Average Translational KE per Molecule (½mv²_rms = (3/2)kBT)
jee-mainjee-advanced
½mv²_rms = (3/2)kBT
What each symbol means
| Symbol | What it stands for |
|---|---|
| R | Universal gas constant = 8.314 J mol⁻¹ K⁻¹ (for per-mole form: KE = 3RT/2) |
| T | Absolute temperature (K) |
| m | Mass of one molecule (kg) |
| kB | Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹ |
| v_rms | Root mean square speed (m/s) |
| KE_trans | Average 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.