Diatomic ideal gas heat capacity at constant volume

Description

Heat capacity or thermal capacity is a physical quantity equal to the ratio of the heat that is added to (or removed from) an object to the resulting temperature change.

The SI unit of heat capacity is joule per kelvin (J/K). However, several other units of measure have been used for this quantity in the past, and are still used in certain contexts.

Heat capacity is an extensive property of matter, meaning that it is proportional to the size of the object. To express the corresponding intensive property of a substance, the heat capacity of a sample is divided by the amount of substance in it.

If the amount is taken to be the mass of the sample, the result is the specific heat capacity, often called simply specific heat (with the SI unit of joule per kelvin per kilogram, J/K/kg). If the amount is taken to be the number of moles of the substance, one gets the molar heat capacity (with the SI unit of joule per kelvin per mole, J/K/mol). If the amount is taken to be the volume of the sample (as is sometimes done in engineering), one gets the volumetric heat capacity (with the SI unit of joule per kelvin per cubic meter, J/K/m3).

In the somewhat more complex case of an ideal gas of diatomic molecules, the presence of internal degrees of freedom are apparent. In addition to the three translational degrees of freedom, there are rotational and vibrational degrees of freedom.

Each rotational and translational degree of freedom will contribute R/2 in the total molar heat capacity of the gas. Each vibrational mode will contribute R to the total molar heat capacity, however. This is because for each vibrational mode, there is a potential and kinetic energy component. Both the potential and kinetic components will contribute R/2 to the total molar heat capacity of the gas. Therefore, a diatomic molecule would be expected to have a molar constant-volume heat capacity like what is shown here

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