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 monoatomic gas has 3 degrees of freedom and diatomic gas has 5 degrees of freedom.
For monoatomic gas,

$C_V=\frac{3}{2}R\text{ and }{C}_p=C_V+R=\frac{3}{2}R+R=\frac{5}{2}R$

For a diatomic gas,

$C_V=\frac{5}{2}R\text{ and }{C}_p=C_V+R=\frac{5}{2}R+R=\frac{7R}{2}$

Hence, we can conclude that the molecules of the gas can be monoatomic or rigid diatomic.