Physics
Physics
Problem
Two identical square plates act as perfect blackbodies. Plate A has its maximum emission at 750 nm, while Plate B is heated so that its maximum emission occurs at 500 nm. Calculate the ratio of the power emitted per unit area by Plate B to that emitted per unit area by Plate A.Intuitive explanation
Wien's displacement law tells you the temperature from the peak wavelength, and Stefan–Boltzmann law connects temperature to radiated power per unit area. The key insight is that power scales as , so even though the wavelengths differ by only a factor of 1.5, the temperature ratio cubed makes the power ratio dramatic. Find each plate's temperature first, then use the relationship to compare their intensities.
Intuitive explanation
Wien's displacement law tells you the temperature from the peak wavelength, and Stefan–Boltzmann law connects temperature to radiated power per unit area. The key insight is that power scales as , so even though the wavelengths differ by only a factor of 1.5, the temperature ratio cubed makes the power ratio dramatic. Find each plate's temperature first, then use the relationship to compare their intensities.