Mixing Gases, temperature, and the Kinetic Model of Matter

1. Nov 25, 2013

evaengineer

1. The problem statement, all variables and given/known data
Consider the following statement: "The temperature of a gas is a measure of the speed of its particles (atoms and molecules). Now suppose that I mix two gases together, for example oxygen and carbon dioxide, which are initially at different temperatures; if I wait long enough, eventually all the oxygen and the carbon dioxide molecules will be traveling at exactly the same speed."

Discuss the scientific accuracy of this statement.

2. Relevant equations
These may or may not be relevant.
Using the Kinetic Model of Matter (for gas)
p α T (pressure is directly proportional to temperature)
V α T (volume is directly proportional to temperature)
p α V (pressure is directly proportional to volume)

3. The attempt at a solution
If both O and CO2 are in the same container, they will have the same volume (using V α T...?), as the container's volume won't change by adding more gas. When the gas is added, the pressure will increase (using p α V...?) as there will be more atoms per cubic area. So, when they are in the same container, they will then have the same temperature, based on their pressure (using p α T...?).

I have a feeling that my use of mathematics in this situation is far too complex or incorrect. My answer feels like a shot in the dark more than anything. So, input?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 25, 2013

hjelmgart

Well, your reasoning sounds good to me, but I am no professor. Anyway, you might want to use some kind of statistics for this, if you want to use more mathematics. I could probably help you with that, but if it isn't a statistical course, I guess you shouldn't go that deep. Also putting temperature and pressure proportional to the volume is wrong in the manner, that the volume stays constant.

However, the fact that you have constant volume, would make it possible to use the last one, where you say, that pressure is proportional to temperature. This wouldn't be the case, if the volume didn't stay constant, as you could then use either of the previous mentioned.

Also you should not assume that the volume is constant, unless it is actually mentioned in the task.

I would probably answer it in a relation like this:
Relate the speed of the particles to kinetic energy, and then express the kinetic energy in terms of temperature. That way, you can say, that when the temperature becomes constant, so does the speed of the particles. If you wait long enough, you obtain constant temperature, because the kinetic energy will be evenly distributed among all particles due to the conservation of energy between each collision.