Kinetic Theory — Formula Sheet

PV = KT

P1V1/(N1T1) = P2V2/(N2T2) = constant = k_B

PV = μRT

μ = M/M0 = N/N_A

PV = k_BNT or P = k_BnT

P = (1/3) n m v̄²

E = (3/2) k_BNT ; (1/2) mv̄² = (3/2) k_BT

PV = (2/3)E

v_rms = (v̄²)^(1/2) = √(3k_BT/m)

Each mode has average energy = (1/2) k_B T

For vibration: 2 × (1/2) k_B T = k_B T

R = 8.314 J mol⁻¹ K⁻¹ and k_B = 1.38 × 10^-23 J K⁻¹.

An ideal gas satisfies PV = μRT exactly, and also PV = k_B NT.

The average kinetic energy per molecule is (1/2) m v̄² = (3/2) k_B T.

The rms speed is v_rms = sqrt(3k_B T / m).