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Prove the equivalence between the two statements of the 2nd law of thermodynamics (i. e., a violation of one statement leads to the violatio the other statement)

For each of the following process: a) sketch the p-v diagram, b)sketch t-s diagram, c) sketch t-v diagram, d) sketch the boundary work on one of the diagrams (a, b or c) and e) sketch the reversible heat transfer on one of the diagrams (a, b or c): 1- isobaric process from compressed liquid to superheated vapor 2- isothermal process from compressed liquid to superheated vapor 3- isentropic process from compressed liquid to superheated vapor

How to increase the thermal officiency of an ideal simple rankino cycle? among these methods, which one is the best and why?