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.

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.