# Thermal conductivity in gases

I've been musing about thermal conductivity and came upon the following question.

Heat is transported through matter by molecules passing their kinetic energy onto other molecules, or simply by the matter itself being transported.

In gases, the first option should happens way more slowly than in bodies or liquids as the molecules are less likely to have contact. The second, however, happens very quickly.

If we now think of a small amount of a gas with a some temperature being released into a larger amount of gas with a different temperature, all of which is confined in a box, then the smaller amount will diffuse into the box, both gases become mixed.

If the pressure is low and the molecules rarely meet, they should be able to keep their respective temperatures and the overall temperature is not a single value, but a spectrum - with two spikes in this case.

I would expect the gases' temperatures to merge the faster the more pressure the gases are under.

I was wondering especially if the effect would be strong for air in the range of Earth's surface temperatures.

If not, how low would pressure have to for the effect to become relevant?

I'm sure there will be nice diagrams by physicists that describe the speed of the temperature merging process depending on pressure and temperature, but I don't know the right buzzwords to Google for them.

Can somebody help me out?

• An important consideration is the mean free path of the gases, which is readily calculated for an ideal gas. That tells you how far a molecule gets before scattering (on average). In air at Earth-normal pressures it isn't very far at all (<100nm), so your scenario will not work. – Jon Custer Oct 20 '14 at 13:31
• The mean free path concept is very useful, thanks for that. I've edited the question a bit to make it more meaningful in the light of the fact that earth's atmosphere may be not very interesting in that regard. I didn't know it was so crowded. – John Oct 20 '14 at 13:40
• If the gas is a plasma the term you are looking for is "thermal equilibration rate". Might help. – kotozna Jan 9 '16 at 11:54