a body made of the material in question (J/K), n is the amount of substance in the body (mol), R is the gas constant (J/(K⋅mol)), N is the number of molecules in the body (dimensionless), kB is the Boltzmann constant (J/(K⋅molecule)). In the ideal gas article, dimensionless heat capacity is expressed as and is related there directly to half the number of degrees of freedom per particle. This holds true for quadratic degrees of freedom, a consequence of the equipartition theorem. More generally, the dimensionless heat capacity relates the logarithmic increase in temperature to the increase in the dimensionless entropy per particle , measured in nats. Alternatively, using base-2 logarithms, relates the base-2 logarithmic increase in temperature to the increase in the dimensionless entropy measured in bits. Heat capacity at absolute zero From the definition of entropy the absolute entropy can be calculated by integrating from zero to the final temperature Tf: Thermodynamic derivation In theory, the specific heat capacity of a substance can also be derived from its abstract thermodynamic modeling by an equation of state and an internal energy function. State of matter in a homogeneous sample To apply the theory, one considers the sample of the substance (solid, liquid, or gas) for which the specific heat capacity can be defined; in particular, that it has homogeneous composition and fixed mass . Assume that the evolution of the system is always slow enough for the internal pressure and temperature be considered uniform throughout. The pressure would be equal to the pressure applied to it by the enclosure or some surrounding fluid, such as air. The state of the material can then be specified by three parameters: its temperature , the pressure , and its specific volume , where is the volume of the sample. (This quantity is the reciprocal of the material's density .) Like and , the specific volume is an intensive property of the material and its state, that does not depend on the amount of substance in the sample. Those variables are not independent. The allowed states are defined by an equation of state relating those three variables: The function depends on the material under consideration. The specific internal energy stored internally in the sample, per unit of mass, will then be another function of these state variables, that is also specific of the material. The total internal energy in the sample then will be