How Does Entropy Explain Heat Transfer Between Two Einstein Solids?

[heyjude619]

Homework Statement

Consider two identical Einstein solids. One solid has been placed in boiling water and the other in ice water. Then the two solids are placed in good contact with each other within an insulated box. Using the concept of entropy, prove that heat will spontaneously transfer from the hotter block to the colder block. Explanations that use concepts other than entropy will receive zero credit. Make sure the logic of your explanation is clear. Equations (and perhaps graphs) should make up the bulk of your answer. Use only a minimum number of words.

Homework Equations

deltaS(total)=deltaS(A)+deltaS(B), where A is the hot solid and B is the cold solid
deltaS=deltaQ/T, where Q is energy due to heat transfer, and T is temperature

The Attempt at a Solution

deltaS(total)=deltaS(A)+deltaS(B)=deltaQ(A)/T(A) + deltaQ(B)/T(B)
deltaQ(A)=-deltaQ(B)
T(A) much greater than T(B)
-so deltaS(total) will be negative, which implies that the heat should transfer from the higher entropy object to the lower entropy object
-this is what I have so far, but I turned it in and got zero credit... any suggestions? I'm wondering if I need to use the second law of thermodynamics somewhere...

Thanks!

 

[nickjer]

How does the total change in entropy imply what is happening with the individual bodies, let alone how is it negative? And I do suggest the second law of thermodynamics, especially since you broke it.

Also, you might not want to use delta, since the temperature isn't constant through out the whole process. So it is best to use differentials, such as dS and dQ.

 

[heyjude619]

Awesome, thanks!

Yeah, I realized yesterday that the deltaS(total) couldn't be negative, since entropy can't be destroyed, so that was a slip on my part. Thanks for pointing it out!