JEE Physics 2023 Question with Solution

Given: Heat supplied is $184 \, \text{kJ}$, mass of ice is $0.600 \, \text{kg}$, initial temperature is $-12^\circ C$, specific heat of ice is $2222.3 \, \text{J/kg/}^\circ \text{C}$, and latent heat of fusion is $336000 \, \text{J/kg}$.

Find: The final state of the system.

First raise the temperature of ice from $-12^\circ C$ to $0^\circ C$:

Remaining heat after bringing the ice to $0^\circ C$ is:

Heat required to melt all the ice is:

Since $167999.44 \, \text{J} < 201600 \, \text{J}$, all the ice does not melt.

Mass of ice melted is:

Mass of remaining ice is:

Therefore,

Therefore, the final system is a mixture of ice and water at $0^\circ C$, so the correct statements are A and D. The source the solution says A, but the working clearly supports A and D only, which corresponds to the combined answer.

From the working, the final temperature remains $0^\circ C$, so statement A is true and statement B is false. The ratio obtained is $1:5$, so statement D is true, while statement C is false. Statement E is false because some ice remains. Hence the combined correct choice is A and D only.