Question

If a gas has ${}^{\prime }{f}^{\prime }$ degree of freedom, the ratio of specific heats of the gas $\left(\frac{C_P}{C_V}\right)$ is

• A. $\frac{1+f}{2}$
• B. $1+\frac{f}{2}$
• C. $1+\frac{1}{f}$
• D. $1+\frac{2}{f}$

Answer 1

The correct option is D $1+\frac{2}{f}$

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

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