Heat and Thermodynamics

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 ‌

3C

7

.