Black Hole Temperature: Stephen Hawking Equation & Calculation Results

[sabanation12]

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

 

[BillSaltLake]

I'm getting closer to 10^-16 °K, so a Black Hole Sun would evaporate very slowly, unlike the Soundgarden video.

 

[Chalnoth]

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

$$T = {h c^3 \over 16\pi^2 GMk}$$

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]

Shouldn't that be $$\hbar c^3 / 8 \pi GMk$$ or did I miss something?

 

[Chalnoth]

Shouldn't that be $$\hbar c^3 / 8 \pi GMk$$ or did I miss something?

It's just a difference of whether to use $h$ or $\hbar$ :)

 

[Chronos]

My error, I am so accustomed to hbar I overlooked the obvious equivalence.

 

[sabanation12]

Thanks for your help guys! And thanks Chalnoth for the calculator and link :)