A solid sphere at temperature T radiates energy at a rate of R J/s.If the radius of the sphere were doubled (its temperature remains at T),then the rate of radiating energy would go up by a factor of
A)stays the same
B)2
C)4
D)8
E)16

Question

Quizplus · Accepted Answer

The rate at which a body radiates energy is given by the Stefan-Boltzmann law:

R1 = σT1^4

Where R1 is the rate at which the body radiates energy, T1 is the temperature of the body, and σ is the Stefan-Boltzmann constant.

If the radius of the sphere is doubled, its surface area will increase by a factor of 4 (since the surface area of a sphere is proportional to the square of its radius).

Therefore,

R2 = σT1^4 * 4

= 4σT1^4

= 4R1

So the rate of radiating energy will go up by a factor of 4 (i.e., choice C).

A Solid Sphere at Temperature T Radiates Energy at a Rate