Juan fills two separate beakers with boiling water. The first beaker holds 500 ml, and the second beaker holds 75 ml. Juan then measures the temperature of both beakers and calculates how long it takes the water in each beaker to reach room temperature. Which of the following is true?

A. The water in the 75 ml beaker will cool down at the same rate as the water in the 500 ml beaker.
B. The water in the 500 ml beaker will never cool down to the temperature of the room.
C. The water in the 500 ml beaker will cool down more rapidly than the water in the 75 ml beaker.
D. The water in the 75 ml beaker will cool down more rapidly than the water in the 500 ml beaker.

The water in the 75 ml beaker will cool down more rapidly than the water in the 500 ml beaker due to differences in surface area. The correct answer is d.

Explanation:

The correct answer is d: the water in the 75 ml beaker will cool down more rapidly than the water in the 500 ml beaker.

This is because the rate at which an object cools down is dependent on its surface area. The water in the 75 ml beaker has a smaller volume and therefore a larger surface area compared to the water in the 500 ml beaker. With a larger surface area, there is more area for heat to escape from the water, resulting in a faster cooling rate.

On the other hand, the water in the 500 ml beaker has a larger volume and a smaller surface area, which means there is less area for heat to escape from. As a result, the water in the 500 ml beaker will cool down more slowly compared to the water in the 75 ml beaker.