Question

A block of ice, mass 3.20 kg and initial temperature of -8 ^oC, is placed in an insulating container. 5.00 kg of water at temperature 13 ^oC, is added to the container. The water and ice exchange heat, but no other heat flows into or out of the container.

In the process of the water and ice reaching equilibrium, how much ice melts?

Give your answer in kg to three digits.

Note: It is possible that the answer is zero.

Answer 1

The absorbed/released heat in changing the temperature of the substance is given by

The absorbed/released heat in phase transition is

  

Where L is latent heat, m is mass of the substance, C is the specific heat capacity, and is the change in temperature.

The heat required to change the temperature of ice from -8⁰C to 0⁰C is

  

The required heat for converting ice into the water at 0-degree Celsius is

   (L = 80 cal/gram for ice)

And the heat released by water in changing the temperature from 13 degrees to 0-degree Celsius is

(C = 1 cal/g.⁰C for water)

After changing the temperature of ice from -8⁰C to 0⁰C, the remaining heat is

  

In 52200 cal,the amount of ice gets converted into water is

  

Hence, 0.65 kg of ice will melt in this process.