The entropy for a certain monatomic gas has been empirically determined to be given by the expression \(S=\frac{7}{2} N \ln E_{\mathrm{th}}+N E_{\mathrm{th}}^{2} / 15\). Express the factor \(1 / k_{\mathrm{B}} T\) for this gas in terms of \(N\) and \(E_{\mathrm{ch}}\).