$$2$$ kg of ice at $$-200C$$ is mixed with $$5$$ kg of water at $$200C$$ in an insulating vessel having a negligilble heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are $$1$$ $$kcal/kg$$ per $$0C$$ and $$0.5$$ $$kcal/kg/$$ $$0C$$ while the latent heat of fusion of ice is $$80$$ $$kcal/kg$$

Question

$$2$$ kg of ice at $$-200C$$ is mixed with $$5$$ kg of water at $$200C$$ in an insulating vessel having a negligilble heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are $$1$$ $$kcal/kg$$ per  $$0C$$ and $$0.5$$ $$kcal/kg/$$ $$0C$$ while the latent heat of fusion of ice is $$80$$ $$kcal/kg$$

Infinity Learn · Accepted Answer

Initially ice will absorb heat to raise its temperature to $$00C$$ then its melting takes place If $$mi=$$ Initial mass of ice, mi' $$=$$ Massof ice that melts and mw $$=$$ initial mass of waterBy Law of mixture Heat gained by ice $$=$$ Heat lost by water ⇒ mi×c×(20)+mi$$'×$$80$$ $$=$$ $$5$$×$$1$$×$$20$$   ⇒ mi' $$=$$ $$1$$ kg⇒ $$2$$×$$0.5(20) $$+$$ $$m1$$'×$$80$$ $$=$$ $$5$$ ×$$1$$×$$20$$   ⇒  $$m1$$' $$=$$ $$1$$ kgSo final mass of water $$=$$ Initial mass of water $$+$$ Mass of ice that melts $$=$$ $$5+1$$ $$=$$ $$6$$ kg.

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