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

𝑝 𝑉 = 𝜈 𝑅 𝑇

where $𝜈 : m o l$ is number of moles and $𝑅 = 8.314 J \cdot K - 1$ is the universal gas constant; and the particular form

𝑝 𝑉 = 𝑁 𝑘 𝑇

where $𝑁$ is the number of particles and $𝑘 = 1.381 \times 10 - 23 J K - 1$ is Boltzmann's constant. These two proportionality constants are related by Avogadro's number $𝑁 𝐴$

𝑁 𝐴 = 𝑁 𝑛 = 𝑅 𝑘 = 6.02 \times 1023 m o l - 1

Simplified form

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

𝑝 1 𝑉 1 𝑇 1 = 𝑝 2 𝑉 2 𝑇 2

Derivation

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

𝑝 𝑉 = 23 𝑁 (12 𝑚 ―― 𝑣 2)

where $\sqrt ―― 𝑣 2$ is the Thermal speed. This demonstrates the Relationship between Kinetic Energy and Temperature.

#state/tidy | #SemBr

For this reason, it is sometimes called the ideal gas equation of state ↩
2022. Heat and thermodynamics lecture notes 2022, pp. 23–26 ↩

Ideal gas law

Simplified form

Derivation

Footnotes