The Boltzmann constant k is the gas constant per molecule, just as R is the gas constant per mole
Thermal Physics - OCR A-Level Physics
$$k = \frac{R}{N_A}$$
- The Boltzmann constantThe gas constant per molecule. Relates the average kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. of gas molecules to temperature. k = 1.38 x 10⁻²³ J K⁻¹. k is the gas constant per molecule, just as R is the gas constant per mole.
- This relationship connects the molar scale (n, R) with the molecular scale (N, k).
- Mean KE per molecule = $\frac{3}{2}$kT. Mean KE per mole = $\frac{3}{2}$RT.
- Total internal energyThe capacity to do work. Measured in joules (J).The sum of the randomly distributed kinetic and potential energies of all the molecules in a system. of an ideal monatomic gas = $\frac{3}{2}$NkT = $\frac{3}{2}$nRT.
Examiner Tips and Tricks
- Check your answer is sensible: the KE of one molecule should be of order \(10^{-21}\) J at room temperature.
- If you get a value much larger or smaller, check your units.