When define heat engine efficiency as:n = W/ W1 , that is, replacing Q1 in the original definition n=W/ Q1 with W1 , W still is the net work the heat engine applied to the outside in one cycle,W1 is the work the heat engine applied to the outside in the cycle,let the element reversible cycle be Stirling cycle , if circuit integral dQ/T =0 is tenable,we can prove circuit integral dW/T =0 and circuit integral dE/T =0 !
If circuit integral dQ/T=0, dW/T=0 and dE/T=0 really define new system state variables, the three state variables are inevitably different from each other; on the other side, their dimensions are the same one, namely J/K, and they are all state variables. So, we have to “make” three different system state variables with same dimensions, and we don’t know what they are, no doubt, this is absurd.
In fact , replaceing delta Q with dQ is taking for granted, if only we review the definition of differential, we know that the prerequisite of differential is there is a derivability function as y=f(x), however,there is not any function as Q=f(T) here at all, so, delta Q can not become dQ.
On the other side, when delta Q tend towards 0, lim(deltaQ/T)=0 but not lim(deltaQ/T)= dQ/T.
So, circuit integral dQ/T=0,circuit integral dW/T=0 and circuit integral dE/T=0 are all untenable at all !
Read paper Entropy : A concept that is not physical quantity
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