Question

A solid cylinder is radiating power. It has a length that is ten times its radius. It is cut into a number of smaller cylinders, each of which has the same radius. Each small cylinder has the same temperature as the original cylinder. The total radiant power emitted by the pieces is twice that emitted by the original cylinder. How many smaller cylinders are there? Give your answer as a number with no units.

Answer 1

According to Stefan’s law, the total radiant power is

P = AεσT⁴

where A = surface area, ε = emissivity, σ = Stefan’s constant.

Because we have multiple cylinders, so all are made of same material, so their ε must be same but we have different temperature, so the surface area makes the difference.

The radiance will be twice if total surface of the pieces need to be twice that of the original cylinder.

The L and R be the length and radius of the original cylinder. Then its surface area is

if we cut cylinder into n pieces of same length (L/n) each has the surface area of