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B Units for entropy

  1. Mar 16, 2017 #1
    Hello. I recently discovered Gerard 't Hooft's (what a complicated name to type, isn't it?*apostrophe*apostrophe*apostrophe) equation for the entropy of a simple black hole (what is meant by "simple" I have no idea). It is:

    Where "S" is the entropy of a simple black hole
    A is the area of the black hole's event horizon
    h is (reduced?) Planck's Constant
    G is the gravitational constant

    S = A/(4hG)

    Unless there is a conversion constant missing in this equation (is there?), I get units for entropy as (s^3)/(m^3).

    That is,

    Entropy = [m^2]/[(kg*m^2/s)*(m^3/kg*s^2)]

    = seconds cubed per meters cubed? What does this signify? Is there some "speed" associated with entropy such that entropy is inversely proportional to the cube of this "speed"?

    Or am I way off track here?
     
  2. jcsd
  3. Mar 16, 2017 #2
    I've never heard of entropy referred to in ##\frac {s^3} {m^3}##. Generally it's given as ##\frac J K##.
     
  4. Mar 16, 2017 #3

    Chalnoth

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    You're missing a factor of ##k_B c^3##. The three factors of ##c## cancel out the ##s^3/m^3##, while the Boltzmann constant ##k_B## has units of energy per unit temperature (typically J/K, as TJGilb mentioned). You can see this at the Wikipedia page here:
    https://en.wikipedia.org/wiki/Black_hole_thermodynamics
     
  5. Mar 17, 2017 #4
    Ah. Okay. So there was a couple constants missing. Thanks.
     
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