Monatomic ideal gas heat capacity at constant volume


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 physics and chemistry, monatomic is a combination of the words “mono” and “atomic”, and means “single atom”. It is usually applied to gases: a monatomic gas is one in which atoms are not bound to each other. All chemical elements will be monatomic in the gas phase at sufficient high temperatures. The thermodynamic behavior of monatomic gas is extremely simple when compared to polyatomic gases because it is free of any rotational or vibrational energy. The motion of a monatomic gas is translation (electronic excitation is not important at room temperature). Thus in an adiabatic process, monatomic gases have an idealised γ-factor (Cp/Cv) of 5/3, as opposed to 7/5 for ideal diatomic gases where rotation (but not vibration at room temperature) also contributes. Also, for ideal monatomic gases.

Related formulas


Cv heat capacity at constant volume (J/K)
nnumber of moles (mole)
Rmolar gas constant