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Question

A 5 g piece of ice at 20C is put into 10 g of water at 30C. Assuming that heat is exchanged only between the ice and the water, find the final temperature of the mixture. Specific heat capacity of ice = 2100 J kg1C1, specific heat capacity of water = 4200 J kg1C1 and latent heat of fusion of ice = 3.36 × 105 J kg1.


  1. - 10°C

  2. - 5°C 

  3. 20°C

  4. 0°C


Solution

The correct option is D

0°C


The heat given by the water when it cools down from 30C to 0C is

(0.01 kg) (4200 J kg1C1) (30C) = 1260 J.

The heat required to bring the ice to 0C is

(0.005 kg) (2100 J kg1C1) (20C) = 210 J.

The heat required to melt 5g of ice is

(0.005 kg)(3.36 × 105 J kg1) (20C) = 1680 J.

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 0C. Thus the final temperature of the mixture is 0C with some of the ice melted.

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