Discussion
Clausius inequality is written as
Answer: C
The Clausius inequality is \(\oint \dfrac{\delta Q}{T} \le 0\).
For any closed cycle, the cyclic integral of heat transferred divided by the absolute temperature at the boundary where it crosses is zero for a reversible cycle and negative for an irreversible one. It is a statement of the second law, and leads directly to the definition of entropy, \(dS = (\delta Q/T)_{rev}\).
The cyclic integral of \(\delta Q\) alone equals the net work of the cycle by the first law and can be positive (an engine) or negative (a refrigerator), so the first two options are not the inequality. \(\oint \delta Q/T \gt 0\) would describe a cycle that violates the second law.
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