GR9677 #74



Alternate Solutions 
asdfman 20091105 00:11:38  Used POE.
Expect there to be a change in entropy  E is out.
Know the typical integral to find S will involve a  A is out.
Expect the entropy to increase for the system  D is out.
Based on the numbers, expect there to be a ratio as an argument of the  C is tentatively out.
I'd come back to it if there was time and run the math to see if B is actually correct. If not this logic narrows it down to 2 choices.  

Comments 
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physicsphysics 20111011 08:24:13 
Sorry. I confused two cases. Just reversible case is zero. irreversible case is S>=0.

  mrTrig 20101105 13:50:32  yosun, you can reduce the logarithms much faster by simply knowing that addition of two results in multiplication of arguments.   asdfman 20091105 00:11:38  Used POE.
Expect there to be a change in entropy  E is out.
Know the typical integral to find S will involve a  A is out.
Expect the entropy to increase for the system  D is out.
Based on the numbers, expect there to be a ratio as an argument of the  C is tentatively out.
I'd come back to it if there was time and run the math to see if B is actually correct. If not this logic narrows it down to 2 choices.   dstahlke 20091009 10:53:51  But isn't it true that with equality only in the case where the process is reversible? This process doesn't seem reversible to me.
kroner 20091011 20:16:00 
In the context of the whole system it's not a reversible process. From that perspective dQ = 0 so you are correct that dS > dQ/T = 0. Clearly the change in entropy is positive.
But considering the two objects separately, they're each undergoing a reversible process (being uniformly heated or cooled). The change in entropy for each can be found by setting dS = dQ/T where dQ is the heat flowing into that object. Then you sum the changes contributed by each object.

  vinograd19 20070202 10:27:17  I think there is a mistake in solution. One integral is positive, the other is negative. But in solution they are both positive.
hungrychemist 20071007 21:34:32 
Solution is correct. The sign of integral is determined solely from the limits of integration. Notice ln(3/5) itself is a minus number as expected.

 




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