Problem 49 - Master Resource Book in JEE Main Physics

Question

It is known that wax contracts on solidification. If molten wax is taken in a large vessel and it is allowed to cool slowly, then (a) it will start solidifying from the top to downward (b) it will starts solidifying from the bottom to upward (c) it will start solidifying from the middle, upward and downward at equal rates (d) the whole mass will solidify simultaneously

Step-by-Step Solution

Answer

Wax will start solidifying from the top to downward.

Step 1: Understanding Wax Solidification

Wax contracts when it solidifies, meaning that the density of solid wax is higher than that of liquid wax. Hence, the solid wax will tend to occupy less volume and stay above the molten wax.

Step 2: Heat Loss Consideration

As the molten wax is in a large vessel and allowed to cool slowly, the surface is exposed to the surrounding air. Thus, the top of the wax will lose heat more rapidly compared to the base or the middle.

Step 3: Solidifying Process Analysis

Due to faster heat loss at the surface, the wax will start solidifying at the top first. The contracting solid wax will not allow the molten wax underneath to solidify first.

Step 4: Conclusion

Given these factors, the correct answer is that the wax will start solidifying from the top to downwards.

Key Concepts

Heat Transfer in Solids

When it comes to solid materials, heat transfer primarily occurs via conduction. This process involves the transfer of heat energy through the vibrations of molecules without the movement of the material itself. In the case of wax solidification, heat from the warmer wax molecules at the top moves towards the cooler surface exposed to air, gradually reaching the molten wax below.
The rate of heat transfer in solids is also determined by the material's thermal conductivity, the temperature difference, and the surface area exposed. In wax, this process is quite slow due to its low thermal conductivity. As a result, the surface cools and solidifies first, because it loses heat faster to the surrounding air.
In summary, heat transfer in solids like wax involves conduction and depends on various factors that influence how heat is lost across the material.

Density Changes

Density is a measure of how much mass is contained in a given volume. When wax transitions from liquid to solid, its density increases. This means that solid wax molecules occupy a smaller volume compared to when they are in a liquid state.
This change in density upon solidification is crucial in understanding why solid wax appears floating on the remaining molten wax. Since the solid phase is denser, it contracts and takes up less space, contributing to the downward progression of solidification.
Interestingly, this density change is inherent in the solidification process of wax and many other substances, affecting how they cool and solidify.

Phase Transition

A phase transition occurs when a substance changes from one state of matter to another, such as from liquid to solid. This shift involves a change in the arrangement of molecules and often comes with the absorption or release of energy.
For wax, the transition from liquid to solid (solidification) takes place when it loses enough thermal energy. This change begins at the top due to quicker heat loss and then moves downward.
During a phase transition, physical properties like density and structure dramatically change. For wax, solidification affects its structural integrity, with molecules aligning more rigidly in the solid state.

Solidification Process

The process of solidification involves the gradual transformation of a liquid into a solid as it cools. In our wax example, this starts at the top due to greater exposure to air and faster heat dissipation.
The progression of solidification downwards is predominantly guided by the continuous cooling and contracting of the solid wax above. This cooling stops the expansion of molten wax, leading to a consistent solid layer forming from top to bottom.
As heat continues to transfer away from the liquid wax, the solidification process continues until the entire mass becomes solidified. The contracting nature of the wax during solidification predominantly defines its behavior and the way it interacts with heat loss.