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Question

# A 5 g piece of ice at - 20∘C is put into 10g of water at 30∘C. Assuming that heat is exchanged only between the ice and the water, find the final temperature of the mixture.

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Solution

## The correct option is A Specific heat capacity of ice = 2100 J/kg∘C, Specific heat capacity of water = 4200 J/kg∘C Latent heat of fusion of ice = 3.36×105 J/kg. The heat given by the water when it cools down from 30∘C to 0∘C is (0.01 kg)(2100 J/kg∘C)(20∘C)=210J The heat required to melt 5 g of ice is (0.005 kg)(3.36×105 J/kg)=1680J We see that whole of the ice cannot be melted as the required amount of heat is not provided by the water. Also, the heat is enough to bring the ice to 0∘C. Thus the final temperature of the mixture is 0∘C with some of the ice melted.

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