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The volumetric heat capacity of a material is the heat capacity of a sample of the substance divided by the volume of the sample. It is the amount of energy that must be added, in the form of heat, to one unit of volume of the material in order to cause an increase of one unit in its temperature.
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 ...
J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 6, Thermodynamic Properties; Table 6.3, Enthalpies and Gibbs Energies of Formation, Entropies, and Heat Capacities of the Elements and Inorganic Compounds
In chemistry, heat amounts are often measured in calories. Confusingly, two units with that name, denoted "cal" or "Cal", have been commonly used to measure amounts of heat: The "small calorie" (or "gram-calorie", "cal") is exactly 4.184 J. It was originally defined so that the heat capacity of 1 gram of liquid water would be 1 cal/°C.
This is a derivation to obtain an expression for for an ideal gas. An ideal gas has the equation of state: = where P = pressure V = volume n = number of moles R = universal gas constant T = temperature. The ideal gas equation of state can be arranged to give:
Thus water behaves as though it is an ideal gas that is already under about 20,000 atmospheres (2 GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100 kPa to 200 kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002 ...
However, in a process without a constant volume, the heat addition affects both the internal energy and the work (i.e., the enthalpy); thus the temperature changes by a different amount than in the constant-volume case and a different heat capacity value is required.
To achieve the same increase in temperature, more heat energy is needed for a gram of that substance than for a gram of a monatomic gas. Thus, the specific heat capacity per mole of a polyatomic gas depends both on the molecular mass and the number of degrees of freedom of the molecules. [25] [26] [27]