\begin{align} \Delta U = 0 \end{align}
\begin{align} W_a = Q \end{align}
\begin{align} \frac{p_1 V_1}{T_1} &= \frac{p_2 V_2}{T_1} \\ \therefore \ \ V_2 &= \frac{p_1 V_1}{p_2} \end{align}
\begin{align} \kappa = \frac{c_p}{c_v} \end{align}
\begin{align} W_b = m c_v (T_1 - T_2) \ \ \ \ \ \ \ \ \text{ (?) } \end{align}