Application of law of equipartition energy in specific heat of a gas, Meyer’s relation Cp – Cv = R connects the two specific heats for one mole of an ideal gas.
Equipartition law of energy is used to calculate the value of Cp – Cv and the ratio between them \(γ = \frac{C_P}{C_V}\) . Here γ is called adiabatic exponent.
(i) Monoatomic molecule : Average kinetic energy of a molecule = [\(\frac{3}{2}\)kT]
Total energy of a molecule of gas = \(\frac{3}{2}\) kT x NA = \(\frac{3}{2}\)RT
For one mole, the molar specific heat at constant volume
(ii) Diatomic molecule : Average kinetic energy of a diatomic molecule at low temperature = \(\frac{5}{2}\)kT
Total energy of one mole of gas = \(\frac{5}{2}\) kT x NA = \(\frac{5}{2}\) RT
(Here, the total energy is purely kinetic For one mole specific heat at constant volume)
Note that the Cv and Cp are higher for diatomic molecules than the mono atomic molecules. It implies that to increase the temperature of diatomic gas molecules by 1°C it require more heat energy than monoatomic molecules.
(iii) Triatomic molecule
(a) Linear molecule:
(b) Non-linear molecule:
Note that according to kinetic theory model of gases the specific heat capacity at constant volume and constant pressure are independent of temperature. But in reality it is not sure. The specific heat capacity varies with the temperature.
