If the temperature of an object is doubled, how does its thermal radiation chang

If the temperature of an object is doubled, how does its thermal radiation change according to the Stefan-Boltzmann law?

If the temperature of an object is doubled, how does its thermal radiation change according to the Stefan-Boltzmann law?

Step 1: Understand the Stefan-Boltzmann law, which states that the thermal radiation emitted by an object is proportional to the fourth power of its absolute temperature (T).
Step 2: Write the formula for thermal radiation: R = σT^4, where R is the thermal radiation and σ is the Stefan-Boltzmann constant.
Step 3: If the temperature (T) is doubled, we replace T with 2T in the formula: R = σ(2T)^4.
Step 4: Calculate (2T)^4: (2T)^4 = 2^4 * T^4 = 16 * T^4.
Step 5: This means the new thermal radiation (R') is R' = σ(16 * T^4) = 16 * σT^4.
Step 6: Since σT^4 is the original thermal radiation (R), we can say R' = 16R.
Step 7: Therefore, when the temperature is doubled, the thermal radiation increases by a factor of 16.

Stefan-Boltzmann Law – The law states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature (E ∝ T^4).