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Answer to Question #5549 in Molecular Physics | Thermodynamics for cncrowell

Question #5549
750 J is conducted from a reservoir at 400 K
to one at 270 K.
What is the change in entropy of the uni-
versity?
Answer in units of J/K
Expert's answer
The entropy change of the cold hot object is
<img style="width: 76px; height: 44px;" src="data:image/png;base64,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" alt="">
The hot object loses energy, and its entropy change is
<img style="width: 98px; height: 48px;" src="data:image/png;base64,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" alt="">
We consider the two objects to be isolated from the rest of the Universe. Thus, the entropy change of the Universe is just that of our two-object system, which is
<img style="width: 424px; height: 40px;" src="data:image/png;base64,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" alt="">

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