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Relation Between Entropy and Temperature
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[QUOTE="Ghost Repeater, post: 6048188, member: 610484"] Thanks for your reply! So using ##S = kln(\Omega)## seems to still leave me in a quandary, because for the macropartition ##0:6## (where object A has no bits of energy, object B has all 6), ##\Omega_{A} = 0## and therefore ##\Omega_{AB} = \Omega_{A} \Omega_{B} = 0##, which gives me an undefined/unphysical entropy, since there is no ##ln(0)##. As to which expression I use for multiplicity, my understanding was that the expression $$\Omega(N,U) = \frac{(3N+q-1)!}{(3N-1)!q!}$$ is essentially just a combinatorics result. In fact, we derived it as part of the homework, and that's exactly what it was: how many ways to distribute q bits of energy amongst 3N oscillators of an Einstein solid. So I was (am) confused by this problem, because I don't see the point of redefining multiplicity and then seeing what happens, since multiplicity just is what it is. It is math, not physics (though it does give rise to physics). I mean, it makes no sense, purely from a combinatorics standpoint, that there is not exactly 1 way of distributing 0 bits of energy among the oscillators of object A. Yet that's what the problem's definition of 'multiplicity' gives me. That just seems absurd and not worth thinking about, but at the same time I trust the textbook author to give me meaningful problems, so I conclude I must be missing something. Anyway, thus far I have two conclusions about these 'alien objects': 1) They are normal in the sense that they have well-defined temperatures, etc. (which I suspect is incorrect, but if I graph S vs U, I essentially just get an ln function with decreasing slope, i.e. decreasing temperature, as for a normal object 2) The system of the two objects in contact has no entropy for the macropartitions where one of them has zero energy, which is different from Einstein solids. [/QUOTE]
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