Find the rms speed of a sample of helium gas at 300 K. Note that the mass has to be expressed in kg to get an answer in m.s -1 . Even though molecules move at high speed their diffusion from one place to another is slow because collisions send them off in randomised directions. The Microscopic explanation of Temperature For a microscopic picture of the Ideal Gas Equation, the idea of the gram mole has to be removed. The constant k B is called the Boltzmann constant and has the unit of J.K -1 . From this, the microscopic picture of temperature emerges.
Temperature is then a measure of the average kinetic energy per particle.
The mean free path, l , is the average distance travelled between collisions. Now a molecule with effective diameter, d , and travelling with the average speed v av sweeps out, in one second, a kinky cylinder. Now any molecules having their centres within a radial distance, d, of the cylinders axis will be struck. The calculation is oversimplified because all the other molecules are taken as being at rest. Qualitatively, since all the molecules are moving the chance of collisions will be increased.