An irreversible heat engine extracts heat from a high temperature source at a rate of $$100kW$$ and rejects heat to a sink at a rate of $$50kW.$$ The entire work output of the heat engine is used to drive a reversible heat pump operating between a set of independent isothermal heat reservoirs at $${17^ \circ }C$$ and $${75^ \circ }C$$. The rate (in $$kW$$) at which the heat pump delivers heat to its high temperature sink is

A heat transformer is a device that transfers a part of the heat, supplied to it at an intermediate temperature, to a high temperature reservoir while rejecting the remaining part to a low temperature heat sink. In such a heat transformer, $$100kJ$$ of heat is supplied at $$350$$ $$K.$$ The maximum amount of heat in $$kJ$$ that can be transferred to $$400K,$$ when the rest is rejected to a heat sink at $$300K$$ is

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