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The specific heat at constant pressure and at constant volume for an ideal gas are ${ }^{C_p}$ and $C_v$ and its adiabatic and isothermal elasticities are $E_\phi$ and $E_\theta$ respectively. The ratio of $E_\phi$ to $E_\theta$ is
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$C_p / C_v$
Ratio of adiabatic and isothermal elasticities
$\frac{E \phi}{E \theta}=\frac{\gamma P}{P}=\gamma=\frac{C_p}{C_\gamma}$
$\frac{E \phi}{E \theta}=\frac{\gamma P}{P}=\gamma=\frac{C_p}{C_\gamma}$
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