Fastest frozen temperature for a thermodynamic system

Abstract

For a thermodynamic system obeying both the equipartition theorem in high temperature and the third law in low temperature, the curve showing relationship between the specific heat and the temperature has two common behaviors: it terminates at zero when the temperature is zero Kelvin and converges to a constant value of specific heat as temperature is higher and higher. Since it is always possible to find the characteristic temperature TC to mark the excited temperature as the specific heat almost reaches the equipartition value, it is also reasonable to find a temperature in low temperature interval, complementary to TC. The present study reports a possibly universal existence of the such a temperature ϑ, defined by that at which the specific heat falls fastest along with decrease of the temperature. For the Debye model of solids, below the temperature ϑ the Debye’s law manifest itself.