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

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

Options:

Correct Answer: It quadruples

Solution:

According to the Stefan-Boltzmann law, if the temperature is doubled, the thermal radiation increases by a factor of 2^4 = 16, not quadruples.

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).