Black Hole Temperature: Stephen Hawking Equation & Calculation Results

In summary, the conversation discusses an equation presented by Stephen Hawking to calculate the temperature of a black hole, and the correct values for the variables used in the equation. The correct equation is T = {h c^3 \over 16\pi^2 GMk}, and after plugging in the values for the mass of the sun and the speed of light, the temperature is calculated to be about 10^-8 K. The conversation also mentions a calculator for values related to black holes and a discussion about whether to use h or \hbar in the equation.
  • #1
sabanation12
21
0
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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  • #2
I'm getting closer to 10-16 °K, so a Black Hole Sun would evaporate very slowly, unlike the Soundgarden video.
 
  • #3
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/
 
  • #4
Shouldn't that be [tex]\hbar c^3 / 8 \pi GMk[/tex] or did I miss something?
 
  • #5
Chronos said:
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] :)
 
  • #6
My error, I am so accustomed to hbar I overlooked the obvious equivalence.
 
  • #7
Thanks for your help guys! And thanks Chalnoth for the calculator and link :)
 

1. What is the Stephen Hawking equation for calculating black hole temperature?

The Stephen Hawking equation for calculating black hole temperature is T = ħc3 / 8πGMkB, where T is the temperature, ħ is the reduced Planck constant, c is the speed of light, G is the gravitational constant, M is the mass of the black hole, and kB is the Boltzmann constant.

2. How did Stephen Hawking come up with this equation?

Stephen Hawking used quantum field theory to study the properties of black holes and their interaction with matter. He applied this theory to the event horizon of a black hole and derived the equation for black hole temperature, which is now known as the Hawking radiation.

3. Can black holes really have a temperature?

Yes, according to the laws of thermodynamics, all objects with mass have a temperature. Black holes, although they are known to have a gravitational pull so strong that even light cannot escape, still have a temperature due to the emission of Hawking radiation.

4. How is the temperature of a black hole related to its mass?

As per the Hawking equation, the temperature of a black hole is inversely proportional to its mass. This means that as the mass of a black hole increases, its temperature decreases. This relationship is important in understanding the behavior and evolution of black holes.

5. Can the temperature of a black hole be measured?

Since black holes are invisible, their temperature cannot be directly measured. However, scientists can infer the temperature of a black hole by observing the radiation emitted from its event horizon. The hotter the radiation, the lower the temperature of the black hole.

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