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Question

2 kg of ice at 20C is mixed with 5 kg of water at 20C in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that specific heats of water and ice are 1 Kcal kg1 C1 and  0.5 Kcal kg1 C1 while the latent heat of fusion of ice is 80 kcal/kg
  1. 6 kg 
  2. 4 kg 
  3. 2 kg 
  4. 7 kg


Solution

The correct option is A 6 kg 
Heat released by 5 kg of water when its temperature falls from 20C to 0C is,
Q1=mcΔθ=(5)(103)(200)=105 cal
when 2 kg ice at 20C comes to a temperature of 0C, it takes an energy
Q2=mcΔθ=(2)(500)(20)=0.2×105 cal
the remaining heat
Q=Q1Q2=0.8×105 cal will  melt a mass m of the ice, where
m=QL=0.8×10580×103=1 kg
So, the temperature of the mixture will be 0C, mass of water in it is 5+1=6 kg and mass of ice is 21=1 kg

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