State the equipartition theorem and describe how it explains

State the equipartition theorem and describe how it explains the temperature behavior the molar heat capacity of gases.

Solution

The equipartition theorem states that energy is shared equally amongst all energetically accessible
degrees of freedom of a system. This is not a particularly surprising result, and can be thought of as
another way of saying that a system will generally try to maximise its entropy (i.e. how ‘spread out’ the
energy is in the system) by distributing the available energy evenly amongst all the accessible modes
of motion.

The average translational kinetic energy of a particle in a gas is therefore 3/2 kT, or ½ kT per
translational degree of freedom, in agreement with the equipartition theorem.