- Inversion temperature
The inversion temperature in
thermodynamics andcryogenics is the critical temperature below which a non-ideal gas (all gases in reality) that is expanded at constant enthalpy will experience a temperature decrease, and above which will experience a temperature increase. This temperature change is known as theJoule-Thomson effect , and is exploited in theliquefaction of gases .Theory
The
Joule-Thomson effect cannot be described in the theory ofideal gases , in which interactions between particles are ignored. Instead, one must use a theory that accounts for theVan der Waals force between interacting particles that becomes much stronger as a gas becomes a liquid.For a van der Waals gas we can calculate the
enthalpy "H" usingstatistical mechanics asH = frac{5}{2} N k_B T + frac{N^2}{V} (b k_B T - 2a),
where N is the number of molecules, V is volume, T is temperature (in the
Kelvin scale ), k_B isBoltzmann's constant , and a and b are constants depending on intermolecular forces and molecular volume, respectively.From this equation, we note that if we keep enthalpy constant and increase volume, temperature must change depending on the sign of b k_B T - 2a. Therefore, our inversion temperature is given where the sign flips at zero, or
k_B T_ extrm{inv} = 2a / b = frac{27}{4} k_B T_c ,
where T_c is the
critical temperature of the substance. So for T > T_ extrm{inv}, an expansion at constant enthalpy increases temperature as the work done by the repulsive interactions of the gas is dominant, and so the change inenergy is negative. But for T < T_ extrm{inv}, expansion causes temperature to decrease because the work of attractive intermolecular forces dominates, giving a positive change in energy. [cite book|author=Charles Kittel and Herbert Kroemer|title=Thermal Physics|edition=2nd Edition|publisher=W.H. Freeman|year=1980|id=ISBN 0-7167-1088-9]ee also
*
critical point
*phase transition References
External links
* [http://stp.clarku.edu/notes/chap2.pdf Thermodynamic Concepts and Processes (Chapter 2)] (part of the Statistical and Thermal Physics (STP) Curriculum Development Project at
Clark University )
Wikimedia Foundation. 2010.