Are the number of microstates of a gas just equivalent to pressureby PiersNewberry Tags: equivalent, microstates, number, pressure 

#1
Jan613, 08:01 AM

P: 7

I am quite confused about this area.
First entropy does not contain any reference to volume. So if we can theoretically set the entropy of A and B gas samples as the same but in different volumes. If A is in a larger volume it would be able to exhibit a larger number of microstates? Yet the Boltzman equation gives the same result for both as it also ignores volume. I would also be interested to know if the concept of microstates is actually at all useful, or is it just a bystander in real world physics. Thanks 



#2
Jan613, 09:48 AM

Mentor
P: 10,809





#3
Jan613, 10:08 AM

P: 7

So E, S and T are all the same, but Boltzman states should be different. (Lets assume radiatively reflective housing to eliminate infrared heat loss.) 



#4
Jan613, 10:57 AM

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P: 10,809

Are the number of microstates of a gas just equivalent to pressureBut then you get a different number of microstates, and a different entropy. 



#5
Jan713, 01:42 AM

P: 789





#6
Jan713, 05:53 AM

P: 7

Sorry for the basic confusion there. I has always imagined microstates visually  making the volume and locations of the particles an aspect of the calculations, whereas it is actually just about the distribution of energies according to one source I have just read and not about the volume. And it follows that this is true from:
Entropy = energy over temperature  nothing to do with volume Entropy = k log.w  nothing to do with volume either (Though not 100% sure how W is assessed) (If we are being finicky about it, in reality, the volume does make a difference due to gravitation reducing the maximum energy probable away from the earth.) An important exception is if we vapourise a few hunderd molecules of gold  there is the likelihood of, on average, a nice normal distribution of energies in the atoms in a confined space, however if we distribute these molecules in a sufficiently large space wherein they will not collide evidently they will retain their initial energies. So the law of entropy breaks down here. 



#7
Jan713, 07:17 AM

P: 7

I have just been thinking about this a little more and it turns out that volume does make a difference to the number of available microstates as multiatom collisions become less likely in a less dense substance wherein the momentum of two atoms in vector x might add up to produce a high value otherwise rarely produced (?).




#8
Jan713, 08:05 AM

Mentor
P: 10,809

More volume > more states for the particles at same energy > more microstates for a given temperature. It is as simple as that. 



#9
Jan713, 09:30 AM

P: 7

Brilliant; thanks; that is a lot clearer now.




#10
Jan713, 11:27 AM

P: 789




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