2 kg of ice at – 20°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
Text Solution
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Initially ice will absorb heat to raise it's temperature to 0 o C then it's melting takes place
If m i = Initial mass of ice, m i ' = Mass of ice that melts and m W = Initial mass of water
By Law of mixture Heat gained by ice = Heat lost by water ⇒ ⇒ 
= 
⇒ ⇒ 
= 
⇒ ⇒ 
= 1kg
So final mass of water = Initial mass of water + Mass of ice that melts = 5 + 1= 6 kg.
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