In an experiment on the specific heat of a metal, a $$0.20$$ kg block of the metal at $$150$$°C is dropped in a copper calorimeter (of$$ water equivalent $$0.025$$ $$kg) containing $$150$$ cc of water at $$27$$°C. The final temperature is $$40$$°C. If heat losses to the surroundings is not negligible, then the value of specific heat (in$$ $$cal/g$$°$$C) of the metal will $$be_____$$

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Infinity Learn · Accepted Answer

Here, mass of metal, m $$=$$ $$0.20$$ kg $$=200$$ gFall in temperature of metal           Δ$$T=150$$∘C−$$40$$∘$$C=110$$∘CIfe is specific heat of the metal, then heat lost by the metal,                     Δ$$Q=mc$$Δ$$T=200s$$×$$110$$   ……….(i)Volume$$ of water $$=$$ $$150$$ ccMass of water, m' $$=$$ $$150gWater$$ equivalent of calorimeter                         $$w=0.025kg=25gRise$$ in temperature of water in calorimeterΔT′$$=40$$∘C−$$27$$∘$$C=13$$∘CHeat gained by water and calorimeter      ΔQ′$$=m$$′$$+w$$ΔT′$$=(150+25)×$$13$$      ΔQ′$$=175$$×$$13$$    .........(ii)As$$ Δ$$Q=$$ΔQ′∴ From Eqs. $$(i) and (i), we $$get200$$×s×$$110=175$$×$$13s=175$$×$$13200$$×$$110$$≈$$0.10$$ $$J/g$$∘C

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