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Black Hole Temperature

by sabanation12
Tags: black, hole, temperature
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sabanation12
#1
Dec4-11, 12:59 PM
P: 21
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
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BillSaltLake
#2
Dec4-11, 01:13 PM
PF Gold
P: 184
I'm getting closer to 10-16 K, so a Black Hole Sun would evaporate very slowly, unlike the Soundgarden video.
Chalnoth
#3
Dec5-11, 01:52 AM
Sci Advisor
P: 4,782
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/

Chronos
#4
Dec5-11, 04:40 AM
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Black Hole Temperature

Shouldn't that be [tex]\hbar c^3 / 8 \pi GMk[/tex] or did I miss something?
Chalnoth
#5
Dec5-11, 04:57 AM
Sci Advisor
P: 4,782
Quote Quote by Chronos View Post
Shouldn't that be [tex]\hbar c^3 / 8 \pi GMk[/tex] or did I miss something?
It's just a difference of whether to use [itex]h[/itex] or [itex]\hbar[/itex] :)
Chronos
#6
Dec5-11, 06:31 AM
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My error, I am so accustomed to hbar I overlooked the obvious equivalence.
sabanation12
#7
Dec13-11, 10:21 AM
P: 21
Thanks for your help guys! And thanks Chalnoth for the calculator and link :)


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