In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to 250 kJ/kg. The exit of the compressor is superheated at condenser pressure with specific enthalpy equal to 300 kJ/kg. At the condenser exit, the refrigerant is throttled to the evaporator pressure. The coefficient of performance (COP) of the cycle is 3. If the specific enthalpy of the saturated liquid at evaporator pressure is 50 kJ/kg, then the dryness fraction of the refrigerant at entry to evaporator is ________.

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