$$2$$ kg of ice at $$-200C$$ is mixed with $$5$$ kg of water at $$200C$$ 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 $$kg-1$$ $$0C-1$$ and $$0.5$$ kcal $$kg-1$$ $$0C-1$$ while the latent heat of fusion of ice is $$80$$ kcal $$kg-1$$.

Question

$$2$$ kg of ice at $$-200C$$ is mixed with $$5$$ kg of water at $$200C$$ 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 $$kg-1$$ $$0C-1$$ and $$0.5$$ kcal $$kg-1$$ $$0C-1$$ while the latent heat of fusion of ice is $$80$$ kcal $$kg-1$$.

Infinity Learn · Accepted Answer

Initially ice will absorb the heat to raise its temperature at $$00C$$, then its melting takes places.If mi $$=$$ initial mass of ice, m'i $$=$$ mass of ice that melts and mω $$=$$ initial mass of water.By law of mixture, heat gained by ice $$=$$ heat lost by water⇒ $$m1$$×c×(20)+mi$$'×$$L=mwfw(20)⇒ $$2$$×$$0.5(20)+m$$'i ×$$80=5$$×$$1$$×$$20$$⇒mi′$$=1kgSo$$, final mass of water $$=$$ initial mass of water $$+$$ mass of ice that melts $$=$$ $$5$$ $$+$$ $$1$$ $$=$$ $$6kg$$

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