# Show that all these statements of the Second Law are equivalent

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Question description

1) In class we considered various statements of the Second Law before introducing the concept of entropy: (i) According to Clausius, no process is possible whose sole result is cooling of a colder body and heating of a hotter body, i.e. heat will not flow from cold to hot. (ii) According to Kelvin, no process is possible whose sole result is the complete conversion of heat into work, i.e. no heat engine can be 100% efficient. (iii) We showed that the maximum efficiency of a heat engine is 1 − Tc/Th. Finally, when we did get around to entropy itself, we restated the Second Law as “Entropy cannot decrease”. Show that all these statements of the Second Law are equivalent. You may do this by showing that entropy would decrease if (i)-(iii) were false. You may also use particular examples if needed (e.g. a heat engine) and consider the three cases in any order.

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