Given that

The molar specific heat of a gas as given from the kinetic theory is $\frac{5}{2} R$ As we know that

$C _{ v }=\frac{ fR }{2} \text { and } C _{ p }=\left(1+\frac{ f }{2}\right) R$

where $f$ is the degree of freedom and $R$ is gas constant

Case $1:$

If the given specific heat is $C _v$, then $f =5$ then the gas will rigid diatomic

Case $2:$

If the given specific heat is $C _p$, then $f =3$

Then the gas will be monoatomic