Total Translational Kinetic Energy of Gas (E_trans = (3/2)nRT = (3/2)NkBT)
jee-mainjee-advanced
E_trans = (3/2)nRT = (3/2)NkBT
What each symbol means
| Symbol | What it stands for |
|---|---|
| N | Total number of molecules |
| R | Universal gas constant = 8.314 J mol⁻¹ K⁻¹ |
| T | Absolute temperature (K) |
| n | Number of moles (mol) |
| kB | Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹ |
| E_trans | Total translational kinetic energy of the gas (J) |
When to use this
Valid for ALL ideal gases — monatomic, diatomic, polyatomic. This formula gives ONLY translational KE (3 DOF). For total internal energy: monatomic U = (3/2)nRT, diatomic rigid U = (5/2)nRT, diatomic vibrating U = (7/2)nRT. Translational KE is same regardless of gas type at same n, T.