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Let me count the ways

Page history last edited by Joe Redish 3 years, 10 months ago

7.2.3.P2

 

In the figure at the right is shown two systems, labeled A and B, that each can hold thermal energy. A and B each have 8 binary degrees of freedom (i.e., each DoF can either be empty or hold a packet of energy). There are eight available packets of energy. The figure shows one way that the energy packets can be distributed. Express your entries for S as = kB times a numerical factor, and for W as a number.

 

A. How many ways, W, are there to distribute all 8 packets to system A? If we knew the energy was distributed with 8 packets in A and 0 packets in B, what would be the entropy, S, of that state? Explain.

 

B1. Suppose we started out knowing that there were 6 packets in A and 2 packets in B. How many ways would there be to put those 6 packets in A (WA)? How many ways are there to put 2 packets in B (WB)? What are the entropies of the two subsystems (SA and SB)? Show your work.

 

B2. What are the total number of ways, WAB, that the full system can be arranged as described in B1? And what is the total entropy, SAB, of the system? Explain.

 

C. If the energy packets were distributed equally to A and B – 4 packets in each – would you expect the WAB and SAB, of the system to be larger, smaller, or the same as you calculated in B? Don't do the calculation, but explain why you chose the answer you did?

 

D. There are three ways that this problem describes how the system holds thermal energy: In the arrangement shown in the figure (F), in the statement of problem B1 (B), and in the statement of problem C (C). Identify which of these that could be considered a "macrostate" and which could be considered a "microstate". (Choose F, B, or C)

 

 

Joe Redish 3/4/16

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