Blackbody Radiation
Section 2

u( f ) =
Start freq = End freq =

The Planck Distribution Formula

The Planck distribution formula  describes the energy density of blackbody radiation at a particular temperature and frequency.

The area of the light blue region is the value of the integral of the Planck distribution function between the start and end frequencies.  It is the integrated energy density in this range.

Section 2 Exercises:

  1. The default parameters for this page correspond to those given in Example 4-6, page 118 in the text.  The function u( f ) in the text field below the graph is plotted.  Is this the same as equation 4-19 (see also equation 9.55 in Thornton & Rex) in the text?  Check the result of the example.
  2. Using five different temperatures below 30,000K, derive a relation between fmax and T.  The temperature can be changed in the text field and then registered by pressing the "Do Integral" button.  Coordinates in the graph may be found by left-clicking.  Compare your result with the Wien displacement law.
  3. Using five different temperatures below 8000K, determine the relationship between the integral over "all" frequencies and the temperature.  Is it a fourth power of the temperature dependence?  The upper limit of integration should be no larger than 2.0E+15 Hz.
  4. For the visible range, compare the integrated energy densities for the Sun and Sirius A. 

This exercise was written by Dan Boye.

2000 by Prentice-Hall, Inc. A Pearson Company