$\mathrm{~ O ~ W e i r i s o s t y ~ T o p p r}$
The molar specific heats of a gas having $\mathrm{f}$ degrees of freedom is given by :
$$
\mathrm{C}_{\mathrm{r}}=\frac{1}{2} \mathrm{f} \mathrm{R}
$$
and $\mathrm{C}_{\mathrm{p}}=\mathrm{C}_{\mathrm{v}}+\mathrm{R}$ [From $1^{\text {t }}$ law of thermodynamic]
$$
\begin{array}{l}
\mathrm{C}_{\mathrm{p}}=\left(\frac{\mathrm{f}}{2}+1\right) \mathrm{R} \\
\frac{(\mathrm{f}+2)}{2} \mathrm{R}
\end{array}
$$
Thus ratio, $\mathrm{r}=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{(\mathrm{f}+2) \mathrm{R}}{2} \times \frac{2}{\mathrm{fR}}=\frac{\mathrm{f}+2}{\mathrm{f}}$
Derive expression for the ratio of specific heats $\gamma$ if the gas has $\mathrm{f}$ degrees of freedom.
Derive expression for the ratio of specific heats $\gamma$ if the gas has $\mathrm{f}$ degrees of freedom.