Two identical solid spheres have the same temperature. One of the spheres is cut into two identical pieces. These two hemispheres are then separated. The intact sphere radiates an energy Q during a given time interval. During the same interval, the two hemispheres radiate a total energy Q'. What is the ratio Q'/Q?
A)2.0
B)0.50
C)4.0
D)1.5
E)0.25

Question

Quizplus · Accepted Answer

The radiation energy is proportional to the surface area. The intact sphere has a surface area of 4πr². When cut into two hemispheres, the total surface area becomes 2(2πr²) = 4πr² (curved surfaces) + 2(πr²) (flat surfaces) = 6πr². Thus, the ratio of the radiated energy is 6πr²/4πr² = 1.5.

Two Identical Solid Spheres Have the Same Temperature