A Carnot engine having a perfect gas as the working substance is driven backward and is used for freezing water already at $$0$$∘C. If the engine is driven by a $$500$$ W electric motor having a efficiency of $$60$$%, how long (in$$ $$seconds) will it take to freeze $$15$$ kg of water. Take $$15$$∘C and $$0$$∘C as the working temperatures of the engine and assume there are no heat losses in the refrigerating system. Latent heat of ice $$=333$$×$$103J/kg$$

Question

A Carnot engine having a perfect gas as the working substance is driven backward and is used for freezing water already at $$0$$∘C. If the engine is driven by a $$500$$ W electric motor having a efficiency of $$60$$%, how long (in$$ $$seconds) will it take to freeze $$15$$ kg of water. Take $$15$$∘C and $$0$$∘C as the working temperatures of the engine and assume there are no heat losses in the refrigerating system. Latent heat of ice $$=333$$×$$103J/kg$$

Infinity Learn · Accepted Answer

Given,    $$T1=273K$$​                 $$T2=15+273=280K$$​ Useful power  $$=$$ηP​$$=0.6$$×$$500=300J/s$$​ We know that coefficient of performance ​β$$=Q2W=(T2T1$$−$$T2)$$​⇒$$Q2=300$$×$$(273288$$−$$273)=5460J/s$$​ Heat needed to melt the ice $$Q=mL=15$$×$$333$$×$$103J$$​ Time taken in freezing water $$t=QQ2=15$$×$$333$$×$$1035640=914.84s$$​

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