Heat Capacity of an Ideal Gas by Number of Particles
Heat capacity, or thermal capacity, of an ideal gas is a measurable physical quantity equal to the ratio of the heat added (or removed) to the resulting temperature change. An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interaction is perfectly elastic collision.
The isobaric heat capacity of an ideal gas equals the product of a Boltzmann constant, the number of particles and the specific heat capacity. The isochoric heat capacity equals the isobaric heat capacity plus the Boltzmann constant times the number of particles.
Formula
![{QuantityVariable[Subscript["C", "p"], "HeatCapacity"] == Quantity[1, "BoltzmannConstant"]*QuantityVariable["N", "Unitless"]*QuantityVariable["γ", "Unitless"], QuantityVariable[Subscript["C", "V"], "HeatCapacity"] == Quantity[1, "BoltzmannConstant"]*QuantityVariable["N", "Unitless"] + QuantityVariable[Subscript["C", "p"], "HeatCapacity"]}](https://www.wolframcloud.com/objects/resourcesystem/marketplacestorage/resources/924/9245b1de-906a-431b-a615-01b1c8f41c68/Webpage/FormulaImage.png "Copy to Clipboard")
| symbol | description | physical quantity |
|---|---|---|
| Cp | isobaric heat capacity | "HeatCapacity" |
| N | particle number | "Unitless" |
| γ | specific heat capacity | "Unitless" |
| CV | isochoric heat capacity | "HeatCapacity" |