Question

Two identical objects are placed in a room at 23 ∘C. Object 1 has a temperature of 92 ∘C , and object 2 has a temperature of 29 ∘C.

What is the ratio of the net power emitted by object 1 to that radiated by object 2?

Answer 1

As we now that -

Power (radiated or absorbed) is proportional to (absolute temperature)^4 = KT^4

Now, from the given values-

Object 1 power emitted = K(273+ 92)^2
Object 2 power emitted = K(273+ 29)^2

Object 1 power absorbed = Object 2 power absorbed = K(273+23)^2

So -

Object 1 net power emitted, A = K(273+ 92)^2 - K(273+23)^2 = [133225 - 87616]K = 45609K
Object 2 net power emitted, B = K(273+ 29)^2 - K(273+23)^2 = [91204 - 87616]K = 3588K

Therefore, ratio of the net power emitted by object 1 to that radiated by object 2 = 45609K / 3588K = 12.7 (Answer)