Correct Answer - Option 4 : 5/2 R
Concept:
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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:
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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.
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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 (CP is greater than the specific heat at constant volume (CV) 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; CP = R + Cv....(i)
Also Cv = f/2 R...(where,f= degree of freedom = 3 for the monoatomic gases)
Hence, Equation (i) Becomes,
CP = R + (3/2)R = (5/2)R
- 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