Question

When m grams of water at $10^\circ C$ is mixed with m grams of water at $0^\circ C$, which of the following statements are false?
A) The temperature of the system will be given by the equation, $m \times 8$ + $m \times 1 \times (T - 0)$ = $m \times 1 \times (10 - T)$.
B) Whole of ice will melt and the temperature will be more than $0^\circ C$ but lesser than $10^\circ C$.
C) Whole of ice will melt and the temperature will be $0^\circ C$.
D) Whole of ice will not melt and the temperature will be $0^\circ C$.

Answer 1

When water is added to ice then ice absorbs the heat from the water. This hidden heat is called heat of fusion and heat capacity. We have to calculate the amount of heat of fusion of ice and the heat capacity of water. If the heat of fusion is more than ice will not melt whereas if the heat capacity of water is more, then ice will melt.

Complete step by step solution:
According to thermodynamic studies, some of the calculated values we need:
Heat of fusion of ice = $333.55J/g$ and
Heat capacity of water = $4.186JK/g$
First of all, we have to find the amount of heat energy released by cooling M g of water at $10^\circ C$ to $0^\circ C$ to melt M g of ice. We get that the amount of heat can be calculated with the help of the formula $\Delta H = mC\Delta T$. So for 10g of water the amount of heat will be 41.86M Joules of heat. Now the amount of heat of ice fusion is 333.55j/g. Therefore, the ice will not melt and the temperature remains the same i.e. $0^\circ C$.

For melting of ice, it should be given heat more than its heat of fusion. Heat of fusion is defined as the amount of heat required to extract from water to convert into ice. And the heat capacity is defined as the amount of heat in unit mass of water. So to convert a unit mass of water into ice, this heat has to be removed from the water to bring it at $0^\circ C$. And to convert it into ice heat equal to heat of fusion has to be removed from it.

Note: To convert substances from one state to another latent heat of fusion has to be given or extracted from the substances. Also every substance has heat capacity at specific temperature. So firstly the substance has to be brought to $0^\circ C$. Then latent heat of fusion has to be removed in order to convert water into ice.