We have learned two equations that relate the concepts of heat (transfer of ther

Question

We have learned two equations that relate the concepts of heat (transfer of thermal energy), Q, and temperature (density of thermal energy), T. They are: The equation for the heat capacity of an object: Formula The equation for the change in entropy of an object: Formula These look similar. They both have Q's and T's, but the Deltas are in different places! A) Describe carefully what situation each equation describes, what the symbols each mean, and what you think are the similarities and differences between them. B) Now lets consider the implications of these equations for a microscopic object with 12 "bins" (degrees of freedom) where energy can be located, and 30 "chunks" of energy distributed among those bins. The microscopic object is "isolated" in the sense that energy cannot flow into or out of the object B1) Calculate C, T, and S B2) Now consider a process where you are adding three "chunks" of energy to the microscopic object. Which one of the symbols in the two equations above describe the process? What is their value? For the other symbols, what is their end value after the energy is added?

Explanation / Answer

S= logW

And w is work

W= 2N where N = degree of fredom

Therefore

S= log 2N

Or, S= 2 log N

S= 2log 12

S= 2x1.079= 2.158

Given Q = 30x 2.158 = 64.74

Therefore putting values,

S= Q/T

T= Q/S = 64.74/2.158

=30

and therefore C = 64.74/30= 2.158

2 if we add three more chunks to microscopic object then degree of freedom will increase and hence as a consequence entropy will increase. Therefore S will describe the process.

End value after adding three chunks will be 2 log 15

And the other value will also change accordingly as solved above.

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