= Specific heats of a monatomic gas-radiation mixture
{title2=$c_P=\mathcal R(32-24\beta-3\beta^2)/(2\beta^2)$}
For fixed-composition monatomic <ideal gas> plus equilibrium <blackbody radiation>, let $\mathcal R=k/(\mu H)$ and $\beta=P_g/P$. The mass-specific heats are $c_P=\mathcal R(32-24\beta-3\beta^2)/(2\beta^2)$ and $c_V=\mathcal R(24-21\beta)/(2\beta)$. The <specific-heat ratio> is $\Gamma_1/\beta$, not generally any one of the <stellar adiabatic exponents>. Differentiate at constant total pressure rather than at constant $\beta$.
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