Let $P_1, V_1, T_1$ be the initial pressure, volume and the temperature of the gas, respectively. For isothermal expansion (1 to 2), we have

         $V_2 = 2V_1 ; P_1{V}_1 = P_2 V_2$

         $P_2 = P_1\left(\raisebox{1ex}{$V_1$}\!\left/ \!\raisebox{-1ex}{$V_2$}\right.\right) = \raisebox{1ex}{$P_1$}\!\left/ \!\raisebox{-1ex}{$2$}\right. = 0.5 \times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$
 
        $T_2 = T_1 = 300 \mathrm{K}$

For adiabatic expansion (2 to 3),

    ${\mathit{\text{P}}}_2{\mathit{\text{V}}}_2^{\gamma }={\mathit{\text{P}}}_3{\mathit{\text{V}}}_3^{\gamma }$

$\Rightarrow {\mathit{\text{V}}}_3=2{\mathit{\text{V}}}_2$

$\Rightarrow {\mathit{\text{P}}}_3={\mathit{\text{P}}}_2{\left(\frac{{\mathit{\text{V}}}_2}{{\mathit{\text{V}}}_3}\right)}^{\gamma }=\text{0.5}\times 10^5\times {\left(\text{0.5}\right)}^{\text{1.4}}$

$\Rightarrow P_3={\left(0.5\right)}^{2.4}\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$