Page "Absolute zero" Paragraph 10

Using the Debye model, the specific heat and entropy of a pure crystal are proportional to T < sup > 3 </ sup >, while the enthalpy and chemical potential are proportional to T < sup > 4 </ sup >.

( Guggenheim, p. 111 ) These quantities drop toward their T = 0 limiting values and approach with zero slopes.

For the specific heats at least, the limiting value itself is definitely zero, as borne out by experiments to below 10 K. Even the less detailed Einstein model shows this curious drop in specific heats.

In fact, all specific heats vanish at absolute zero, not just those of crystals.

Likewise for the coefficient of thermal expansion.

Maxwell's relations show that various other quantities also vanish.

These phenomena were unanticipated.