Cv value of He is always 3R/2 but Cv value of H2 is 3R/2 at low temperature and 5R/2 at moderate temperature and more than 5R/2 at higher temperature. Explain in two or three lines.
Monoatomic Gas (He):
He is a monoatomic gas. It has only three translational degrees of freedom.
Hence, its energy per mole = (3/2)RT.
∴ CV = (∂U/∂T)V = (3/2)R
Diatomic Gas (H2):
H2 is a diatomic molecule. It has translational, rotational, and vibrational motion. At moderate temperature, contribution by vibrational motion is negligible. It has two rotational degrees of motion, contribution to energy = 2 × (1/2)RT.
Hence, total energy = (5/2)RT.
Therefore, CV = (5/2)R.
On increasing the temperature, contribution from vibrational degrees also starts and hence CV > (5/2)R.