# Is Stefan's Law Truly Valid at All Temperatures?

• the4thamigo_uk
In summary, the conversation discusses two small lectures on black body radiation and a question about the Stefan-Boltzman law. The lecturer introduces the law as the total power radiated by a body at temperature T scales as the fourth power of T, but also mentions that this law breaks down for real bodies at high temperatures. The person questioning the information wonders if this means that a real body would stop radiating if heated beyond a certain temperature, and if this is related to the ultraviolet catastrophe. They also bring up the complexity of absorption and emission spectrums in the real world and how it may not align with the theoretical model based on Planck's little oscillators. Lastly, they question how all bodies are able to radiate enough
the4thamigo_uk
I was watching two small lectures on youtube about black body radiation, they are interesting but I am questioning some of the information they provide :

My question is related to the graph of the Stefan-Boltzman law that the lecturer draws on the blackboard. Specifically he introduces the law as usual saying that the total power radiated by a body at temperature T, scales as the fourth power of T. This is fine. He then says that experimentally this law breaks down for real bodies and drops off to zero at high temperatures. Is this true?

If it was true then if I heat a real body beyond a certain temperature then it will stop radiating, hence it cannot maintain thermodynamic equilibrium and will just heat up, increase its temperature and radiate even less, heat up even more etc.?

My understanding is that this is not explained by the ultraviolet catastrophe (which seems to be an entirely different thing). In particular from wikipedia, it is possible to derive the T^4 law from Plancks law as well classical thermodynamics, so solving the UV catastrophe does not change Stefans Law. So the T^4 law must be true at all temperatures in the real world right?

A further thought occurs to me which is touched on in the lecturer with the 'rock star' example. In the real world, interatomic molecular bonds radiate in the infra red, electron orbital changes radiate in the UV. There is therefore a discontinuous distribution of absorption. Furthermore at certain temperatures interatomic bonds might break and essentially free the atoms from each other, or electrons might escape their orbitals. In other words the absorbtion/emission spectrums are very complicated!

So, the theoretical model obviously doesn't take any of this into account, Plancks little oscillators appear to have an infinite number of energy levels. So I guess they are really analogous to interatomic bonds which never break and there are no other forms of electromagnetic emission and the particles never escape the potential well. This ok?

So, given that the real world is complicated and that no real object really emits Plancks spectrum, isn't it remarkable? that all bodies can radiate enough energy to maintain thermodynamic equilibrium?

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Does anyone have a comment on this?

I would say that the information provided in these lectures is partially correct, but also lacking in some key details. The Stefan-Boltzmann law does indeed state that the total power radiated by a body at temperature T scales as the fourth power of T. This is a fundamental law of thermodynamics and is true for all objects, including real bodies. However, as the lecturer mentions, there are some discrepancies between this law and experimental results at high temperatures. This is known as the "UV catastrophe".

The UV catastrophe refers to the prediction of classical physics that a black body should emit an infinite amount of energy at high frequencies, which is obviously not observed in real bodies. This discrepancy was resolved by Max Planck's introduction of the concept of quantization, which is a key aspect of quantum mechanics. This quantization explains why real bodies do not emit infinite amounts of energy and how the Stefan-Boltzmann law holds true at all temperatures.

The lecturer is correct in pointing out that the T^4 law is not explained by the UV catastrophe, but rather it was derived from Planck's law and classical thermodynamics. However, it is important to note that Planck's law takes into account the quantization of energy levels, which is a crucial factor in understanding the behavior of real bodies at high temperatures.

The lecturer's analogy of Planck's "little oscillators" to interatomic bonds is a good one, as it helps to visualize the concept of quantization. However, it is important to keep in mind that this is just an analogy and does not accurately represent the complex nature of energy levels in real bodies.

In regards to the lecturer's question about the ability of real bodies to maintain thermodynamic equilibrium, it is indeed remarkable that all bodies are able to radiate enough energy to maintain equilibrium. This is due to the fact that the absorption and emission spectra of real bodies are very complicated, as the lecturer mentions. However, the Stefan-Boltzmann law and Planck's law account for this complexity and provide a solid understanding of the behavior of real bodies at all temperatures.

In conclusion, while the lectures do provide some accurate information, they do not fully explain the complexities of black body radiation and the UV catastrophe. it is important to have a thorough understanding of the underlying principles and theories in order to fully grasp the behavior of real bodies at high temperatures.

## 1. What is Stefan's Law and UV Catastrophe?

Stefan's Law and UV Catastrophe are two related concepts in physics. Stefan's Law is a mathematical equation that describes the relationship between the total energy radiated by a black body and its temperature. UV Catastrophe is a problem that arises when applying classical physics to this equation, resulting in an infinite and unphysical prediction for the energy radiated at high frequencies.

## 2. Why is UV Catastrophe a problem?

UV Catastrophe is a problem because it contradicts experimental observations. According to classical physics, the energy radiated by a black body should increase without limit as the frequency increases, but in reality, this is not the case. This contradiction led to the development of quantum mechanics.

## 3. How did Stefan's Law vs UV Catastrophe contribute to the development of quantum mechanics?

The failure of classical physics to accurately predict the energy radiated by black bodies at high frequencies led to the development of quantum mechanics. Max Planck proposed that energy is not emitted continuously, but in discrete packets called quanta. This revolutionary idea laid the foundation for the development of quantum mechanics.

## 4. How does quantum mechanics resolve the UV Catastrophe?

In quantum mechanics, the energy radiated by a black body is not continuous but is instead emitted in discrete packets or quanta. This means that at high frequencies, there is a limit to the amount of energy that can be radiated, resolving the UV Catastrophe and providing a more accurate prediction of the energy emitted by black bodies.

## 5. What are some practical applications of understanding Stefan's Law and UV Catastrophe?

Understanding Stefan's Law and UV Catastrophe has led to advancements in various fields, such as astrophysics, thermodynamics, and quantum mechanics. It has also contributed to the development of technologies such as infrared cameras and lasers, which rely on the principles of black body radiation. Additionally, this understanding has helped scientists gain a better understanding of the behavior of matter and radiation at the atomic level.

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