Final answer:
When the temperature of a black body increases by 10%, the radiation emitted increases by approximately 46%. Therefore, the closest option given is C. 40% after rounding down, although the exact answer is not listed in the options.
Step-by-step explanation:
To answer the question about how the quantity of radiation emitted from a black body changes with an increase in temperature, we can refer to the Stefan-Boltzmann law. This law states that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of the black body's temperature. The formula is typically written as E = σT^4, where E is the energy radiated per unit area, σ (the Stefan-Boltzmann constant) is a constant of proportionality, and T is the absolute temperature of the black body.
If the temperature increases by 10%, let's represent the initial temperature as T and the increased temperature as T' where T' = 1.10T. When we compare the energy radiated before and after the temperature increase, we calculate E' = σ(1.10T)^4 = σ(1.10)^4T^4. This becomes 1.4641 times the original emitted energy, implying that the radiation has increased by 46.41%. Hence, none of the given options accurately represents the correct percentage. However, for a 10% increase in temperature, the closest given option would be C. 40%, if rounded down.