The change in temperature in free expansion of gas is expressed in terms of Joule’s coefficient which is given by :

As In Vanderwall’s gas an internal pressure (P’=a/V^2) developed due to intermolecular attractions.

Therefore Internal work done in Joule’s expansion against internal pressure is :

Due to decrease in internal kinetic energy, the temperature of gas decreases by ΔT and C is heat constant, then decrease in Kinetic energy is :

This is an expression for Joule’s coefficient. I hope you understand this topic, still any query you can write to us in comment box. 😊