Question

There is a liquid with a mass of 642 grams at a temperature of 24 degrees C and a specific heat of 3770J(kgC) A 50 gram ice cube at 0 degrees C is added. What is the final temperature of the mixture?

How many ice cubes must be added to get the mixture to 0 degrees C?

Answer 1

The heat required by a substance of mass m to increases its temperature from T_i to T_f is

where C is the specific heat of the substance.

Let T_f be the final temperature of the mixture. The heat released by the liquid temperature changes from 24^oC to T_f, the heat released by the liquid is

The ice at 0^oC first converts into water. The heat required by the ice is

After ice is completely transformed into water at 0^oC, the temperature of the water increases from 0^oC to T_f. The heat required by the water in this process is

Assuming no heat is transferred to the surroundings, the net heat exchanged between the ice and the liquid is zero.

Using , , we get

The heat required to convert ice cube at 0^oC to water at 0^oC is

Heat released by the liquid to change its temperature from 24^oC to 0^oC is

The heat is negative representing the heat is released by the liquid. The numbers of cubes that this heat released can transform from ice at 0^oC to water at 0^oC.