Every solid-metallic, nonmetallic, crystalline, or even amorphous — can be considered as a more or less regular three-dimensional lattice of atoms. Each of them is fixed in its position by elastic forces that are functions of the atomic distances and the properties of the neighboring atoms. By far the most important contribution to the internal energy of a solid is the energy stored in the thermal vibration of its atoms in the lattice. These vibrations of an average atom are three dimensional and may be resolved into three independent vibrations parallel to the three coordinate axes.

Similar to the kinetic theory of gases, the kinetic theory of solids assigns to each component the energy

\[\dfrac{\tilde{R}T}{\tilde{\mbox{L}}}=kT\;\;\;\;\;\;\mbox{joules per average atom}\]

where \(\tilde{R}/\tilde{\mbox{L}}=\) k is the Boltzmann atomic constant with the value 1.380 × 10^–23 J/K per single atom. (In gases the energy assigned to each degree of freedom is kT/2 due to the absence of elastic forces.)

In consequence, a solid with the mass M, containing \(M\tilde{\mbox{L}}/\tilde{M}_{\rm at}\) atoms, should have the internal energy content