How Could Violating Kelvin-Planck Lead to a Breach of Clausius's Statement?

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Homework Statement



Show that if the Kelvin Planck statement of the 2nd law were not true,a violation of the Clausius statement would be possible.

Homework Equations


The Attempt at a Solution

Please confirm if I am correct

Kelvin Planck statement says that it is impossible for any system to operate in thermodynamic cycle and deliver a net amount of work to its surroudnings while receiving energy by heat transfer from a single thermal reservoir.
Qcool>0 and efficiency <1
Kelvin Planck statement is not true because you can't the net amount of work to its surroundings while receiving energy by heat transfer from a single thermal reservoir.

we know the second law of thermodyanics cycle is that you have hot reservior and cool reservoir. and you can have work output from the hot reservoir by extract heat from and reject heat to cool reservoir.

W_net=Q_h - Q_c
 
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