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Show that the Kelvin–Planck and the Clausius expressions of the second law are equivalent.
If the heat is transfered from cold reservoir to hot reservoir wthout using any work it woul violate the second law of thermodynamics, according to Kelvin -Planck.
But if we define a new version of a system that include taking heat from hot reservoir and transfer it to cold reservoir and do work and the system that transfer heat from cold reservoir to hot reservoir we'll get the system that is in conection with single thermo reservoir with hot reservoir. The cold reservoir is the part of our system also.
Now we managed to contact to a single thermo reservoir with doing work on the enviroment. So the system is violating the Clausius version and as a result we are violating the Kelvin -Planck version.
If we violate one, we are violating other one also.
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