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Thermal efficiency: reversible and irreversible machines

  1. Aug 11, 2015 #1
    In the proof of Clausius inequality ##\oint\frac{\delta Q}{T}<0## for an irreversible cycle, I always find the fact that the thermal efficiency of an irreversible machine is **stricly less** than the thermal efficiency of a reversible machine, both operating between temperatures ##T_H## and ##T_C##.
    Nevertheless my book and all the resources that I have found prove by reductio ad absurdum that, between the temperatures ##T_H## and ##T_C##, the thermal efficiency of an irreversible machine is (only) **less or equal** to the thermal efficiency of a reversible machine because, if it were strictly greater, the positive work done by an irreversible thermal machinee could be used to activate a reversible machine used as a chiller, and the resulting composed machine would produce a flow of heat from a cold source at the temperature ##T_C## to a hot one at the temperature ##T_H##, violating the second principle of thermodynamics.

    How can it be proved that the thermal efficiency of an irreversible machine is strictly less than the thermal efficiency of a reversible machine operating between the same two temperatures ##T_C## and ##T_F##?
    ##\infty## thanks for any answer!
     
  2. jcsd
  3. Aug 11, 2015 #2

    mfb

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    Staff: Mentor

    If you have machine A exactly at the ideal efficiency, you can use another ideal machine B to revert the system to the previous state. Or just run A backwards. Your irreversible process is now part of a reversible process => contradiction
     
  4. Aug 13, 2015 #3
    Brilliant answer! Thank you very much!!!
     
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