Question

Do State Law of equipartition of energy use this law to calculate specific heats of monoatomic diatomic and triatomic gases​

Answer 1

The law states that: “In thermal equilibrium, the total energy of the molecule is divided equally among all Degrees of Freedom of motion”.

Here is the derivation of monoatomic gases i.e. which have 3° of freedom.

Further you can solve by replacing the degrees of freedom .

Answer 2

Law of equipartition of energy and its applications are as follows:

Explanation:

LAW OF EQUIPARTITION:

• The energy of the molecules of a gas, in thermal equilibrium at thermodynamic temperature T and having a large number of molecules, is divided equally among the available degrees of freedom, the energy of each molecule is equal to  $1/2 k_{B} T$, where $k_{B}$ is the Boltzmann constant.

(a) Monoatomic gas:

• For an atomic gas, each atom has only three degrees of freedom because only transfer motion can take place.
• Therefore, the average energy per atom is $3/2 k_{B} T$.
• The total internal energy per mole of gas is E = $3/2 N_{A} k_{B} T$, where $N_{A}$ is the Avogadro number.

(b) Diatomic gas:

• Treating the molecules of a diatomic gas as rigid rotators, each molecule has three translational degrees of freedom and two rotational degrees of freedom.
• Therefore, the average energy per molecule is meaningful
• $3(1/2 k_{B} T) + 2(1/2 k_{B} T) = 5/2 k_{B} T$
• The total internal energy per mole of the gas is
• E = $5/2 N_{A} k_{B} T$