N mole ideal gas with an initial state $P_1,V_1,$ and $T_1,$ experiences a quasi$-$static adiabatic expansion to $P_2,V_2$ and $T_2.$ Please prove, if this $n$ mole ideal gas from $P_1,V_1$ and $T_1$ adiabatically expands against a constant pressure to the same final volume $V_2,$ the final temperature $T_2^{\text{'}}$ must be higher than $T_2.(10$ points$)$