in my OP post, I only mentioned the surface because even if we were able to reach temps at the surface of the sun, it would be too hot that any experiment to test the upper limit would fail horribly.
in my OP post, I only mentioned the surface because even if we were able to reach temps at the surface of the sun, it would be too hot that any experiment to test the upper limit would fail horribly.
what's our suns core temp? would be an interesting comparison to the surface of the hottest star
dullard
Elite Member
- May 21, 2001
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Note: I have to assume you mean the American short version of trillion (10^12), and not the international long version (10^18). If you meant the long version, I am sorry, but you'll have to correct the math yourself.
The posters are on the right lines. Good and short article. I'll summarize it even further:
Temperature is related to the motion of the particles. The motion (speed) of the particles depends on their energy and their mass. If you could take the lightest possible particle and gave all the energy you could possibly give it, then its speed will approach the speed of light.
The planck's temperature is a reasonable approximation of that maximum temperature. At the planck's temperature, we can no longer see additional temperature increases, thus why bother considering higher temperatures? The temperature could exceed the Planck's temperature, but we'd never know it (the particle becomes a black hole).
Planck's temperature is 1.4*10^32 K.
The radiation heat question is even more complicated. Lets consider the case just before it is a black hole.
We need to know the black body properties of that particle (emissivity). That is, does the surface transmit all of the energy or does it absorb some of it? Assuming it is a perfect black body, then the energy it radiates per unit area is:
q/A = 5.67*10^-8 W/m^2K^4 * T^4 where T is the planck's temperature.
Thus, the body radiates 2*10^121 W/m^2 of energy. It would be really hard to maintain the temperature with this amount of energy radiating out of the body, but lets pretend we can do so.
Now, we just need to know the surface area of this black hole. The radius of a black hole is 2*G*M/c^2. Where G=6.67*10^-11 m^3/kg/s^2 and c is the speed of light. M is the mass of the particle, which unfortunately we do not know since mass increases with velocity. Rather than calculate it, I'll just assume the radius is 10^-15 meter. Someone else can come in and calculate that for me.
Thus, if the black hole is 10^-15 m in radius, the amount of heat it radiates is 2.7*10^92 W. At a trillion light years away, we would only receive a small fraction of that radiated energy. In fact, an adult human has only of 1 m^2 area (only half of the adult is facing this particle) and the heat radiating from the particle is passing through an area of 1*10^57 m^2 a trillion lightyears away. Thus, we only receive 1 W out of every 10^57 W radiated from the particle. Or, we'd each recieve 2.4*10^35 W of energy.
Since the sun gives the entire Earth 3.2 *10^13 W of energy, I'd say we'd be toast.
Note 2: Someone had better doublecheck my math.
The posters are on the right lines. Good and short article. I'll summarize it even further:
Temperature is related to the motion of the particles. The motion (speed) of the particles depends on their energy and their mass. If you could take the lightest possible particle and gave all the energy you could possibly give it, then its speed will approach the speed of light.
The planck's temperature is a reasonable approximation of that maximum temperature. At the planck's temperature, we can no longer see additional temperature increases, thus why bother considering higher temperatures? The temperature could exceed the Planck's temperature, but we'd never know it (the particle becomes a black hole).
Planck's temperature is 1.4*10^32 K.
The radiation heat question is even more complicated. Lets consider the case just before it is a black hole.
We need to know the black body properties of that particle (emissivity). That is, does the surface transmit all of the energy or does it absorb some of it? Assuming it is a perfect black body, then the energy it radiates per unit area is:
q/A = 5.67*10^-8 W/m^2K^4 * T^4 where T is the planck's temperature.
Thus, the body radiates 2*10^121 W/m^2 of energy. It would be really hard to maintain the temperature with this amount of energy radiating out of the body, but lets pretend we can do so.
Now, we just need to know the surface area of this black hole. The radius of a black hole is 2*G*M/c^2. Where G=6.67*10^-11 m^3/kg/s^2 and c is the speed of light. M is the mass of the particle, which unfortunately we do not know since mass increases with velocity. Rather than calculate it, I'll just assume the radius is 10^-15 meter. Someone else can come in and calculate that for me.
Thus, if the black hole is 10^-15 m in radius, the amount of heat it radiates is 2.7*10^92 W. At a trillion light years away, we would only receive a small fraction of that radiated energy. In fact, an adult human has only of 1 m^2 area (only half of the adult is facing this particle) and the heat radiating from the particle is passing through an area of 1*10^57 m^2 a trillion lightyears away. Thus, we only receive 1 W out of every 10^57 W radiated from the particle. Or, we'd each recieve 2.4*10^35 W of energy.
Since the sun gives the entire Earth 3.2 *10^13 W of energy, I'd say we'd be toast.
Note 2: Someone had better doublecheck my math.
I "think" that at the actual big bang temperature was indeed infinite?
I'm not talking after it, the actual bang itself.
I'm not talking after it, the actual bang itself.
DrPizza
Administrator Elite Member Goat Whisperer
Wrong. Horribly wrong. Counter-example: The Tokomat Fustion Test Reactor (at Princeton) set a world record for temperature:
510 MILLION DEGREES C (fwiw, a temperatures like that, it makes no difference in using K or degrees C, since they always differ by a constant amount = to the the temperature (in degrees C) of absolute zero)
So, your 6000 degree C temperature (a little less actually) at the surface of the sun is pretty pathetic compared to the TFTR. Even the coronal or core temperatures of the sun are puny in comparison.
edit: oh, link
Lets assume the speed of light is the upper limit of how fast a molecule can move.
Is there a function that can translate vibration speed of a molecule directly to a temperature? If so cant we compute what temperature molecules moving at the speed of light would be?
I have a feeling this might be different for each element.
DrPizza
Administrator Elite Member Goat Whisperer
interesting... I'll admit, I know nothing about all of this but what was stopping whatever was generating this amount of heat from melting through and killing everything?
But that didn't come about until AFTER the big bang. The actual big bang was hotter, infinity. Plank temperature is related to plank time which is AFTER the big bang.
What I'm trying to say is you can go hotter than plank temp.
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