Question

A polyatomic gas has $f$ vibrational degrees of freedom, then the ratio of the specific heat at constant pressure to that at constant volume will be

• A. $\frac{4+f}{3+f}$
• B. $\frac{4-f}{3-f}$
• C. $\frac{3+f}{4+f}$
• D. $\frac{3-f}{4-f}$

Answer 1

Answer: (A)

For a polyatomic atom value of specific heat at constant volume, $C_{V}=(3+f) R$
where, $f=$ vibration degree of freedom and $R=$ gas constant.
Now, $C_{p} =C_{V}+R$
$C_{p} =(3+f) R+R$
$C_{p} =(4+f) R$
Now, ratio of $C_{p}$ and $C_{V}$
$\frac{C_{p}}{C_{V}}=\frac{4+f}{3+f}$