Joule expansion

The Joule expansion (also called free expansion) is an irreversible process in thermodynamics in which a volume of gas is kept in one side of a thermally isolated container (via a small partition), with the other side of the container being evacuated. The partition between the two parts of the container is then opened, and the gas fills the whole container.

The Joule expansion, treated as a thought experiment involving ideal gases, is a useful exercise (often called a free expansion) in classical thermodynamics. It provides a convenient example for calculating changes in thermodynamic quantities, including the resulting increase in entropy of the universe (entropy production) that results from this inherently irreversible process. An actual Joule expansion experiment necessarily involves real gases; the temperature change in such a process provides a measure of intermolecular forces.

This type of expansion is named after James Prescott Joule who used this expansion, in 1845, in his study for the mechanical equivalent of heat, but this expansion was known long before Joule e.g. by John Leslie, in the beginning of the 19th century, and studied by Joseph-Louis Gay-Lussac in 1807 with similar results as obtained by Joule.

The Joule expansion should not be confused with the Joule-Thompson effect.

The process begins with gas under some pressure, ${\displaystyle P_{\mathrm {i} }}$, at temperature ${\displaystyle T_{\mathrm {i} }}$, confined to one half of a thermally isolated container (see the top part of the drawing at the beginning of this article). The gas occupies an initial volume ${\displaystyle V_{\mathrm {i} }}$, mechanically separated from the other part of the container, which has a volume ${\displaystyle V_{\mathrm {0} }}$, and is under near zero pressure. The tap (solid line) between the two halves of the container is then suddenly opened, and the gas expands to fill the entire container, which has a total volume of ${\displaystyle V_{\mathrm {f} }=V_{\mathrm {i} }+V_{\mathrm {0} }}$ (see the bottom part of the drawing). A thermometer inserted into the compartment on the left (not shown in the drawing) measures the temperature of the gas before and after the expansion.

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