# Assumptions for derivation of Plancks' law

• tom.stoer
In summary, the most general assumptions for deriving Planck's law in quantum statistical mechanics are thermodynamical equilibrium and a discretization condition, similar to that used in Bose's 1924 paper on non-interacting bose gas. There are no further assumptions mentioned. There may be possible applications for fermionic radiation, such as neutrinos, but it would require fermi-dirac statistics and further research.
tom.stoer
What are the most general assumoptions for the derivation of Planck's law in quantum statistical mechanics:
- thermodynamical equilibrium
- non-interacting bose gas (photons)

Do I miss anything?

Hi Tom,

you need to impose a discretization condition a la Bose in his ~1 page 1924 paper:

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Bose_1924.pdf

"Let there be different species of quanta each characterized by the number N_s and energy hv_s"

edit: you may have meant this by "bose gas" in which case, no there are no further assumptions

unusualname said:
you need to impose a discretization condition

...

edit: you may have meant this by "bose gas" ...
yes, that's what I meant; thanks

are there examples for "fermionic radiation"? what about the neutrino spectrum from the sun? (OK, there's the problem that the neutrinos are not in equilibrium, but what would happen if they were? is there a similar derivation for a non-interacting fermi gas in thermodynamic equilibrium with fermionic radiation?)

I guess that would require fermi-dirac statistics, but I don't know much about specific applications to neutrinos or other non-interacting fermion situations - probably worth a search in academic archives.

## 1. What is Planck's law and how is it derived?

Planck's law is a fundamental equation in physics that describes the distribution of energy emitted by a blackbody at a given temperature. It was derived by German physicist Max Planck in 1900 using assumptions about the quantization of energy.

## 2. What are the main assumptions used in the derivation of Planck's law?

The main assumptions used in the derivation of Planck's law are the existence of discrete energy levels in a system and the principle of equipartition of energy, which states that energy is distributed equally among all available degrees of freedom.

## 3. Can Planck's law be applied to all objects, or only to blackbodies?

Planck's law can be applied to any object that absorbs and emits radiation at all wavelengths, not just blackbodies. However, it is most accurate for objects that behave like ideal blackbodies, which absorb and emit all radiation that falls on them and have a constant emissivity at all wavelengths.

## 4. Is Planck's law only applicable at thermal equilibrium?

Planck's law is derived under the assumption of thermal equilibrium, but it can still be used to describe the radiation emitted by a body even if it is not in thermal equilibrium. However, the resulting spectral distribution may not follow the exact shape predicted by Planck's law.

## 5. How does Planck's law relate to other laws and principles in physics?

Planck's law is closely related to other fundamental laws and principles in physics, including the laws of thermodynamics, the principle of conservation of energy, and the wave-particle duality of light. It also forms the basis for other important equations, such as the Stefan-Boltzmann law and Wien's displacement law.

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