2 kg of ice at -200C is mixed with 5 kg of water at 200C in an insulating vessel having a negligilble 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  0C and 0.5 kcal/kg/ 0C while the latent heat of fusion of ice is 80 kcal/kg

Initially ice will absorb heat to raise its temperature to 00C then its melting takes place If mi= Initial mass of ice, mi' = Massof ice that melts and mw = initial mass of waterBy Law of mixture Heat gained by ice = Heat lost by water ⇒ mi×c×(20)+mi'×80 = 5×1×20   ⇒ mi' = 1 kg⇒ 2×0.5(20) + m1'×80 = 5 ×1×20   ⇒  m1' = 1 kgSo final mass of water = Initial mass of water + Mass of ice that melts = 5+1 = 6 kg.