Chemical Forums
Chemistry Forums for Students => Physical Chemistry Forum => Topic started by: Twickel on August 15, 2012, 10:04:16 AM
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Hi
This has been doing my head can anyone explain how they get nidlnni+lnnidi - dni
Cansomeone explain it to me mathematically.
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Stirlings approximation of N!.
lnN! ~ NlnN-N
You can find many, many sources online that explain it in various detail.
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I understand that, so then where does dlnni*!=nidlnni+lnnidni-dni come from should it only be dlnni*!=nidlnn-dni
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This notation is very difficult to read, but I think the problem is that you are forgetting to use the product rule when finding a differential.
lnN! ~ NlnN-N
d(NlnN-N) = (dN)lnN + N(dlnN) - dN, where the first time two terms come from d(NlnN).
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Doh!
Thanks, ok so how do they cancel the next line, where does the ln dissapear to?
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Doh!
Thanks, ok so how do they cancel the next line, where does the ln dissapear to?
dlnx/dx = 1/x so it cancels with the third term.
NdlnN = dN as dlnN = (1/N)dN
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Thank you, so what I am puzzled about is if I have taken the derivative to simplify the expression, why then do I keep the d in the simplified term. E.g
dinx= 1/x I dont write dlnx=d1/x
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Thank you, so what I am puzzled about is if I have taken the derivative to simplify the expression, why then do I keep the d in the simplified term. E.g
dinx= 1/x I dont write dlnx=d1/x
It's neither of those. dlnN = (1/N)dN. Think chain rule.
You're not taking the derivative - the derivative showed up as part of the chain rule. You're finding the total differential. \
That's what we're actually trying to do here. Find the total differential of W (the multinomial coefficient). If you don't know what total differentials are, it's worth reviewing. They are pervasive throughout all of thermodynamics.