Equipartition theorem

As we discussed yesterday the equipartition theorem states that
 
where s is the number of microscopic degrees for each of the N molecules in the system. Correspondingly the constant volume specific heat reads:

Thus the magnitude of the specific heat is governed by the total amount of microscopic degrees of freedom, Ns, of the material in question. Examples of microscopic degrees of freedom are

• translational degrees of freedom of which there are always three corresponding to , and .
• Rotational degrees of freedom around axes with a finite moment of inertia.
• Vibrational degrees of freedom: motion of individual atoms in direction along which they are constrained by their interactions with other atoms.

We note that Eq. 1 is in fact very general. It even applies to solids as we shall discuss below in greater detail.

 
• Quantum mechanics limits when degrees of freedom are thermodynamically active
• Mon-atomic and molecular gases
• Degrees of freedom per water molecule at room temperature
• Microscopic degrees of freedom for a solid: the law of Dulong and Petit
• Calorimetry demonstration experiment