Heat Capacity

Abstract

The heat capacity of any solid body is determined by the normal modes of vibrations available to its structure. If the spectrum of vibrational states, ρ(ω)dω, which gives the number of modes of vibration whose frequencies lie between ω and ω + dω, is established for a solid body the heat capacity C of a unit volume of the body can be immediately determined as

$$ C = {k_B}\int {p(\omega )} {\left( {\frac{{\hbar \omega }}{{{k_B}T}}} \right)^2}\frac{{\exp \left( {\hbar \omega /{k_B}T} \right)}}{{{{\left[ {\exp (\hbar \omega /{k_B}T) - 1} \right]}^2}}}$$

((1.1))

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