LECTURE PHYSICAL CHEMISTRY 3rd EDITION ROBERT G. MORTIMER

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When we sum over all the cycles inside the heavy line
the inside "lines" of the cycles (for example the blue
filled Carnot cycle in the center) will cancel because
each inside line is traversed once clockwise and once
counterclockwise. Therefore, only the outside lines (the
heavy lines) remain. If we index the (small) cycles
making up the complete cycle, by an index, k, where k
ranges over all the cells inside the heavy line, this
gives,
And
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The equal sign holds when the entire path is reversibly,
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