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

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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One of the statements of the second law is that “heat cannot flow from a colder body to a
warmer one without external aid”. Assume two systems, 1 and 2, at T1 and T2 (where
T2 > T1 ). Show that if a quantity of heat q did flow spontaneously from 1 to 2, the process
would result in a decrease in the entropy of the universe. [You may assume that the heat flows
so slowly that the process can be regarded as reversible. Assume also that the loss of heat by
the system 1 and the gain of heat by 2 do not affect T1 and T2 .]

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