We might ask what the work would be if, once the Joule expansion has occurred, the gas is put back into the left-hand side by compressing it. The best method (i.e. the method involving the least work) is that of a reversible isothermal compression, which would take work W given by W = − − ∫ ∫ 2 V 0 V 0 P d V = − − ∫ ∫ 2 V 0 V 0 n R T V d V = n R T ln ⁡ ⁡ 2 = T Δ Δ S gas .