Well obviously, that's why I'm asking here.phinds said:What's going on at the surface and what's going on in the core are WAY different things. You can't compute the temperature of one based on the other, or at least certainly not in the straightforward way you are trying to do.
Yeah, well somehow there are people who know all of the internal temperatures of the Sun, so I'd like to find out how they calculate it. For example, my first thought to correct this is that the convective zone doesn't follow the inverse square law, but perhaps the core and radiative zones may follow it? Need know if that's the case or not.Matterwave said:What went wrong was the entire approach used to try to find the temperature at the core. There is no reason to expect, as far as I can tell, that the internal temperature of the Sun should follow an inverse square dependency on radius.
bbbl67 said:Yeah, well somehow there are people who know all of the internal temperatures of the Sun, so I'd like to find out how they calculate it. For example, my first thought to correct this is that the convective zone doesn't follow the inverse square law, but perhaps the core and radiative zones may follow it? Need know if that's the case or not.
Well mainly I expected it to conform to an inverse square law because that's what happens outside the surface of the Sun. All of the energy that flows from the Sun to Earth is through radiation. So I expected that the inner radiative zone would be the same behaviour, since it's also done through radiation.mfb said:Why do you expect an inverse square law anywhere? You need constant energy flow in radiative zones. The blackbody radiation scales with the temperature to the 4th power, the heat flow is proportional to its derivative - but it also depends on how opaque the region is. The inner regions have a high density, radiation is scattered quickly, you need large temperature gradients to maintain the heat flow. This doesn't lead to any easy relation between temperature and radius.
Well, the 0C and 100C examples are special cases, as those are the regions where a phase transition happens. So the temperature stays constant even if the actual heat content is changing. In the case of fusion, it's not a phase transition situation, so temperatures and pressures can vary greatly to enable fusion to take place. For example the inside of the Sun would be 15 million K, but inside a tokamak you'd need 100 million K+ to get fusion. The Sun has a lot more pressure than a Tokamak, so the Tokamak has to compensate with higher temperature.stefan r said:I thought it was the fusion people. They can test how often hydrogen atoms will fuse if you accelerate protons and smash them into each other. Temperature is equivalent to particle velocity. We know how much fusion is taking place because we know how much energy the Sun radiates. We also know how much total gas there was when it started fusing. The temperature is "hot enough". You know that a glass of soda is 0C because it has ice cubes floating in it. You know that a pot of boiling soup is 100C because it has steam bubbles. The Sun's core has to be hot enough for fusion to be happening at the rate that fusion happens.
bbbl67 said:Well mainly I expected it to conform to an inverse square law because that's what happens outside the surface of the Sun.
bbbl67 said:...
...Well, the 0C and 100C examples are special cases, as those are the regions where a phase transition happens. So the temperature stays constant even if the actual heat content is changing. In the case of fusion, it's not a phase transition situation, so temperatures and pressures can vary greatly to enable fusion to take place. For example the inside of the Sun would be 15 million K, but inside a tokamak you'd need 100 million K+ to get fusion. The Sun has a lot more pressure than a Tokamak, so the Tokamak has to compensate with higher temperature.
The Sun's core temperature is estimated to be around 15 million degrees Celsius (or 27 million degrees Fahrenheit).
The Sun's core temperature is calculated by using mathematical models and data collected from observations of the Sun's energy output and composition.
Knowing the Sun's core temperature helps scientists understand the processes and reactions happening within the Sun, which in turn helps us understand the formation and behavior of other stars in the universe.
The Sun's core temperature is responsible for the energy and heat that sustains life on Earth. Without the Sun's heat, our planet would be too cold for life to exist.
No, the Sun's core temperature has not always been the same. As the Sun goes through different stages of its life cycle, its core temperature changes, and it is estimated that it will continue to increase over time until it becomes a red giant star.