An object with an emissivity of 0.90 and a temperature of 400K radiates heat at a given rate. Which of the objects below radiate heat at the fastest rate?

Question

An object with an emissivity of 0.90 and a temperature of 400K radiates heat at a given rate. Which of the objects below radiate heat at the fastest rate?

An object with the same emissivity and a temperature 10% higher than the reference object.
It depends on how σ changes.
An object with an emissivity 10% higher and the same temperature as the reference object.
All objects radiate at the same rate.

Answer 1

An object with the same emissivity and a temperature 10% higher than the reference object will radiate heat at the fastest rate. This is because the rate at which an object radiates heat is proportional to the fourth power of its temperature (Stefan-Boltzmann law). Since the temperature of this object is higher, it will radiate heat at a faster rate compared to the other objects listed.