Question

Derive expression for the ratio of specific heats $\gamma$ if the gas has $f$ degrees of freedom.

Answer 1

The molar specific heats of a gas having $f$ degrees of freedom is given by :

$C_v=\frac{1}{2}fR$

and $C_p=C_v+R$ [From $1^{st}$ law of thermodynamic ]

$C_p=(\frac{f}{2}+1)R$

$\frac{(f+2)}{2}R$.

Thus ratio, $r=\frac{C_p}{C_v}=\frac{(f+2)R}{2}\times \frac{2}{fR}=\frac{f+2}{f}$