Question

A solid sphere has a temperature of 773 K.The sphere is melted down and recast into a cube that has the same emissivity and emits the same radiant power as the sphere.What is the cube's temperature?

Answer 1

• The cube temperature is 732 K.

Given-

Temperature of the solid sphere = 773 K.

The sphere is melted down and recast into a cube that has  the same emissivity and emits the same radiant power as the sphere.

And we know that total radiant power is given by Stefan Boltzmann law-

P = AεσT⁴

Since both the sphere and cube emits same power so we have

As ε σ Ts⁴ = Ac ε σ Tc⁴

So the temperature of the cube is given by-

Tc = (As/Ac) ^1/4 Ts

Mass of sphere and cube is same so volume will also be same if their densities will be same.

So, 4/3 πr³ = a³ , where r is radius of the sphere and a is the side of the cube.

So, a = r (4π/3) ^ 1/3

Now, As/Ac = 0.806

Tc = (0.806) ^1/4 × 773

Tc = 732 K.