Question

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure $\left(C_p\right)$ and at constant volume $\left(C_v\right)$ is

• A. $\frac{5}{2}$
• B. $\frac{7}{5}$
• C. $6$
• D. $\frac{7}{2}$

Answer 1

Answer: (B)

$\frac{7}{5}$

For degree and freedom $=5$

$C_v=\frac{5}{2}R=20.8J/mol{K}^{-1}$

Now

$C_p=C_v+R$

$=5/2R+R$

$=(5/2+1)R$

$C_p=\frac{7}{2}R$

$\frac{C_p}{C_v}=\frac{7}{2}R\times \frac{2}{5R}$

$\frac{C_p}{C_v}=\frac{7}{5}$