An ideal gas initially at P1, V1, T1 undergoes a reversible isothermal expansion to P2, V2, T1. The same change in state of the gas can be accomplished by allowing it to expand adiabatically to P3, V2, T2 and then heating it at constant volume to P2, V2, T1. Show that the entropy change for the reversible isothermal expansion is the same as the sum of the entropy changes in the reversible adiabatic expansion and the reversible heating to P2, V2, T1. This shows that S is independent of path and is therefore a state function