Average Translational KE per Molecule (½mv²_rms = (3/2)kBT)

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½mv²_rms = (3/2)kBT

What each symbol means

SymbolWhat it stands for
RUniversal gas constant = 8.314 J mol⁻¹ K⁻¹ (for per-mole form: KE = 3RT/2)
TAbsolute temperature (K)
mMass of one molecule (kg)
kBBoltzmann constant = 1.38 × 10⁻²³ J K⁻¹
v_rmsRoot mean square speed (m/s)
KE_transAverage translational kinetic energy per molecule (J)

When to use this

Valid for ideal gas. Translational KE only — does not include rotational or vibrational. Independent of gas type, depends only on temperature. Per-mole form: (3/2)RT.