Free expansion

A free expansion is the irreversible rush of a gas into an evacuated space when a valve or partition is opened. Because the gas expands against nothing, it does no work (W = 0); if the container is insulated, no heat is exchanged (Q = 0); so by the first law the internal energy is unchanged, ΔU = 0. It is the cleanest example of a process that is adiabatic yet violently irreversible.

James Joule performed the experiment in the 1840s and found that, for a dilute gas, the temperature did not change. Since U was constant and the volume changed while the temperature did not, the internal energy of an ideal gas cannot depend on volume at all — it must depend on temperature alone, U = U(T). This is the assumption that makes ΔU = 0 along every isotherm legitimate.

For real gases there is a small temperature change on free expansion, because intermolecular forces store a little potential energy that shifts as the spacing changes; this is the basis of the Joule–Thomson effect used in refrigeration. The ideal-gas result is the limiting case as the gas becomes dilute. A free expansion has no path on a PV diagram, since the gas has no single pressure while it is rushing outward.

Performed by Joule (and refined with Kelvin in the Joule–Thomson experiments of the 1850s) to test whether a gas's internal energy depends on its volume; the null result for dilute gases anchored the ideal-gas relation U = U(T).