Two objects are placed in a room with a temperature of 20°C. Object A has a temperature of 70°C, while object B has a temperature of 140°C. They have the same emissivity, but different areas. What should the ratio of the area of object A to that of object B be if the net power emitted by both objects is the same?
A) 2.0
B) 3.4
C) 5.2
D) 17
E) 21

Question

Quizplus · Accepted Answer

The rate at which an object radiates energy is proportional to the fourth power of its temperature and proportional to its surface area. Therefore, the net power emitted by object A is proportional to (70-20)^4 * A, and the net power emitted by object B is proportional to (140-20)^4 * B, where A and B are the areas of the two objects. Since the net power emitted by both objects is the same, we have (70-20)^4 * A = (140-20)^4 * B, or equivalently, A/B = [(140-20)/(70-20)]^4 = 3.4^4. Therefore, the ratio of the area of object A to that of object B should be 3.4.

Two Objects Are Placed in a Room with a Temperature