Blackbody Radiation
Section 1

Room Temperature  

300K

Red Hot Heater

900K

Betelgeuse

3700K

Sun

5800K

Sirius A

11,000K

Sirius B

32,500K

Change Temperature 

Blackbody Spectrum:  Every object that has a temperature above absolute zero emits blackbody radiation.  You do not normally notice it because your eyes are only sensitive to a very small portion of the electromagnetic spectrum.  An object must be quite hot for it to emit a significant amount of visible light.  This applet shows the spectrum and the apparent color of an object.  The apparent color, indicated by the color circle labeled "Appearance,"  is meant to give a general idea of the mixture of visible radiation a body is emitting.  It assumes that the eye has a flat response over the entire visible spectrum.  However, the eye is most sensitive to yellow light and the sensitivity diminishes rapidly when moving to higher and lower frequencies.  Note that the Energy Density axis is autoscaled.

Changing the temperature:  The temperature in the applet can be varied in three ways. The first is to press the preprogrammed buttons. The temperature may also be changed by typing in a new value in the text field and pressing the Change Temp. button.  The third way is to move the peak wavelength by click-dragging on the graph itself.  Note that the total energy radiated by a black body increases dramatically with temperature by observing changes in the vertical scale.

Section 1 Exercises:

  1. A resistive heating element on a stove that glows "red hot" has a temperature of over 900K !  This temperature is much higher than you would think given that this could be the same current setting for the heating element that you would use to boil water.  Why is this temperature so high when all you want to do is boil water at 373K?   What happens to the pot once the water has boiled away?  DON'T TRY THIS EXPERIMENT!!!  
  2. The melting point of tungsten is about 3700K.  What is the wavelength of the peak energy density at this temperature.  The temperature of the filament under normal operating conditions is about 2800K.  What is the apparent color of the filament at this temperature?  
  3. Matching the Planck distribution to a measured blackbody spectrum allows us to determine the temperature of an object.  In fact, this is the primary means astronomers use for determining the temperatures of stars.  The buttons below the applet have been preset to values corresponding to familiar stars.  Betelgeuse is a red supergiant star located at one of the shoulders of Orion. Sirius A, "the dog star," is the brightest visible star in the sky and is located in Canis Major near Orion.  It is coupled to a white dwarf called Sirius B and these stars form a binary star system.  Measure the peak wavelength and describe the apparent color of the four stars above.
  4. Using five different temperatures below 30,000K, derive a relation between Lambda max and T.   Coordinates in the graph may be found by left-clicking there.  Compare your result with the Wien displacement law.
  5. Look at the circle in the lower left hand corner of the color swatch that is labeled "Appearance."  Does this color swatch accurately reproduce all aspects of a blackbody radiator?  What aspects are accurately represented by this simulation?  Where does this simulation fail?

 

The applet was written by Wolfgang Christian, Mike Lee, and Ansel Singer-Barnum at Davidson College.  This exercise was written by Dan Boye.

2000 by Prentice-Hall, Inc. A Pearson Company