1.14.57: Reversible Change
In thermodynamics the term 'reversible' means that in such a system the affinity for spontaneous change \(\mathrm{A}\) is zero; we can in fact characterize the composition of the system by the symbol \(\xi^{\mathrm{eq}}\), indicating a time independent extent of chemical reaction. The composition of the system does not change because the affinity for spontaneous change is zero.
For a reversible change the affinity for spontaneous change is zero at all stages. The composition is represented by \(\xi^{\mathrm{eq}}\), and the rate of change \(\mathrm{d} \xi^{\mathrm{eq}} / \mathrm{dt}\) is zero, at defined \(\mathrm{T}\) and \(\mathrm{p}\). We represent the volume of the system using following equation.
\[\mathrm{V}=\mathrm{V}\left[\mathrm{T}, \mathrm{p}, \xi^{\mathrm{eq}}, \mathrm{A}=0\right] \nonumber \]
This equation means that the volume, a dependent variable, is unambiguously defined by the set of variables in the square brackets, [... ]. The pressure is changed from \(\mathrm{p}\) to \(\mathrm{p} + \Delta \mathrm{p}\), such that the new equilibrium composition is \(\xi + \Delta \xi\) where the affinity for spontaneous change is zero.
\[\mathrm{V}=\mathrm{V}\left[\mathrm{T},(\mathrm{p}+\Delta \mathrm{p}), \xi^{\mathrm{eq}}(\mathrm{p}+\Delta \mathrm{p}), \mathrm{A}=0\right] \nonumber \]
Under these circumstances the change from \(\mathrm{V}(\mathrm{p})\) to \(\mathrm{V}(\mathrm{p} + \Delta \mathrm{p})\) is from one equilibrium state where \(\mathrm{A} = 0\) to another equilibrium state where \(\mathrm{A}\) is also zero. Such an equilibrium transformation is, in thermodynamic terms, reversible. All changes under the constraint that \(\mathrm{A}\) remains at zero are reversible.