In a gas of diatomic molecules, the ratio of the two specific heats of gas  is:

Concept-

• The molar specific heat capacity of a gas at constant volume is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume.

• The molar specific heat of a gas at constant pressure is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.

• Internal energy (U) of a system is the total energy possessed by the system due to molecular motion and molecular configuration.
• Equipartition of energy states that the average energy of molecule in a gas associated with each degree of freedom is  where k is the Boltzmann constant and T is its absolute temperature.
• According to the equipartition theorem, the average energy of a molecule in a monoatomic gas is  as the degree of freedom is 3.
• According to the equipartition theorem, the average energy of a molecule in a diatomic gas is  if the molecules translate and rotate but do no vibrate, and is  if they vibrate also.

Explanation-

Now consider a sample of amount n moles of ideal gas. The total number of molecules is nN_A where N_A  is the Avogadro number. If the gas is diatomic, the internal energy of the gas is-

If molecules do not vibrate. In this case,

And

Then,

∴ In a gas of diatomic molecules, the ratio of the two specific heats of gas is 1.40.