Partial Temperature of a Gas in a Mixture

[hairless_ape]

Is there such a thing as a partial temperature of a gas in a mixture? Partial pressure is commonly accounted for and used. It seems that if there are molecules of different masses colliding in a mixture, their average respective velocities in a mixture should be different based on transfer of momentum and conservation of energy equations. Am I missing something?

Also if this is a thing, wouldn't there be an application regarding Maxwell's demon paradox? For example if a mesh small enough to only allow single atoms through is used to separate chambers in a gas mixture container?

 

[Vanadium 50]

If the gas is equilibrium, all components have the same temperature, otherwise heat would flow between them until they did.

 

[hairless_ape]

If the gas is equilibrium, all components have the same temperature, otherwise heat would flow between them until they did.

Thanks for the reply. If by same temperature you mean the same molecule velocity, is where I am not quite clear. We typically assume elastic collisions between gas molecules. If two objects of different masses undergo an elastic collision starting at equal and opposite velocities, the magnitudes of resulting velocities would be different.
As for flow of heat/energy, I would argue that the dynamic equilibrium principle can apply here. More over temperature is a macroscopic quantity, it would be highly unlikely for all molecules in an even homogeneous substance to be moving at the same velocity at least based on what I've known, which isn't very much clearly...

 

[Vanadium 50]

Even a single component gas at temperature T does not have its molecules moving at the same velocity. It's a distribution.

 

[phyzguy]

Temperature is a measure the average kinetic energy of the molecules in a gas. In a gas at equilibrium with different components, all components have the same temperature and hence the same average energy, as @Vanadium 50 said. The heavier molecules will have a slower average velocity than the lighter molecules, because energy is 1/2 mv^2.

 

[guy531]

I think partial temperature can be relevant in a specific scenario.
We think about partial pressure when we take, say 3 boxes of different gas species, all in the same temperature and volume, and combine them into one box (which again has the same temperature and volume). Then, the total pressure of the combined box is dependent on the partial pressure, i.e., the pressure of each of the original boxes.

Say we do the following experiment: again we take 3 boxes, but this time each box has the same volume and same pressure, but not necessarily the same temperature. The temperature of each box is now dependent on the number of moles in the box and we call this the partial temperature.
When we combine the boxes into a new box, which still has the same pressure and volume, the new temperature will depend in some way on the partial temperatures of the 3 boxes.

However, the relationship is not as straightforward as in the partial pressure case because temperature, in the ideal gas case, is not linearly proportional to the number of moles, n, but on 1/n. I think in this case the total temperature will have an equation of the form 1/T = n1/T1 + n2/T2 + n3/T3, where T1, T2, T3 are the partial temperatures.

This is a strange experiment to do but it is the only case I can think of of where partial temperature might be relevant.