Kinetic Theory of Gases — Formula Sheet

P = \frac{1}{3} \rho \overline{c^2}

PV = \frac{1}{3} M \overline{c^2}

\frac{1}{2} m \overline{c^2} = \frac{3}{2} kT

c_{\text{rms}} = \sqrt{\frac{3kT}{m}} = \sqrt{\frac{3RT}{M}}

Boyle’s Law

At constant T, P ∝ 1/V — derived from constant \overline{c^2}.

Charles’s Law

At constant P, V ∝ T — because \overline{c^2} ∝ T.

Gay-Lussac’s Law

At constant V, P ∝ T — pressure increases with temperature.

Average kinetic energy = (3/2)kT

At T = 0 K, molecular motion stops