# What is the difference between the Joule and Joule–Thomson coefficients?

Is there a difference between the Joule coefficient and the Joule–Thomson coefficient? Also, I am having a hard time understanding what they mean.

## 1 Answer

The Joule coefficient is $$\left(\frac{\partial T}{\partial V}\right)_U$$

Experimentally, Joule attempted to measure this value by expanding gas into an evacuated, insulated container, thus ensuring $$U$$ is constant.

The Joule–Thomson coefficient is $$\left(\frac{\partial T}{\partial P}\right)_H$$

Experimentally, this is realized by expanding a flow of gas in an insulted pipe from a high pressure upstream region to a lower pressure downstream region, the two regions being seperated by a porous frit.

For more information see THE JOULE AND JOULE-THOMSON EXPERIMENTS by Dr. J. B. Tatum, University of Victoria.

• So, the Joule coefficient is a ratio of the change in temperature to the change in volume with constant internal energy, and the Joule-Thomson coefficient is a ratio of the change in temperature to the change in pressure under constant enthalpy? In the Joule experiment, the gas does no work, and the temperature doesn't change? – user4696 Feb 11 '15 at 15:19
• This almost correct, only your statement "the temperature doesn't change" is incorrect. Joule didn't detect a temperature change, because his equipment wasn't good enough, but for a real gas (not an ideal gas) there is a temperature change. – DavePhD Feb 11 '15 at 15:22