Question

One mole of an ideal gas initially at 10.00 bar and 298.0K is allowed to expand against a constant external pressure of 2.000 bar to a final pressure of 2.000 bar. During this process, the temperature of the gas falls to 253.2K. We wish to construct a reversible path connecting these initial and final steps as a combustion of a reversible isothermal expansion followed by a reversible adiabatic expansion. To what volume should we allow the gas to expand isothermally so that subsequent adiabatic expansion is guaranteed to take the gas to the final state? Assume that C_v,m= (3/2)R