For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is

A solar energy based heat engine which receives $$80$$ $$kJ$$ of heat at $${100^ \circ }C$$ and rejects $$70$$ $$kJ$$ of heat to the ambient at $${30^ \circ }C$$ is to be designed. The thermal efficiency of the heat engine is

For two cycles coupled in series, the topping cycle has an efficiency of $$30\% $$ and the bottoming cycle has an efficiency of $$20\% $$. The overall combined cycle efficiency is

An iron cube at a temperature of $$400$$ deg $$C$$ is dropped into an insulated bath containing $$10$$ $$kg$$ water at $${25^ \circ }C.$$ The water finally reaches a temperature of $${50^ \circ }C$$ at steady state. Given that the specific heat of water is equal to $$4186$$ $$J/kgK,$$ find the entropy changes for the iron cube and the water. Is the process irreversible ? If so, why?