What is the reason behind the phenomenon of Joule-Thomson effect?

For an ideal gas there is no heating or cooling during an adiabatic expansion or contraction, but for real gases, an adiabatic expansion or contraction is generally accompanied by a heating or cooling effect. What is the reason behind such a phenomenon? Is it related to the property of real gases or is it something else?

1 Answer

In a reversible adiabatic expansion or compression, the temperature of an ideal gas does change.

In a Joule-Thompson type of irreversible adiabatic expansion (e.g., in a closed container), the internal energy of the gas does not change. For an ideal gas, its internal energy depends only on its temperature. So, for an irreversible adiabatic expansion of an ideal gas in a closed container, its temperature does not change. But, the internal energy of a real gas depends not only on its temperature but also on its specific volume (which increases in an expansion). So, for a real gas, its temperature changes. The Joule-Thompson effect is one measure of the deviation of a gas from ideal gas behavior.

ADDENDUM

This addresses a comment from the OP regarding the effect of specific volume on the internal energy of a real gas.

Irrespective of the Joule-Thompson effect, one can show (using a combination of the first and second laws of thermodynamics) that, for a pure real gas, liquid, or solid (or one of constant chemical composition), the variation of specific internal energy with respect to temperature and specific volume is given by: $$dU=C_vdT-\left[P-T\left(\frac{\partial P}{\partial T}\right)_V\right]dV$$The first term describes the variation with respect to temperature and the second term describes the variation with respect to specific volume. For an ideal gas, the second term is equal to zero. However, for a real gas, the second term is not equal to zero, and that means that, at constant internal energy (as in the Joule-Thompson effect), the temperature will change when the specific volume changes. This is a direct result of the deviation from ideal gas behavior.

• Could you elaborate on the internal energy dependency of real gases in the Joule-Thompson effect? – J_B892 Mar 21 '18 at 8:18
• See my Addendum. – Chet Miller Mar 21 '18 at 12:15
• It's my understanding that, in a Joule-Thompson expansion, the internal energy can change, and what stays constant is the enthalpy, i.e., U + PV. – theorist Jan 10 at 22:23
• @theorist There are actually two versions of JT. One is the version you referred to involving steady flow through a porous plug or valve. The other version is a closed system containing two chambers separated by a partition. The initial pressures in the two chambers are unequal, and the partition is either totally removed or punctured. In this case, the total internal energy is constant. – Chet Miller Jan 10 at 23:35
• I believe what you were initially describing is typically referred to as a Joule expansion, as distinguished from a Joule-Thomson expansion. At least that's how I've always seen the two distinguished (e.g., www-thphys.physics.ox.ac.uk/people/AlexanderSchekochihin/A1/…) (though that author really shouldn't be putting deltas in front of W or Q). – theorist Jan 11 at 1:27