A model in solid state theory, giving the internal energy as
where is the number density of atoms, is the maximum vibrational frequency, h is Planck's constant, k is Boltzmann's constant, and T is the temperature. This equation can be integrated in closed form in terms of polylogarithms. is defined as
where is Avogadro's number, is the density, m is the atomic weight, is the P-wave speed, and is the S-wave speed. The Debye temperature is then defined as
where the mean velocity is defined by
The thermal pressure is then defined as
Bloch-Grüneisen Resistivity, Debye Frequency, Debye Temperature
