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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.
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.
Formula Natural variables ... Derivation of heat capacity (constant volume) ... Thermodynamic equation calculator This page was last edited on 9 December 2024, at 23: ...
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. [1] The SI unit of heat capacity is joule per kelvin (J/K).
The left-hand side is the specific heat capacity at constant volume of the material. For the heat capacity at constant pressure, it is useful to define the specific enthalpy of the system as the sum (,,) = (,,) +. An infinitesimal change in the specific enthalpy will then be
Then the molar heat capacity (at constant volume) would be c V,m = 1 / 2 fR. where R is the ideal gas constant. According to Mayer's relation, the molar heat capacity at constant pressure would be c P,m = c V,m + R = 1 / 2 fR + R = 1 / 2 (f + 2)R
If the calorically perfect gas approximation is used, then the ideal gas law may also be expressed as follows = where is the number density of the gas (number of atoms/molecules per unit volume), = / is the (constant) adiabatic index (ratio of specific heats), = is the internal energy per unit mass (the "specific internal energy"), is the ...
The Mayer relation states that the specific heat capacity of a gas at constant volume is slightly less than at constant pressure. 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.