🌡️ v_rms = √(3kT/m): hotter is faster, heavier is slower

The average kinetic energy of a molecule, ½ m ⟨v²⟩ = ³⁄₂ kT, depends only on the absolute temperature. So v_rms = √(3kT/m) = √(3RT/M) rises as √T and falls as 1/√m — at the same temperature a light molecule (H₂) outruns a heavy one (O₂). Faster molecules are drawn larger and redder.

Walkthrough 1 / 3

Every molecule shares the same average kinetic energy ½ m ⟨v²⟩ = ³⁄₂ kT — set purely by T.

Temperature T 300 K

Molar mass M 28 g/mol

½ m <v²> = ³⁄₂ kT · v_rms = √(3kT/m) = √(3RT/M)
v_rms = — m/s · KĒ = — J · T = — K

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