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The difference relation allows one to obtain the heat capacity for solids at constant volume which is not readily measured in terms of quantities that are more easily measured. The ratio relation allows one to express the isentropic compressibility in terms of the heat capacity ratio.
The term specific heat may also refer to the ratio between the specific heat capacities of a substance at a given temperature and of a reference substance at a reference temperature, such as water at 15 °C; [5] much in the fashion of specific gravity. Specific heat capacity is also related to other intensive measures of heat capacity with ...
Since both the heat capacity of an object and its volume may vary with temperature, in unrelated ways, the volumetric heat capacity is usually a function of temperature too. It is equal to the specific heat c ( T ) {\displaystyle c(T)} of the substance times its density (mass per volume) ρ ( T ) {\displaystyle \rho (T)} , both measured at the ...
The corresponding intensive property is the specific heat capacity, found by dividing the heat capacity of an object by its mass. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity. The volumetric heat capacity measures the heat capacity per volume.
In the first, constant-volume case (locked piston), there is no external motion, and thus no mechanical work is done on the atmosphere; C V is used. In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case.
This relation was built on the reasoning that energy must be supplied to raise the temperature of the gas and for the gas to do work in a volume changing case. According to this relation, the difference between the specific heat capacities is the same as the universal gas constant. This relation is represented by the difference between Cp and Cv:
The first law of thermodynamics is essentially a definition of heat, i.e. heat is the change in the internal energy of a system that is not caused by a change of the external parameters of the system. However, the second law of thermodynamics is not a defining relation for the entropy.
where α is an exponent specific to the system (e.g. in the absence of a potential field, α = 3/2), z is exp(μ/k B T) where μ is the chemical potential, Li is the polylogarithm, ζ is the Riemann zeta function, and T c is the critical temperature at which a Bose–Einstein condensate begins to form.