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.

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