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How to calculate entropy of mixing in 2d systems 
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#1
Oct1011, 03:40 PM

P: 28

Hello physics forums,
I am writing a paper and I am wondering how to calculate the entropy of mixing in a two dimensional system. I am sure that entropy increases with mixing in a two dimensional system, but I do not know what equation to use. Would I just use the same equation as for 3d systems? In which case V (volume) should be replaced with A (area) .. and R would be removed altogether to become ΔS=S1*ln((A1+A2)/A1) Is this right? I would appreciate any help. I don't think it would be very scientific if I just said 'the entropy of the system surely increases when size increases'... 


#2
Oct1511, 05:14 PM

P: 2,499




#3
Oct1611, 05:05 PM

P: 28




#4
Oct1611, 05:23 PM

P: 2,499

How to calculate entropy of mixing in 2d systems
Also, you left out [itex]n_1 R[/itex] in your own equation, so why are you now saying you're more interested in a physical model? In the purely abstract model, the entropy is simply a function of the number of particles and specifically the relative change in entropy, [itex] ln[(n_1 + n_2)/n_1] [/itex], which you chose to model by area A. Your equation gives sensible answers for the relative change in entropy as far as I can tell. 


#5
Oct1611, 06:49 PM

P: 28

But then, this doesn't seem right since you can still extract energy from a system before it equalizes, so its entropy shouldn't be going up that soon. Something about total microstates definitely sounds right though. 


#6
Oct1711, 02:49 AM

P: 2,499

It seems you are trying to invoke some aspects of the holographic principle which was developed for the entropy of black holes. According to this principle the increase in entropy at the surface as a result of infalling matter is [itex] dS = dM/T[/itex]. However for ordinary physical models involving ideal gases, the 2D model makes no sense.. Diffusion is not described by the equations you wrote. I would suggest you clarify your question before you repost.



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