The Joule and Joule–Thomson Experiments

Consider an adiabatic system, where chamber A is filled with a gas at a fixed temperature, pressure, and volume, while chamber B is empty.

When the gas is forced through a rigid porous barrier from the high-pressure region in A to the low-pressure region in B, the gas expands, changing its volume and temperature, and, as a result, its internal energy.

Because no heat is transferred, the internal energy change equals the difference between work done on and by the gas.

Rearranging the terms and replacing the sum U + pV with enthalpy shows this process to be isenthalpic.

Whether the gas cools or warms during this expansion depends on the Joule–Thomson coefficient, ��. It is defined as the rate at which temperature changes with pressure at constant enthalpy.

It can also be written as the negative of the change in enthalpy with pressure at constant temperature, divided by the heat capacity at constant pressure.

For ideal gases, μ equals zero, so expansion causes no temperature change. But for real gases, �� can be positive or negative, implying cooling or heating during expansion.