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

At a hydro electric power plant site, available head and flow rate are $$24.5$$ $$m$$ and $$10.1{m^3}/s$$ respectively. If the turbine to be installed is required to run at $$4.0$$ revolution per second ($$rps$$) with an overall efficiency of $$90\% $$, the suitable type of turbine for this site is _______________.