3 Consider the different possible distributions of 4 units of energy among 5 par
ID: 1043468 • Letter: 3
Question
3 Consider the different possible distributions of 4 units of energy among 5 particles. Write out a representation of each possible distribution. (These representations should be similar in style to the diagrams at the top of page 52 in the Practice Problems.) b) Determine the number of microstates (W) that are possible for each distribution. c Calculate W/W s for each distribution to determine the probability of each distribution. Which distribution is the most probable? Calculate the entropy of the most probable and the least probable distributions. d)Explanation / Answer
3.
a) Write out a representation of each possible distribution.
Energy particles
4 1
3 _
2 _
1 _
0 4
Energy PARTICLES
4 _
3 _
2 2
1 _
0 3
Energy PARTICLES
4 _
3 1
2 _
1 1
0 3
Energy PARTICLES
4 _
3 _
2 1
1 2
0 2
Energy PARTICLES
4 _
3 _
2 _
1 4
0 1
b) W = 5!/(1!4!) = 5 P = 5/70 = 1/14 = 0.071
W = 5!/(2!3!) = 10 P = 10/70 = 1/7 = 0.143
W = 5!/(1!1!3!) = 20 P = 20/70 = 2/7 = 0.286
W = 5!/(1!2!2!) = 30 P = 30/70 = 3/7 = 0.429 ***Most Probable Distribution
W = 5!/(4!1!) = 5 P = 5/70 = 1/14 = 0.071
c) Wtotal = 5 + 10 + 20 + 30 + 5 = 70
d) Most Probable: S = klnW = (1.38
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