Question #42592

A rigid, adiabatic container of total volume $V$ is divided by a thin, insulating partition. One side contains $4$ moles of a monatomic ideal gas at $240\text{ K}$, and the inner walls in contact with this gas have a heat capacity of $C_{cal} = 4R$. The other side contains $2$ moles of a diatomic ideal gas at $900\text{ K}$ (the walls on this side have negligible heat capacity). The partition is removed, allowing the gases to mix and reach thermal equilibrium. For the diatomic gas, vibrational degrees of freedom are completely frozen below $600\text{ K}$ and fully active at or above $600\text{ K}$ (assume a sharp transition). What is the final partial pressure of the diatomic gas? ($R$ is the universal gas constant).