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Black Hole Temperature

  1. Dec 4, 2011 #1
    Ok so first I know that this equation was presented by Stephen Hawking to describe to Temperature of a black hole:

    T = hc2 / 16∏2GMk

    so I did the calculations and got that the temperature of a black hole with the mass of our sun would be ≈ .57°

    Is this right? Is this the right equation?

    Here is what I used for the variables can you guys check if these are correct?:

    g = 6.67*10^-11

    h = 62606956*10^-34

    k = 1.3806583*10^-23

    and then just the mass of our sun and the speed of light

    Thanks
     
  2. jcsd
  3. Dec 4, 2011 #2

    BillSaltLake

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    I'm getting closer to 10-16 °K, so a Black Hole Sun would evaporate very slowly, unlike the Soundgarden video.
     
  4. Dec 5, 2011 #3

    Chalnoth

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    Looks like you missed a factor of the speed of light in your equation. Should be:

    [tex]T = {h c^3 \over 16\pi^2 GMk}[/tex]

    Anyway, the easiest way to calculate these things is to just plug them into Google. The Google calculator knows about units, fundamental constants, and a lot of common values, so you can simply type in:

    h*c^3/(16*pi^2*G*(mass of sun)*k)

    ...to Google, and it will give you the right result (about 10^-8 K).

    Oh, and there's also a nifty calculator for all of the values related to a black hole:
    http://xaonon.dyndns.org/hawking/
     
  5. Dec 5, 2011 #4

    Chronos

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    Shouldn't that be [tex]\hbar c^3 / 8 \pi GMk[/tex] or did I miss something?
     
  6. Dec 5, 2011 #5

    Chalnoth

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    It's just a difference of whether to use [itex]h[/itex] or [itex]\hbar[/itex] :)
     
  7. Dec 5, 2011 #6

    Chronos

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    My error, I am so accustomed to hbar I overlooked the obvious equivalence.
     
  8. Dec 13, 2011 #7
    Thanks for your help guys! And thanks Chalnoth for the calculator and link :)
     
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