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Counting energy arrangements

Page history last edited by Joe Redish 5 years, 2 months ago

 

7.3.2.P5

 

In this problem we will consider the distribution of energy, microstates, macrostates, and entropy. To do this, consider a simple model consisting of two boxes each with 10 bins (degrees of freedom) in which to put energy. To simplify our counting, we will assume that each bin can hold only one packet of energy and that energy packets are indistinguishable. Show your work and briefly explain your reasoning.

 

1. Suppose we have 4 packets of energy. In how many ways can we distribute them so that they're all in box A?

 

2. How many ways can we distribute those packets of energy so that they are equally divided between box A and box B?

 
 

3. The states described in parts 1 and 2 are macrostates. What is the entropy of macrostate 2?

 

4. The temperature of a system is related to the average energy in a degree of freedom by = ½ kBT. In units of energy packets, (defining one flame = 1 ep), what are the temperatures of boxes A and B in macrostates in parts 1 and 2?

 

5. If these flames were in thermal equilibrium in this system of 20 DoFs, would you ever expect to find the flames distributed as in part 1? Explain why you think so.

 

 

Joe Redish and Bill Dorland 5/3/18

 

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