Final answer:
The total energy radiated by a black body is proportional to the fourth power of its temperature, as stated in the Stefan-Boltzmann law. The law's formula is F = σT^4, with σ being the Stefan-Boltzmann constant. Quintupling a temperature would proportionally increase energy radiated by that body.
Step-by-step explanation:
Is Total Energy Radiated by a Black Body Proportional to Its Temperature?
Yes, the total energy radiated by a black body is indeed proportional to its temperature. This is described by the Stefan-Boltzmann law, which states that the energy flux (or power emitted per square meter) from a blackbody is proportional to the fourth power of its absolute temperature (in kelvins). The equation representing this law is F = σT4, where F is the energy flux and σ (Stefan-Boltzmann constant) is 5.670 × 10⁻⁸ W/(m²K⁴). When the temperature of a black body is tripled, the power it radiates increases by 81 times since (34 = 81).
Hotter objects, like stars, emit significantly more power across all wavelengths. A perfect blackbody is an idealized concept that absorbs all incoming electromagnetic radiation and re-emits it. Practical examples of blackbodies are stars and planets, which nearly follow this idealized behavior. The total power that a blackbody emits, which can be estimated using the Stefan-Boltzmann law, allows us to understand the energy output of celestial bodies.