A blackbody is a substance that absorbs radiation of all wavelengths and radiates in a continuous spectrum at all wavelengths. It is given the name blackbody because an object that absorbs light at all wavelengths appears black to the human eye.
By the end of the 19th century, several properties of blackbody radiation had been established. First, the total intensity (the average rate of radiation of energy per unit surface area) emitted from a blackbody was shown to be proportional to the fourth power of its temperature:
.This is called the Stefan-Boltzmann law for a blackbody. The constant of proportionality is known as the Stefan-Boltzmann constant and was determined to be . It had also been discovered that the wavelength at which the radiation intensity was maximum varied inversely with temperature. This result, known as the Wien displacement law, is written
,where is the wavelength with the greatest radiated intensity.One aspect of blackbody radiation that remained unexplained was the full wavelength dependence of the intensity of the radiation, . In 1900, largely through trial and error, Max Planck formulated the following equation that successfully explained the wavelength dependence of the intensity:
Consider a blackbody that radiates with an intensity at a room temperature of . At what intensity will this blackbody radiate when it is at a temperature of ?
Express your answer in terms of .
At what wavelength would the intensity of blackbody radiation be at a maximum when the blackbody is at ?
Express your answer in meters to two significant figures.
An astronomer is trying to estimate the surface temperature of a star with a radius of by modeling it as an ideal blackbody. The astronomer has measured the intensity of radiation due to the star at a distance of and found it to be equal to . Given this information, what is the temperature of the surface of the star?
Express your answer in kelvins to two significant digits.