The molar specific heat capacity of a diatomic gas at constant pressure is C. The molar specific heat capacity of a monoatomic gas at constant volume is
Molar heat capacity at constant pressure for a diatomic gas, Cp=C We need to find the molar heat capacity at constant volume for a monoatomic gas, CV. Calculations: For a Diatomic Gas: For a diatomic gas, the molar heat capacity at constant volume is: CV=‌
5
2
R Therefore, the relation between Cp and CV is: Cp=CV+R=‌
5
2
R+R=‌
7
2
R Since Cp=C, we have: ‌
7
2
R=C Solving for R, we get: R=‌
2C
7
For a Monoatomic Gas: The molar heat capacity at constant volume for a monoatomic gas is: CV=‌
3
2
R Substituting the value of R from Equation (i): CV=‌
3
2
⋅‌
2C
7
=‌
3C
7
Therefore, the molar specific heat capacity of a monoatomic gas at constant volume is ‌