Final answer:
The temperatures of black holes are related to their size, with smaller black holes being hotter than larger ones due to higher energy emissions through Hawking radiation. The correct answer to the question is b) The small black hole is hotter.
Step-by-step explanation:
The relationship between the temperatures of a small and large black hole suggests that the smaller black hole is hotter. This counterintuitive phenomenon arises from the properties of black holes as described by Hawking radiation, according to which smaller black holes radiate energy more quickly than larger ones. Thus, the correct answer to the question is b) The small black hole is hotter.
To clarify further, as a black hole's size decreases, its surface gravity increases, leading to greater energy emissions (Hawking radiation) and consequently higher temperatures. On the contrary, larger black holes have less surface gravity, emit less radiation, and are therefore cooler.
This is not directly intuitive as we see objects in our daily lives radiate heat in a manner not related to their size, such as how a black object can absorb and radiate energy differently than a white one, or how the surface area of an object affects the speed of heat transfer, but the physics of black holes operate distinctly due to their unique nature.