Pressure (Kinetic Theory)

P = \frac{1}{3} ρ ⟨ v^{2} ⟩ = \frac{2}{3} \frac{N}{V} K E_{a v g}

Pressure from molecular collisions. Connects microscopic motion to macroscopic pressure.

Variables

Pressure

Gas pressure

Density

Mass density

kg/m³

⟨v²⟩

Mean square speed

Average of v²

m²/s²

Number of molecules

Total molecules

unitless

Volume

Container volume

m³

KE_avg

Average KE

Average kinetic energy per molecule

From momentum transfer of molecules hitting walls: P = (1/3)ρ⟨v²⟩ = (1/3)(Nm/V)⟨v²⟩ = (2/3)(N/V)KE_avg.

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