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Temperature of filament using its area, power, and emissivity

  1. Feb 26, 2013 #1
    2a6qpw3.png

    I have entered the emissivity in the calculation so that we can treat it as a blackbody, allowing us to use [itex]I_{tot} = \sigma T^4[/itex]. My book tells me the correct answer is [itex]2.06*10^4[/itex], which I'd normally put down to a misprint, but if I use my value, I get a value for the next part which is a factor of 10 off. So either I'm wrong, or they followed through with an error of theirs?

    Thanks for any help.
     
  2. jcsd
  3. Feb 26, 2013 #2

    CWatters

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    26 or 0.26 ?
     
  4. Feb 26, 2013 #3
    [itex]e = 0.26 = \frac{26}{100}[/itex]. Which is why there is a 26 on the bottom and a second 100 on the top.

    Edit: If you don't understand why I have put e there, or why it's even in the calculation, I'd be fine if you could help me achieve the answer via a different method.
     
  5. Feb 27, 2013 #4

    CWatters

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    Sorry that was the only possible error I could see.
     
  6. Feb 27, 2013 #5
    Is this to say I should assume that the book has this answer wrong and, as a consequence, the other answer is wrong, too?

    Either way, thank you :)
     
  7. Feb 27, 2013 #6

    haruspex

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    Fwiw, a typical temperature for an incandescent light bulb would be around 3000K. At 20000K the tungsten would evaporate.
    Btw, you didn't need to add a pi r squared term. The ends of the wire are not exposed.
     
  8. Feb 28, 2013 #7
    Sorry, I don't understand why I don't need the pi r squared term? Isn't the fillament just a cylinder, so the radiations comes from the whole of the surface area?
     
  9. Feb 28, 2013 #8

    CWatters

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    Won't make much difference either way as the area of the ends is small.
     
  10. Feb 28, 2013 #9

    haruspex

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    The ends of the filament will be the electrical connection into the circuit. They will leak a small amount of heat by conduction, perhaps more than would be lost by the same area through radiation, but you've no information on that.
     
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