# Effusion of Ideal Gas

I just calculated that for an ideal gas inside a container, the average kinetic energy for molecules that are striking the walls of the container is larger than the average kinetic energy of the molecules comprising the entire gas. Specifically, my result was $$\frac{E_{walls}}{E} = \frac{4}{3}$$ where $E=\frac{3}{2}T$. I am pretty sure that this is correct. My question is then if I have a container of gas in vacuum and I poke a hole in it, let some gas escape, and then close the hole before all of it escapes, am I right in thinking that due to my result above, the molecules that escape are more likely to have higher energy than the average energy of the whole gas, and as a result the energy and temperature of my system will have decreased?

• The average kinetic energy of the molecules hitting the walls of the container is greater than the average kinetic energy of the molecules comprising the entire gas when the system is in thermal equilibrium? That doesn't sound right. Never heard of that before. Can you provide or reference a proof of that?
– user93237
Commented Oct 19, 2016 at 6:00
• Landau and lifshitz statistical mechanics section 39
– pmal
Commented Oct 19, 2016 at 6:01
• @SamuelWeir: the faster moving particles cross the container faster and therefore strike the walls more frequently than the slower moving particles. Commented Oct 19, 2016 at 6:01
• Paul, note that for real gases at STP, even though they closely follow the ideal gas equation of state, the mean free path is a few microns. So for a real gas you'd never see this effect. Commented Oct 19, 2016 at 6:19
• Back to the original question, I would think that the situation is similar to the cooling of a liquid by evaporation, in which excess energy is carried away by the more energetic molecules, leaving the less energetic ones behind. A practical problem would seem to be that the hole or holes have to be really small so that individual molecules are exiting the hole(s) and you don't just have a large-scale hydrodynamic flow of gas from the hole(s).
– user93237
Commented Oct 19, 2016 at 6:21