Intrinsic Luminosity in Stars

As we will later learn, the entire energy generation of stars occurs through thermonuclear fusion in the stellar core. However, all of the energy that is generated in that core must escape the star, and hence if we can measure that escaping energy, we can infer the total energy generated.

In the case of Black body radiation, there is a straight forward relation between the energy generated (which is the total area under the Planck curve). This relation is of the form:


Energy Emitted  (Temp)n


Rather than simply telling you the value of n, or having you look it up in a textbook or on the Internet, it is more instructive if you do a virtual experiment and actual measure this value. Then you will better understand the relation. The procedure for doing this is explained below. After you have tried this, you will be able to click on "the answer" so that you can confirm your measurement.

The simulation for this should appear below.

The exercise here is fairly simple. If you drag the left (red) or right (blue) thermometers up to some temperature, the blackbody curve for that selected temperature will appear in the graph. The background graph is gridded into a number of boxes. If you count the boxes under the curve, that is the total area under the curve which is the total amount of energy emitted.


 Experimental Procedure:
 
  1. Raise the right thermometer to a temperature of 9400 K (it doesn't have to be exact; +/- 10 degrees off is okay)
  2. Raise the left thermometer to a temparture of 4700 +/- 10 K. Now notice that the high temperature (9400) is 2 times larger than the low temperature (4700).

Refer back to the (Temp)n scaling relation. We have just increased the temperature by a factor of two, so the total energy emitted has now increased by 2n. Before actually counting the boxes, it should be clear that the value of n must be large than 1. If n=1 then there would be twice as many boxes under the blue curve as under the red curve; clearly there are more than twice as many boxes under the blue curve.

You can then determine the value of by counting the boxes under the blue curve and counting the boxes under the red curve. Taking the ratio of the blue box count to the red block count has then experimentally determined n.  After you have done this procedure you may Click Here to reveal the exact scaling relation - your value of n should be close to the exponent that is shown

The strong scaling of this relation means that small changes in blackbody temperature produce large changes in the total energy emitted. You can experimentally verfiy this using the simulation. For instance, set one side to 6000 degrees and the other side to 5000 K - by counting boxes you should be able to verify that the 6000K blackbody emits about twice as much energy as the 5000K blackbody.

Please note: any math we will do in this class is always in the form of a scaling calculation, not plugging into a memorized formula. Scaling calculations are done by comparing the ratio of the inputs and determining the ratio of the outputs. When doing a scaled relation one makes use of relative units, instead of aboslute ones. Most students do not think like this, but this process greatly simplifies many calculations.

Follow this link for more insight into the concept of relative units and scaled calculations:
The Concept of Relative Units - a Brief Video Tutorial