[hardman]

I am a bit confused to how to work out how many collisions an atom makes in a given amount of time. This is the question:

How many collisions does a single Ar atom make in one second when the temperature is 25 degrees centigrade and the pressure is 10 bar.

I think it has something to do with working out the mean free path but after that has been worked out don't you need to know what speed the atom is travelling at? Also I am not sure what units to use when calculating the mean free path. Should temperature be converted to kelvin and pressure to kpa etc?

Am grateful for any help.

[sjb]

You have the temperature, so you have the average energy per atom, and so you have the speed (via some mathematical manipulations).

It doesn't really matter to some degree what you measure the pressure and temperature in, again as long as you manage to manipulate them correctly at the end.

However, it's probably best to convert to SI (so yes, [k]Pa and kelvin) in the early stages unless you're confident in your mathematical abilities.

See http://en.wikipedia.org/w/index.php?title=Mean_free_path&oldid=227963001

[hardman]

this is probably a stupid question but how would i go about working out the energy of an atom with just the temperature, and how would that then relate to speed.

[Yggdrasil]

http://en.wikipedia.org/wiki/Root_mean_square_speed

The result given in the wikipedia article can be derived from the equipartition theorem which states that the molecule will have k_BT/2 of energy per degree of freedom.  Since the atom can move in three dimensions, its kinetic energy will be (3/2)k_BT.

[hardman]

i see. so i have to work out the mean free path to find out how far the atom travels between each collision, then calculate the speed it travels at.

One final question, What will the units of Urms be?

[sjb]

Assuming Urms is a speed, what are the units of *any* speed?