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Thermodynamics
Thermodynamics

Pressure (Kinetic Theory)

P=13ρ⟨v2⟩=23NVKEavgP = \frac{1}{3}\rho \langle v^2 \rangle = \frac{2}{3}\frac{N}{V}KE_{avg}

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

Variables

P
Pressure
Gas pressure
Pa
ρ
Density
Mass density
kg/m³
⟨v²⟩
Mean square speed
Average of v²
m²/s²
N
Number of molecules
Total molecules
unitless
V
Volume
Container volume
m³
KE_avg
Average KE
Average kinetic energy per molecule
J

Derivation

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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Common questions

What is the Pressure (Kinetic Theory) formula?

Pressure (Kinetic Theory) is written P = 1/3ρlangle v² rangle = 2/3N/VKEₐᵥg. Pressure from molecular collisions. Connects microscopic motion to macroscopic pressure. It belongs to Thermodynamics, under Kinetic Theory.

What are the units in P = 1/3ρlangle v² rangle = 2/3N/VKEₐᵥg?

In SI units, P is pressure, measured in kg/(m·s²); ρ is density, measured in kg/m³; ⟨v²⟩ is mean square speed, measured in m²/s²; N is number of molecules (dimensionless); V is volume, measured in m³; KE_avg is average ke, measured in kg·m²/s².

How is the Pressure (Kinetic Theory) formula derived?

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