Thermodynamics MOC

Ideal gas law

The ideal gas law relates the macroscopic state parameters¹ of an Ideal gas in Thermal equilibrium. It comes in two forms, the molar form

where is number of moles and is the universal gas constant; and the particular form

where is the number of particles and is Boltzmann’s constant. These two proportionality constants are related by Avogadro’s number

Simplified form

When the number of gas particles is constant the law can be simplified to

Derivation

Originally, the ideal gas law was discovered empirically. However, a very similar equation can be derived microscopically from first principles of newtonian physics²:

where is the Thermal speed. This demonstrates the Relationship between Kinetic Energy and Temperature.

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Footnotes

1. For this reason, it is sometimes called the ideal gas equation of state ↩

2. 2022. Heat and thermodynamics lecture notes 2022, pp. 23–26 ↩