Stefan-Boltzmann lab

  1. ideasrule

    ideasrule 2,323
    Homework Helper

    1. The problem statement, all variables and given/known data
    A few weeks ago I did an experiment that involved empirically determining the exponent on the Stefan-Boltzmann law. I used a light bulb and measured the voltage and current across it for different voltages. Since P=k*Tn and R=cT (i.e. resistance of the filament is proportional to temperature), P=k*(R/c)n. Taking the logarithm of both sides gives ln P=const + nlnR. At equilibrium, the bulb should emit just as much power in the form of blackbody radiation as the power supply provides, so P=VI.

    I graphed ln P vs. ln R and measured the slope of the line: 2.78, a far cry from 4. However, the line was nearly perfect! All of the points were nearly touching the line of best fit I drew! Moreover, many other people did this experiment, and almost all of them got 2.5-2.9.

    My question is: why 2.78?

    3. The attempt at a solution

    I'm thinking that if R doesn't increase linearly with T but is instead proportional to a power of T, the value of 2.78 would make sense. However, that's clearly an ad hoc approach. I've no idea why R would be proportional to anything other than T.

    Edit: Please reply quickly, because I'm kind of on a deadline.
     
    Last edited: Jul 10, 2009
  2. jcsd
  3. ehild

    ehild 11,920
    Homework Helper
    Gold Member
    2014 Award



    You are right, the temperature dependence of the resistivity of the tungsten wire in the bulb is rather a power 2 relationship at high temperatures than linear.

    http://hypertextbook.com/facts/2004/DeannaStewart.shtml

    ehild
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?