If the temperature doubles for a perfect blackbody, by what factor does the radiated power change?

If the temperature doubles for a perfect blackbody, by what factor does the radiated power change?

• A. 8 times.
• B. 16 times.
• C. 4 times.
• D. 2 times.

Answer: (B)

The key idea is the Stefan-Boltzmann law: the radiated power per unit area from a perfect blackbody is proportional to the fourth power of its temperature. If the temperature doubles, the power becomes (2T)^4 = 16 T^4, so it increases by a factor of 16. The radiated power (per area) scales as T^4, which is why the correct factor is 16. If the temperature dependence were linear, squared, or cubic, the factors would be 2, 4, or 8, respectively, but for a blackbody it’s the fourth power that matters.

The key idea is the Stefan-Boltzmann law: the radiated power per unit area from a perfect blackbody is proportional to the fourth power of its temperature. If the temperature doubles, the power becomes (2T)^4 = 16 T^4, so it increases by a factor of 16. The radiated power (per area) scales as T^4, which is why the correct factor is 16. If the temperature dependence were linear, squared, or cubic, the factors would be 2, 4, or 8, respectively, but for a blackbody it’s the fourth power that matters.