$$2$$ kg of ice at – $$10$$°C is mixed with $$5$$ kg of water at $$20$$°C 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 °C and $$0.5$$ $$kcal/kg/$$°C while the latent heat of fusion of ice is $$80$$ $$kcal/kg$$

Question

Infinity Learn · Accepted Answer

Initially ice will absorb heat to raise it's temperature to $$0oC$$ then it's melting takes place If mi $$=$$ Initial mass of ice, mi' $$=$$ Mass of ice that melts and mW $$=$$ Initial mass of water By Law of mixture Heat gained by ice $$=$$ Heat lost by water  ⇒mi×c×$$(10)+mi$$' ×$$L=mWcW$$[$$20$$]⇒$$2$$×$$0.5(10)+mi$$'×$$80=5$$×$$1$$×$$20$$⇒mi'$$=98$$ kgSo final mass of water $$=$$ Initial mass of water $$+$$ Mass of ice that melts  $$=5+98=498kg$$

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