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(a) “It is impossible for heat to ﬂow spontaneously from a colder to a warmer body without causing other changes”

(b) “It is impossible to convert all the heat taken from a body of uniform temperature into work without causing other changes”

(hint: one can prove the equivalence of the two statements by showing that if one is violated then so is the other and vice versa.)

**The attempt at a solution**

I have no idea how to approach this question mathematically....