Why would all of the molecules of air in your room not have the same average speed? Or would they?

Answer 1

If the room is uniform in temperature, then most of the molecules will be traveling in random directions at roughly the same speed.

Since they will bump into each other more or less at random, they will average a "typical" speed.

If you heat or cool the room you change the speed the molecules are travelling. So turing on a heater introduces a group of speedier molecules into the room.

Answer 2

Well, the way you worded it is a bit vague, I'm afraid.

You can take the average of anything, so even if all the molecules are traveling at greatly different speeds, they would all still have the same average speed. But they will all, individually, travel at different speeds.

An average is just the sum of all the speeds divided by the number of molecules. (At least if we're talking about the "mean", which is what most people are talking about when they talk about averages.)

Answer 3

Because the average speed of a molecule is dependant on its mass, and some molecules in the air have more mass than others.

Answer 4

The velocity of the molecules is randomly distributed, but their mean velocity increases with temperature.