1.2 mol of a monatomic ideal gas at 450 K expands adiabatically until it has cooled to 310 K…

Adiabatic: $Q = 0$, so $W = -\Delta U = nC_v(T_1 - T_2) = \dfrac{p_1V_1 - p_2V_2}{\gamma - 1}$. Along the way $pV^\gamma$ and $TV^{\gamma - 1}$ stay the same. Squeezed, the gas warms; expanding, it cools.

Molar heat capacities: $C_v = \tfrac{f}{2}R$ and $C_p = C_v + R$ (Mayer), with $\gamma = \dfrac{C_p}{C_v}$. Monatomic: $12.5\ \text{J mol}^{-1}\text{K}^{-1}$, $20.8\ \text{J mol}^{-1}\text{K}^{-1}$, $\gamma = 1.67$. Diatomic: $20.8\ \text{J mol}^{-1}\text{K}^{-1}$, $29.1\ \text{J mol}^{-1}\text{K}^{-1}$, $\gamma = 1.40$. $Q = nC\,\Delta T$, and $\Delta U = nC_v\,\Delta T$ in every process.