@@ -99,7 +99,9 @@ An empirical observation, also known as the **law of Dulong–Petit** (1819):
This corresponds to what we know from statistical physics. Under the assumption that the atomic potential is parabolic, the equipartition theorem states that each degree of freedom contributes $k_B/2$ to the heat capacity. As we consider a 3D solid, each atom contains 3 spatial and 3 momentum degree of freedom. Therefore, the total heat capacity per atom is given by $C = 3k_B$.
### Complication
However, at low temperatures a discrepancy is observed between the heat capacity of diamond[^2] and the law of Dulong–Petit. This suggests that we need a different model to describe the heat capacity at low temperatures.
However, at low temperatures we see that the heat capacity of diamond drops below the prediction of the law of Dulong–Petit.
This suggests that we need a different model to describe the heat capacity at low temperatures.
Following Einstein's reasoning[^2] we will now explain this puzzle.
