Isochoric molar heat capacity of ideal gas via degrees of freedom

The internal energy of an ideal gas consisting of molecules whose energy is all kinetic depends only on the degrees of freedom of the molecule and the temperature of the gas. From that one can derive the expression of the isochoric heat capacity of ideal gases.

Notation:

1. \(R\) (R) is molar_gas_constant.

Notes:

1. For applications, see internal energy of ideal gas.

2. \(f = 3\) for monatomic molecules.

3. \(f = 5\) for diatomic molecules.

4. \(f = 6\) for non-linear polyatomic molecules.

Conditions:

1. Gas is ideal.

2. Works in the classical theory of heat capacity of gases. For a more accurate representation refer to the quantum theory, which accounts for the “freezing” of the degrees of freedom and other phenomena.

Links:

1. Physics LibreTexts, “Equipartition Theorem”.

isochoric_molar_heat_capacity

molar_heat_capacity at constant volume.

Symbol:

c_Vm

Latex:

\(c_{V, m}\)

Dimension:

energy/(amount_of_substance*temperature)

degrees_of_freedom

Number of degrees_of_freedom of gas molecules.

Symbol:

f

Latex:

\(f\)

Dimension:

dimensionless

law

c_Vm = f / 2 * R

Latex:

\[c_{V, m} = \frac{f}{2} R\]