An insulating calorimeter contains a certain amount of water and ice both at 0 d

Question

An insulating calorimeter contains a certain amount of water and ice both at 0 degree C. The calorimeter is instrumented with a thermometer and a weight scale. Further, it has an intake that allows steam to be injected into the water. You find that when 30 grams of steam at 100 degree C is injected into the water, the temperature starts to rise above zero. When a total of 35 grams of steam is injected into the water, the temperature of the mixture is at 5 degree C. How mu Ch ice was in the calorimeter before the steam is introduced? How mu Ch water was in the calorimeter before the steam is introduced?

Explanation / Answer

Initially, steam enters and loss heat to melt the ice during this

As heat loss by steam = heat gained by ice

(ms)(ss)(100) = (mi)(L)

(30)(1.996)(100) = (mi)(334)

So mi = 17.928 grams

Then steam enters and rises the temperature and hence

As heat loss by steam = heat gained by the system

(ms)(ss)(95) = (mi + mw)(sw)(5)

(35)(1.996)(95) = (mi + mw)(4.187)(5)

(mi + mw) = 317.0145 grams

Hence

mw = 317.0145 - 17.928 = 299.0865 grams

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