A solar collector receiving solar radiation at the rate of $$0.6$$$$kW/{m^2}$$ transforms it to the internal energy of a fluid at an overall efficiency of $$50\% $$. The fluid heated to $$350$$ $$K$$ is used to run a heat engine which rejects heat at $$313$$ $$K.$$ If the heat engine is to deliver $$2.5$$ $$kW$$ power, then minimum area of the solar collector required would be

A heat engine having an efficiency of $$70\% $$ is used to drive a refrigerator having a coefficient of performance of $$5.$$ The energy absorbed from low temperature reservoir by the refrigerator for each $$kJ$$ of energy absorbed from high temperature source by the engine is

A gas contained in a cylinder is compressed, the work required for compression being $$5000$$ $$kJ.$$ During the process, heat interaction of $$200$$ $$kJ$$ causes the surroundings to the heated. The change in internal energy of the gas during the process is

A centrifugal pump is required to pump water to an open water tank situated $$4$$ $$km$$ away from the location of the pump through a pipe of diameter $$0.2$$ $$m$$ having Darcy’s friction factor of $$0.01.$$ The average speed of water in the pipe is $$2$$ $$m/s.$$ if it is maintain a constant head of $$5$$ $$m$$ in the tank, neglecting other minor losses, the absolute discharge pressure at the pump exist is ______________