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# prexam4a - Which macrostate(s is(are the most probable What...

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3. Consider a pair of standard dice. There are 11 “macrostates” of the dice corresponding to the total of their face values, i.e. 2 , 3 , 4 , · · · , 12 (see the Table below). a) Figure out how many “microstates” there are for each macrostate and enter these numbers into the 3rd column of the Table. To do this, draw pictures of the microstates, following the example for state ”3” which is filled in for you. Draw the microstates for at least half of the Table, after which you may see a trend and can simply fill in the 3rd column without drawing. b) What is the total number of microstates for the pair of dice?
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Unformatted text preview: Which macrostate(s) is(are) the most probable? What is that probability? c) Compute the change in entropy in going from macroscopic state ”2” to macroscopic state ”8”. Macro. Micro. # of Micro. 2 3 4 5 6 7 8 9 10 11 12 2 , , , 3 1 , , , 4 5 6 5 4 3 2 1 , , , , , , , , , , , , , Solution: a) ⇒ b) There are 6 2 = 36 microstates. ”7” is the most probable (most microstates per macrostate), with a probability p = 6 / 36 = 1 / 6. c) Δ S 2 → 8 = k B ln w 8-k B ln w 2 Δ S 2 → 8 = k B ln ± w 8 w 2 ¶ With w 8 = 5, w 2 = 1, we have, Δ S 2 → 8 = k B ln5 ....
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