Calculate the contribution of the first excited electronic state, namely \({ }^{1} \Delta\) with \(g_{e}=2\), of the \(\mathrm{O}_{2}\) molecule toward the Helmholtz free energy and the specific heat of oxygen gas at a temperature of \(5000 \mathrm{~K}\); the separation of this state from the ground state, namely \({ }^{3} \Sigma\) with \(g_{e}=3\), is \(7824 \mathrm{~cm}^{-1}\). How would these results be affected if the parameters \(\Theta_{r}\) and \(\Theta_{v}\) of the \(\mathrm{O}_{2}\) molecule had different values in the two electronic states?