Question

A beaker contains 40g of water at $ 20^\circ C $ . Now 50g of ice at $ 0^\circ C $ is put into the beaker. The resulting temperature will be:
A) $ - 7^\circ C $
B) $ 0^\circ C $
C) $ 10^\circ C $
D) $ 1.5^\circ C $

Answer 1

Hint: In this solution, we will use the concepts of latent heat and specific heat capacity. The final temperature of the system will be due to the heat transfer from the water to the ice.

Formula used: In this solution, we will use the following formula:
 $ Q = mL $ where $ Q $ is the amount of energy needed to convert the state of matter of a substance of mass $ m $ and latent heat capacity $ L $
 $ Q = mc\Delta T $ where $ Q $ is the amount of energy needed to change the temperature of a substance of mass $ m $ and specific heat capacity $ c $ by temperature $ \Delta T $

Complete step by step answer:
When the ice is put in the water, the water’s temperature will be used to melt the ice that is put into the water. First, let us see how much heat energy is required to convert all the ice into water.
To convert 50 g of ice into water, we need heat energy of
 $ Q = 50 \times 80 $
 $ \Rightarrow Q = 4000\,cal $
Now, the maximum amount of heat energy that will be released when the water drops its temperature to $ 0^\circ C $ will be
 $ Q = 40 \times 1 \times (20 - 0) $
 $ \Rightarrow Q = 800\,cal $
Hence the energy released when water drops its temperature will not be sufficient to convert all the mass of the ice into water. However, the water will still drop to $ 0^\circ C $ to try to establish an equilibrium. In the process, some of the ice will be converted to water as well.
The temperature of the water will be $ 0^\circ C $ hence the correct choice is option (B).

Note:
We should be familiar with and be able to differentiate between the concepts of latent heat capacity and specific heat capacity. The former is applicable when an object is being converted from one state to the other e.g. water to ice and the latter is applicable when the temperature of a substance is being changed without a change in its state.