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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 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

A
7 kg
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B
6 kg
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C
4 kg
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D
2 kg
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Solution

The correct option is B 6 kg
Initially ice will absorb heat to raise it's temperature to 0C then it's melting takes place
If m = Initial mass of ice, m' = Mass of ice that melts and mw = Initial mass of water
By Law of mixture Heat gain by ice = Heat loss by water
m×c×(20)+m×L=mwCw[20]2×0.5(20)+m×80=5×1×20m=1kg
So final mass of water = Initial mass of water + Mass of ice that melts = 5 + 1= 6 kg.

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