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Black Body Work

  1. Oct 7, 2006 #1
    Hi all,

    I hope everyone is well and that life is treating you all good.

    I am going to be honest with my question and say that I have not tried to do it myself yet. I, unfortunately, do not have time now to try and then repost so I do hope you will all forgive me for just stating a question. I do intent to attempt it tonight incase I can do it but for safety sake I am going to ask here as well, as on inspection it does not look to simple.

    I will also say that this is for a University problem set that I have to do so, in a way it is homework. If the Mentors wish to move the thread then please do so and let me know via the messaging service please.

    The problem is this: I need to differentiate the formula for the Energy Density of a Black Body:

    [tex]U(\nu) = \frac{8 \pi \nu^3 h}{c^3 (e^{\frac{h \nu}{kT}} - 1)}[/tex]

    So I need: [tex] \frac{dU}{d \nu} = 0[/tex]

    As I said, I have not attempted it but please assume I understand the main rules of A-leve Mathematics. Again, I apologise for not having attempted it but I am in a rush and really cannot do it before I go. I will attempt it tonight and report what I find tomorrow but it maybe too little too late.

    Thanks in advance.

    The Bob (2004 ©)

    P.S. Please note that there is a h (for Planck's Constant) missing from the numberate of the equation and that dU by dv needs to equal 0, in the end. See next post.
    Last edited: Oct 7, 2006
  2. jcsd
  3. Oct 7, 2006 #2
    Correct equations

    [tex]U(\nu) = \frac{8 \pi \nu^3 h}{c^3 (e^{\frac{h \nu}{kT}} - 1)}[/tex]


    [tex] \frac{dU}{d \nu} = 0[/tex]


    The Bob (2004 ©)
  4. Oct 8, 2006 #3
    As promised, I attempted the differentiation myself last night.

    I got to [tex]\frac{dU}{d \nu} = \frac{8 \pi h \nu^2}{c^3} \cdot \frac{e^{\frac{h \nu}{kT}}(3 - \frac{h \nu}{kT}) - 3}{e^{\frac{h \nu}{kT}(e^{\frac{h \nu}{kT} - 2) + 1}[/tex]

    but something tells me I did the differentiation wrong in the first place. I used the equation as a quotient but did nothing with the T, because it is a constant for different graphs but can be varied.

    Can anyone shine a million watt torch's light on this problem please.


    The Bob (2004 ©)
  5. Oct 12, 2006 #4
    Don't worry about it guys. I solved it for low frequencies and had the correct magnitude. I also used Maple for a more accurate value.

    Thanks for all the help. :smile:

    The Bob (2004 ©)
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