Heat Capacity of Blackbody

In Mathematical Physics of Blackbody Radiation I derive an expression for the heat capacity C(T) of a blackbody in the form of a forced damped wave equation as function of temperature T, of the form

• C(T)= c T

with c a constant, thus with a linear dependence on T. This fits pretty well with observations for several solid metals for temperatures T smaller than 200 K, and for diamond up to 500 K, as shown above.

Recall that the theory of specific heats was studied intensely in the beginning of the 20th century: Einstein and Debye offered improvements for low temperatures of the classical Dulong-Petit Law C(T) = constant, using arguments from statistical mechanics.

I do not use statistical mechanics but instead a concept of finite precision computation.