Kelvin statement of the second law

Thus, a net amount of work has been done by the system from heat obtained from a heat reservoir at the temperature of step 2, without at the same time transferring heat from a hot to a cold reservoir. This violates the Kelvin statement of the Second Law. Therefore, the assumption that the two adiabatic reversible paths may intersect is disproven. 

No violation of either physical statement of the second law of thermodynamics has ever been observed in a properly done experiment. We regard the second law as a summary and generalization of experimental fact. A machine that would violate the Kelvin statement of the second law and turn heat completely into work in a cyclic process is called a perpetual motion machine of the second kind. 

From the Kelvin statement of the second law, the efficiency must be less than unity, so that qj, must be negative. It is not possible to run a Carnot engine without exhausting some heat to a cool reservoir. 

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