Molar heat capacity at constant pressure for a diatomic gas,
Cp=CWe 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=‌RTherefore, the relation between
Cp and
CV is:
Cp=CV+R=‌R+R=‌RSince
Cp=C, we have:
‌R=CSolving for
R, we get:
R=‌For a Monoatomic Gas:
The molar heat capacity at constant volume for a monoatomic gas is:
CV=‌RSubstituting the value of
R from Equation (i):
CV=‌⋅‌=‌Therefore, the molar specific heat capacity of a monoatomic gas at constant volume is
‌.