Question

Find the number of degrees of freedom of molecules in a gas if its heat capacities are $C_v=650JK{g}^{-1}{K}^{-1}$ and $C_p=910JK{g}^{-1}{K}^{-1}$.

Answer 1

The relation between $\gamma$(ratio of specific heats) and degree of freedom $f$ is

$\gamma =1+\frac{2}{f}..........\left(1\right)$

$\gamma =\frac{c_p}{c_v}$

$\gamma =1.4$

Put this in equation (1)

$1.4-1=\frac{2}{f}$

$0.4=\frac{2}{f}$

$f=5$

So the degree of freedom of the gas is 5. Hence, the gas is diatomic.