00:01
So now we're talking about a gas of n molecules in flatland or 2d space.
00:09
So instead of talking about volume, i guess we'll be talking about some sort of area, although it's not totally incorrect to say volume.
00:16
It could be sort of arbitrary with the dimensions you're in.
00:19
But now, sort of following the same logic, we have n factors of the given area that we're in.
00:30
We need to divide by, or in 2d.
00:35
Three n but two n factors of the plank constant.
00:42
What doesn't change with these dimensions is that it's n molecules.
00:45
So to compensate for overcounting, we still need this one over n factorial because this is the number of possible ways to interchange the particles.
00:54
Number of particles hasn't changed.
00:56
Still n.
00:58
And then we still need this hypersphere, right? we need for the momentum space factor.
01:05
We need the surface area of a 2 n dimensional hypersphere and we're given the way to find the the surface area of a hyposphere with you know a d -dimensional hypersphere given some radius right we know that as two pi to the d over two and then we have d over 2 minus 1 factorial and this is all times r to the d minus 1.
01:55
And we know that the radius isn't going to change, right? the radius is still dependent on mass and potential energy.
02:02
So it's just 2mu.
02:05
So if we work through all this, we should get our flatland, our two -dimensional space multiplicity function for this gas.
02:14
Let's plug in...