Question

A perfect black body at 100º C emits 10W of power. About how much power would it emit at 0º C?

A) 10 W
B) 20 W
C) 5 W
D) 40 W

Answer 1

The power emitted by a perfect black body at 0ºC is significantly lower than at 100ºC, according to the Stefan-Boltzmann law. Calculation based on the fourth power of temperature ratio gives an emission of approximately 5W, corresponding to option C in the given choices.

Step-by-step explanation:

The question is asking about the power emission of a perfect black body at different temperatures and this can be explained by the Stefan-Boltzmann law, which states that the energy flux (power per unit area) emitted by a black body is proportional to the fourth power of its absolute temperature (F = σT4).

Since we know the power at 100ºC (373K), to find the power at 0ºC (273K), we need to compare the fourth powers of these temperatures. The ratio of power emitted at these temperatures would be (273/373)4 of the initial power. Therefore, the power at 0ºC would be approximately this ratio times 10W. After performing the calculation, the answer is much less than the initial 10W and therefore, the closest approximate answer given the options would be C) 5W.