### Change of state in mixing

Suppose you want to drink cool water on a hot day, but you only have some hot water. So you put in some ice cubes to cool down the water. Let's calculate how much ice is needed to cool down the water to a given temperature.

Example

You are given 200 g of water at 90 . How much ice at 0 is needed to cool down the water to 10 .

Solution

Let kg be the mass of ice required.

Suppose no heat is lost to the surroundings,

Therefore 179 g of ice is needed to cool down the water.

In following animation, we will calculate the temperature of water obtained by mixing ice and hot water.

 Flash animation: Mixing ice and hot water

We can use a domestic electric boiler to boil some water and ice mixture. From the time required, we can estimate the specific latent of fusion of water. See the following activity.

 Fig. 1-14 How would you prepare a cold Horlicks drink?

Have you ever seen how people prepare cold Horlicks drink in a restaurant? They first use a small amount of hot water to dissolve the Horlicks powder completely, and then add some ice cubes to the drink. The ice cubes absorbs latent heat of fusion as they melt, thus cooling down the drink quickly.

People in the restaurant usually put in excess amount of ice cubes to make the drink very cold. But as physics students we are interested in applying the knowledge we have learned to predict the amount of ice needed to prepare a drink of a given temperature. The activity below gives you the chance to do so. You can verify your calculation with an experiment.

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