Two litres of water (density$$ $$=$$ $$1$$ $$g/ml) in an open lid insulated kettle is heated by an electric heater of power $$1$$ kW. The heat is lost from the lid at the rate of $$160$$ $$J/s$$. The time taken for heating water (specific$$ heat capacity $$4.2kJkg$$−$$1K$$−$$1) from $$20$$°C to $$75$$°C is $$___seconds$$.

Question

Two litres of water (density$$ $$=$$ $$1$$ $$g/ml) in an open lid insulated kettle is heated by an electric heater of power $$1$$ kW. The heat is lost from the lid at the rate of $$160$$ $$J/s$$. The time taken for heating water (specific$$ heat capacity $$4.2kJkg$$−$$1K$$−$$1) from $$20$$°C to $$75$$°C is $$___seconds$$.

Infinity Learn · Accepted Answer

Mass of $$2$$ litres of water $$=$$ $$2$$ kg. Heat energy needed to raise the temperature $$of2$$ kg of water from $$20$$°C to $$75$$°C $$isQ=2$$×$$4.2$$×$$103$$×$$55=4.62$$×$$105JIf$$ t is the time taken, heat energy supplied by the heater in time t $$isQ1=($$ power × time $$)=1000$$ t joule Heat energy lost in time t $$isQ2=160$$ t joule Heat energy available for heating water $$isQ=Q1$$−$$Q2=840$$ tEquating $$Q=Q$$′, we get t≃$$550s$$.

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