Derive the reversible steady-flow work relations.

Determine net entropy change of the engine from Clausius inequality and thermal efficiency of the Carnot engine from the definition of heat engine, please show the derivation

(2) Describe briefly why the following statements are wrong. (a) "Hot cup of coffee becoming cold spontaneously is an entropy-decreasing process. So the law of entropy increase can be violated." (b) “Air conditioners require bulky external unit, exhausting heat to outside. With the technology constantly advancing, external unit will be eliminated in the future."