Question

Suppose you want to cool 0.760 L (0.760 kg) of water initially at 31.8 degrees C by adding ice cubes whose initial temperature is 0.0 degrees C. What mass of ice must be added so that the final temperature of the system is 8.10 degrees C? Assume that no heat is lost to the surroundings.

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 released from the water in changing its temperature from -31.8⁰C to 8.10⁰C is

                              (C = 1 cal/g.⁰C for water)

Let the required mass of ice is m.

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

                                      (L = 80 cal/gram for ice)

The heat required to change the temperature of water from 0⁰C to 8.10⁰C is

                            

So, the total heat needed to convert the ice into water and heat it to 8.10⁰C is

                             

If the whole system is at 8.10⁰C then, we can write

                              

                          or,