The molar specific heat of a monatomic gas at constant pressure is:

Concept:

• The molar heat capacity: It is defined as the amount of heat that is needed to raise the temperature of 1 mole of the substance through 1ºC. 

There are two types of molar specific heat:

• The molar specific heat capacity of a gas at constant volume: It 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: It 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.
• If the specific heat is at constant pressure (C_P is greater than the specific heat at constant volume (C_V) then the gas constant can be expressed as CP - CV = R and this relation are termed as Mayer’s Formula.

Where, R = Gas constant, n = molar mass of the substance, CP= molar specific heat at constant pressure, CV = molar specific heat at constant volume.

Explanation:

As we have Mayer's formula;

CP - CV = R; C_P  = R + C_v....(i)

Also Cv = f/2 R...(where,f= degree of freedom = 3 for the monoatomic gases)

Hence, Equation (i) Becomes,

C_P = R + (3/2)R = (5/2)R

Key Points

• The degree of freedom of monoatomic gas is 3
• The degree of freedom of diatomic gas is 5
• The degree of freedom of polyatomic gas is 7