This thermodynamic cycle invalidates the second law of thermodynamics.
I am afraid your problem is not clear.
To invalidate the second law of thermodynamics you have first to understand this second law. According to what you write it is not the case.
I use mathematical formulas to discuss problems, and you can also.
You use mathematical formula of first principle.
The second law or second principle is a principle impossible to explain by the first law. I can assure there is 2 centuries behind thermodynamics.
Science is expressed in mathematics. You can refine each formula. Then come to a conclusion.
In addition, the second law of thermodynamics does not conform to the experiment, see the link for details.
Article The 2nd law of thermodynamics is not consistent with the exp...
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