Question

a) State the principle of equipartition of energy. Write a relation between number of
degrees of freedom, number of particles constituting the system and the total number
of constraints. Calculate the degrees of freedom for (i) single atom, (ii) diatomic
molecule.

Answer 1

Answer on Question #61169-Physics-Molecular physics | Thermodynamics

State the principle of equipartition of energy.

Answer

In a system in thermal equilibrium, on the average, an equal amount of energy will be associated with each independent energy state. This law states specifically that a system of particles in equilibrium at absolute temperature T will have an average energy of $\frac{1}{2}kT$ associated with each degree of freedom. In addition, any degree of freedom contributing potential energy will have another $\frac{1}{2}kT$ associated with it. For a system of s degrees of freedom, of which t have associated potential energies, the total average energy of the system is $\frac{1}{2}(s+t)kT$.

Write a relation between number of degrees of freedom $f$, number of particles constituting the system $p$ and the total number of constraints $c$.

Answer

$$f = 3p - c$$

Calculate the degrees of freedom for (i) single atom, (ii) diatomic molecule.

Solution

(i) $p = 1, c = 0$.

$$f = 3(1) - 0 = 3$$

(ii) $p = 2, c = 1$.

$$f = 3(2) - 1 = 5$$