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Questions based on phase change

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]


So final mass of water = Initial mass of water + Mass of ice that melts  =5+98=498kg

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