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

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