A heat engine extracts heat (𝑄_H) from a thermal reservoir at a temperature of 1000 K and rejects heat (𝑄_L) to a thermal reservoir at a temperature of 100 K, while producing work (𝑊). Which one of the combinations of [𝑄_H, 𝑄_L and 𝑊] given is allowed? 

The Clausius inequality holds good for

A heat pump absorbs $$10$$ $$kW$$ of heat from outside environment at $$250$$ $$K$$ while absorbing $$15$$ $$kW$$ of work. It delivers the heat to a room that must be kept warm at $$300$$ $$K.$$ The Coefficient of performance $$(COP)$$ of the heat pump is _____________.

The heat removal rate from a refrigerated space and the power input to the compressor are $$7.2$$ $$kW$$ and $$1.8$$ $$kW$$, respectively. The coefficient of performance $$(COP)$$ of the refrigerator is ___________