The proof that net entropy of universe increases.

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Chapter 19, Problem 55P

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The proof that net entropy of universe increases.

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One of the statements of the second law is that “heat cannot flow from a colder body to awarmer one without external aid”. Assume two systems, 1 and 2, at T1 and T2 (whereT2 > T1 ). Show that if a quantity of heat q did flow spontaneously from 1 to 2, the processwould result in a decrease in the entropy of the universe. [You may assume that the heat flowsso slowly that the process can be regarded as reversible. Assume also that the loss of heat bythe system 1 and the gain of heat by 2 do not affect T1 and T2 .]

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