A reversible cycle receives $$40$$ $$kJ$$ of heat from one heat source at a temperature of $${127^ \circ }C$$ and $$37$$ $$kJ$$ from another heat source at $${97^ \circ }C.$$ The heat rejected (in $$kJ$$) to the heat sink at $${47^ \circ }C$$ is ___________

A reversible heat engine receives $$2$$ $$kJ$$ of heat from a reservoir at $$1000$$ $$K$$ and a certain amount of heat from a reservoir at $$800$$ $$K$$. It rejects $$1$$ $$kJ$$ of heat to a reservoir at $$400$$ $$K.$$ The net work output (in $$kJ$$) of the cycle 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

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