecule collisions, kinetic energy is temporarily converted into potential energy. As the average intermolecular distance increases, there is a drop in the number of collisions per time unit, which causes a decrease in average potential energy. Again, total energy is conserved, so this leads to an increase in kinetic energy (temperature).  Below the Joule-Thompson inversion temperature, the former effect (work done internally against intermolecular attractive forces) dominates, and free expansion causes a decrease in temperature.  Above the inversion temperature, the latter effect (reduced collisions causing a decrease in the average potential energy) dominates, and free expansion causes a temperature increase.
==Applications==
In practice, the Joule-Thomson effect is achieved by allowing the gas to expand through a throttling device (usually a [[valve]]) which must be very well insulated to prevent any heat transfer to or from the gas. External work must not be extracted from the gas during the expansion (meaning that the gas must not be expanded through a turboexpander).
The effect is applied in the [[Carl von Linde|Linde technique]] as a standard process in the [[petrochemical industry]] for example, where the cooling effect is used to liquefy gases, and also in many [[cryogenic]] applications (e.g., for the production of liquid oxygen, nitrogen and [[argon]]). Only when the Joule-Thomson coefficient for the given gas at the given temperature is greater than zero can the gas be liquefied at that temperature by the Linde cycle. In other words, a gas must be below its inversion temperature to be liquified by the Linde cycle. For this reason, simple Linde cycle liquifiers cannot normally be used to liquify helium, hydrogen or [[neon]].
== References ==
{{reflist}}

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