Which of the following is a limiting case of solidification?

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Question and options:
- Question: Which of the following is a limiting case of solidification?
- Options: (A) equilibrium solidification, (B) solidification with no diffusion in the solid, but perfect mixing in the liquid, (C) solidification with no diffusion in the solid and only diffusional mixing in the liquid, (D) all of the above

Option A: equilibrium solidification. This describes a scenario where the solidifying interface maintains thermodynamic equilibrium as it advances, often implying that diffusion and phase boundary movements occur in a balanced way. As a limiting case, equilibrium conditions are a classic reference point for solidification pathways, so this option captures one aspect of limiting behavior.

Option B: solidification with no diffusion in the solid, but perfect mixing in the liquid. Here, the solid phase transforms without solute diffusion in the solid lattice, while the liquid remains perfectly mixed, which can represent a limiting case where mass transport in the solid is severely restricted and all concentration changes occur in the liquid phase. This paints a stark, boundary-case picture of solidification dynamics.

Option C: solidification with no diffusion in the solid and only diffusional mixing in the liquid. This is a more nuanced variant: the solid does not allow diffusion, while the liquid does permit diffusion, which imposes specific constraints on solute redistribution across the interface. As a limiting scenario, it isolates the extreme of solid-phase immobility coupled with liquid-phase diffusion.

Option D: all of the above. If each of A, B, and C represents a legitimate limiting case under different circumstances or parameter regimes, then the comprehensive statement that all of the above are limiting cases can be valid. In materials science, solidification can approach several distinct limiting behaviors depending on diffusion rates, temperature gradients, and interface kinetics, so the aggregation of multiple limiting scenarios under one umbrella is plausible.

Putting the pieces together, each of A, B, and C describes a boundary or extreme condition that could arise in solidification behavior. Therefore, collectively, they describe a set of limiting cases, which makes option D a comprehensive choice. The reasoning hinges on recognizing that limiting cases in solidification encompass various diffusion and equilibrium scenarios, and the inclusion of all the distinct extremes indicates a complete listing of the limiting behaviors described.

2251-1_20MTEN6070001 Lecture 21 Pre-Class Reading Quiz

Which of the following is a limiting case of solidification?

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