Suppose C_V and C_p denote the molar heat capacities of an ideal...

According to Mayer's relation for an ideal gas, the difference between the molar heat capacity at constant pressure ($C_p$) and the molar heat capacity at constant volume ($C_V$) is equal to the universal gas constant ($R$).

$C_p - C_V = R$

Since $R$ is a universal constant, the expression $C_p - C_V$ is a universal constant.

The other expressions depend on the atomicity (degrees of freedom) of the gas and are not universal constants.