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The specific heat capacity of a substance, especially a gas, may be significantly higher when it is allowed to expand as it is heated (specific heat capacity at constant pressure) than when it is heated in a closed vessel that prevents expansion (specific heat capacity at constant volume).
Table of specific heat capacities at 25 °C (298 K) unless otherwise noted. [citation needed] Notable minima and maxima are shown in maroon. Substance Phase Isobaric mass heat capacity c P J⋅g −1 ⋅K −1 Molar heat capacity, C P,m and C V,m J⋅mol −1 ⋅K −1 Isobaric volumetric heat capacity C P,v J⋅cm −3 ⋅K −1 Isochoric ...
These two factors (constancy of atomic volume and constancy of mole-specific heat capacity) result in a good correlation between the volume of any given solid chemical element and its total heat capacity. Another way of stating this, is that the volume-specific heat capacity (volumetric heat capacity) of solid elements is roughly a constant.
A corresponding expression for the difference in specific heat capacities (intensive properties) at constant volume and constant pressure is: = where ρ is the density of the substance under the applicable conditions.
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.
Replacing work with a change in volume gives = Since the process is isochoric, dV = 0, the previous equation now gives = Using the definition of specific heat capacity at constant volume, c v = (dQ/dT)/m, where m is the mass of the gas, we get =
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.
Constant-volume specific heat capacity of diatomic gases (real gases) between about 200 K and 2000 K. This temperature range is not large enough to include both quantum transitions in all gases. Instead, at 200 K, all but hydrogen are fully rotationally excited, so all have at least 5 / 2 R heat capacity.