If the temperature of a blackbody doubles, by what factor does its radiated power increase?

If the temperature of a blackbody doubles, by what factor does its radiated power increase?

• A. 2
• B. 4
• C. 8
• D. 16

Answer: (D)

The key idea is that a blackbody’s radiated power scales with the fourth power of its temperature (P ∝ T^4) for a given emitting area. If you double the temperature, you multiply the power by 2^4, which is 16. So the radiated power becomes sixteen times larger. The other options would correspond to smaller exponents (2 for a linear relation, 4 for a quadratic, 8 for a cubic), which doesn’t match P ∝ T^4.

The key idea is that a blackbody’s radiated power scales with the fourth power of its temperature (P ∝ T^4) for a given emitting area. If you double the temperature, you multiply the power by 2^4, which is 16. So the radiated power becomes sixteen times larger. The other options would correspond to smaller exponents (2 for a linear relation, 4 for a quadratic, 8 for a cubic), which doesn’t match P ∝ T^4.