Physics

Physics

Problem

Two identical cups of soup, each initially at 92∘C92^{\circ}\text{C}, are placed in different locations. Cup A cools in a room held at 22∘C22^{\circ}\text{C}, while Cup B cools in a hallway held at 18∘C18^{\circ}\text{C}. After 6 minutes, Cup A has cooled to 70∘C70^{\circ}\text{C}. Assuming both cups cool with the same proportionality constant, determine the temperature of Cup B (in °C) at the 6-minute mark.
Intuitive explanation

This problem tests Newton's Law of Cooling, which says that an object cools at a rate proportional to the difference between its temperature and its surroundings. The key insight is that the proportionality constant kk is the same for both cups, so you can find kk from Cup A's data, then apply it to Cup B. The surrounding temperature matters because it sets the "floor" that each cup approaches—Cup B cools toward a lower baseline, so it loses heat faster.

Intuitive explanation

This problem tests Newton's Law of Cooling, which says that an object cools at a rate proportional to the difference between its temperature and its surroundings. The key insight is that the proportionality constant kk is the same for both cups, so you can find kk from Cup A's data, then apply it to Cup B. The surrounding temperature matters because it sets the "floor" that each cup approaches—Cup B cools toward a lower baseline, so it loses heat faster.

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