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

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

Round the clock cooling of an apartment having a load of $$300$$ $$MJ/day$$ requires and air-conditioning plant of capacity about