Question

The molar specific heat of a gas as given from the kinetic theory is $\frac{5}{2} R$. If it is not specified whether it is $C_{p}$ or $C_{V}$, one could conclude that the molecules of the gas

• A. are definitely monoatomic
• B. are definitely rigid diatomic
• C. are definitely non-rigid diatomic
• D. can be monoatomic or rigid diatomic

Answer 1

Answer: (D)

A monoatomic gas has $3$ degrees of freedom and diatomic gas has $5$ degrees of freedom.
For monoatomic gas,
$c_{V}=\frac{3}{2} R$
and $ C_{p}=C_{V}+R$
$=R+\frac{3}{2} R=\frac{5}{2} R$
For a diatomic gas,
$C_{V} =\frac{5}{2} R $
and $ C_{p}=C_{V}+R$
$=R+\frac{5}{2} R=\frac{7 R}{2}$
Hence, we can conclude that the molecules of the gas can be monoatomic or rigid diatomic.