Clausius inequality states that $\oint {\delta Q\over T}$ equals zero for a system undergoing a reversible cycle, whereas it can’t be greater than zero for an irreversible cycle.
But everywhere, I see people and resources mentioning that “it follows” that for irreversible, it is strictly negative. HOW??
Mostly, they mention that since entropy changes for irreversible processes are positive, the above follows, except that this follows from the above once the above is justified! Else, give me an independent justification of this argument!
Otherwise, it is mentioned that irreversible processes involve dissipation, so entropy generation. But wait! An irreversible process doesn’t have to be dissipative. Say, irreversibility is due to non-quasi-staticity. Now what?
Similar is the case with the efficiencies of irreversible engines working between two temperatures.
Carnot’s theorem merely says that an engine working between two temperatures can’t be more efficient than a reversible engine working between the same temperatures.
I know that this implies that all reversible engines working between these temperatures have the same efficiency. But HOW does this imply that an irreversible engine between the same two temperatures will have a strictly less efficiency? Still people and resources blatantly mention this without any justification.
Someone please resolve this!
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