# Why is isothermal expansion reversible?

Oct 8, 2016

Isothermal expansion can surely be irreversible if you make it so. In fact, any process is usually at least a bit irreversible, and truly 100% reversible processes are impossible.

We can construct an irreversible isothermal expansion to disprove the premise of the question (which states that all isothermal expansions are reversible).

Consider the Joule expansion of an ideal gas into a vacuum, which is thermally isolated ($q = 0$) and held at constant volume ($w = 0$). Therefore, $\Delta U \left(T\right) = q + w = 0$ and thus $\Delta T = 0$, an isothermal condition. You clearly cannot undo expansion into a system that had 0 pressure if you only have a piston pushing on one side. Therefore, it is irreversible, as stated first thing in the article.

A reversible isothermal expansion is an infinitisimally slow increase in the volume of the substance at constant temperature.

For an ideal gas, the internal energy $\Delta U \left(T\right) = 0$, but $q \ne 0$ and $w \ne 0$.

So, $q = - w$, i.e. the heat flow out from the system goes back into expanding it. But that would be a particularly perfect situation that doesn't entirely occur in real life. We can only approximate a reversible process.