$$2$$ kg of ice at $$-$$ $$20oC$$ is mixed with $$5$$ kg of water at $$20oC$$ in an insulating vessel having a negligible 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 oC and $$0.5$$ kcal $$kg/oC$$ while the latent heat of fusion of ice is $$80$$ $$kcal/kg$$.

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Initially ice will absorb heat to raise its temperature to $$0oC$$. then its melting takes place.If mi $$=$$ initial mass of ice, mi' $$=$$ Mass of ice that melts and $$mW=$$ Initial mass of waterBy law of mixture, heat gained by ice $$=$$ heat lost by water⇒ mi×c×$$(20)+mi$$′×$$L=mWCW$$[$$20$$]⇒ $$2$$×$$0.5(20)+mi$$′×$$80=5$$×$$1$$×$$20$$⇒mi′$$=1kgSo$$ final mass of water $$=$$ Initial mass of water $$+$$ Mass of ice that melts $$=$$ $$5$$ $$+$$ $$1$$ $$=$$ $$6$$ kg.

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