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Modern Physics
Found in: Page 409
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

The electromagnetic intensity thermally radiated by a body of temperature T is given by I=σT4 where σ=5.67×108 W/m2K4

This is known as the Stefan-Boltzmann law. Show that this law follows from equation (9-46). (Note: Intensity, or power per unit area, is the product of the energy per unit volume and distance per unit time. But because intensity is a flow in a given direction away from the blackbody, the correct speed is not c. For radiation moving uniformly in all directions, the average component of velocity in a given direction is 14c .)

The intensity is 5.64×108Wm2K4T4

See the step by step solution

Step by Step Solution

Energy of photons in container (U)

Expression for energy of photons in container (U) is given by-

U=8π2VkB4T415h3c3 ……. (1)


kB Boltzmann's constant

h Planck's constant

c Speed of light in vacuum

T Temperature

V Volume of container

Alternate expression for intensity -

I=( energy volume )( distance time ) ……. (2)

Find the intensity.

To start, equation (2) can be rewritten slightly:

I= energy volume distance time = energy volume (velocity I=UVv..(3) ….. (3)

Use that the average component of velocity in any particular direction is c/4 , set v equal to c/4, and use equation (1) for the energy U in equation (3):


Substitute 1.38×1023 m2kgs2 for kB,6.63×1034 J.s and 3×103 m/s for c in the above equation and obtain the equation as given below.

I=2π5VkB415h3c3T4=2π51.38×1023JK4156.63×1034 J.s33×108msT4=5.64×108Wm2K4T4

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