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 $C_p=C_V+R$
$=R+\frac{5}{2}R=\frac{7R}{2}$
Hence, we can conclude that the molecules of the gas can be monoatomic or rigid diatomic.