III Consider a container like that shown in Figure \(20.12\), with \(n_{1}\) moles of a monatomic gas on one side and \(n_{2}\) moles of a diatomic gas on the other. The monatomic gas has initial temperature $T_{1{\mathrm{li}}^{-}}$. The diatomic gas has initial temperature \(T_{2 \mathrm{i}}\).

a. Show that the equilibrium thermal energies are

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