In which situation would "unquenchable" best fit?

"Unquenchable" is best suited for a situation characterized by a persistent and insatiable desire or need. In the context of an unending thirst for knowledge, it conveys the idea that the individual has an overwhelming and relentless pursuit of information that cannot be satisfied. This term captures the essence of an intense and ongoing yearning, which aligns perfectly with the concept of a thirst for knowledge that drives a person to continuously seek learning and understanding.

The other contexts do not reflect the same intensity or persistence. For example, after a refreshing drink of water indicates a momentary and satiating experience rather than an enduring need. Similarly, following the end of a heated debate suggests closure and resolution, which doesn't fit with the concept of being unquenchable. Lastly, a brief moment of satisfaction implies a temporary fulfillment, contrasting with the idea of a lasting and insatiable hunger for more. Thus, "unquenchable" aptly applies to a continuous thirst for knowledge, making it the most fitting choice.