Physics
Physics
Problem
Consider an ideal blackened metal plate that behaves as a perfect blackbody. (i) State the physical law that relates the radiant power emitted per unit surface area of the plate to its absolute temperature. (ii) Without performing any numerical calculation, explain qualitatively how the radiant power per unit area will change when the temperature of the plate is raised from 400 K to 600 K. (iii) Three identical such plates are maintained at 350 K, 450 K and 550 K respectively. Arrange the magnitudes of their radiant powers per unit area in ascending order and justify your answer on the basis of the law stated in part (i).Intuitive explanation
The Stefan–Boltzmann law is the key here: radiant power per unit area depends on the fourth power of absolute temperature, . This relationship means even modest temperature increases produce dramatic changes in radiation—a small fractional rise in multiplies the power output. Understanding this nonlinear dependence lets you compare and rank radiative outputs without calculation, just by reasoning about how the fourth power amplifies differences.
Intuitive explanation
The Stefan–Boltzmann law is the key here: radiant power per unit area depends on the fourth power of absolute temperature, . This relationship means even modest temperature increases produce dramatic changes in radiation—a small fractional rise in multiplies the power output. Understanding this nonlinear dependence lets you compare and rank radiative outputs without calculation, just by reasoning about how the fourth power amplifies differences.