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I’m using Atkins thermodynamics book and he has a section I don’t quite understand. The line I’m particuarly question is the one befor (5.2) where he says “by Kelvins formulation of the second law”. I’m not quite sure how this has been used to justify why the integral is less than or equal to 0, (my personal justification was that the reservoir is hotter, and thus providing the heat, therefore wrt it it’s losing heat (thus all the dQ terms are negative, but this seems incorrect or at least not concrete).

If someone could explain this it’d be very useful. enter image description here enter image description here

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