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Energy math question

  1. Sep 18, 2013 #1
    1. The problem statement, all variables and given/known data

    The filament of typical light bulb is at a temperature of about 3,000 K. For a 100 W bulb, what is the surface area of the filament. You can assume that the entire 100 W goes into heating the filament and the filament has an emissivity of 1.


    2. Relevant equations
    The equation is P= e(sigma)(A)(T^4)
    P is power
    e is the emissivity
    sigma is the constant 5.67 x 10 ^-5



    3. The attempt at a solution

    I have gotten to the point where i got 2.2 x 10^-5 m.
    The answer in the back of the book is 22 mm^2.
    I can't figure out how this was gotten.
     
  2. jcsd
  3. Sep 18, 2013 #2

    vela

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    Your answer is a length; the book's answer is an area. Does that give you any ideas?

    You need to convert the units.
     
  4. Sep 18, 2013 #3
    Can someone help me convert these units?
     
  5. Sep 19, 2013 #4

    collinsmark

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    Where did you get this sigma number, and what are the units of the number? Are you sure the exponent on the 10 is correct?

    I think your thinking of the Stefan–Boltzmann law.

    [tex] P = \varepsilon \sigma A T^4 [/tex]
    In SI units, [itex] \sigma = 5.670400 \times 10^{-8} \ [\mathrm{\ J \ s^{-1} \ m^{-2} \ K^{-4}} \ ][/itex].

    Or if you'd rather uses Watts instead of Joules/sec, you could say, [itex] \sigma = 5.670400 \times 10^{-8} \ [\mathrm{\ W \ m^{-2} \ K^{-4}} \ ][/itex]

    Well, it seems that you used the correct "-8" in your [itex] \sigma [/itex] to get that value, instead of the "-5" that you had listed in the relevant equations section. :thumbs:

    But you need to look at the units you ended up with. Is area measured in meters or square meters?

    How many square millimeters are in one square meter? :wink:
     
    Last edited: Sep 19, 2013
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