Two spheres,both at the same temperature,have radii R and 2R.How do the total energies radiated compare for these spheres?
A) They are the same.
B) The larger sphere has twice the value of the smaller sphere.
C) The larger sphere has 4 times the value of the smaller sphere.
D) The larger sphere has 16 times the value of the smaller sphere.

Question

Quizplus · Accepted Answer

The total energy radiated by a body is directly proportional to its surface area. The surface area of a sphere is given by 4πR^2.

For the smaller sphere with radius R, the surface area is 4πR^2.

For the larger sphere with radius 2R, the surface area is 4π(2R)^2 = 4π(4R^2) = 16πR^2.

Therefore, the larger sphere has 4 times the surface area of the smaller sphere.

Since the total energy radiated is directly proportional to the surface area, the larger sphere will radiate 4 times as much energy as the smaller sphere.

Hence, the correct choice is C.

Two Spheres,both at the Same Temperature,have Radii R and 2R