Planck black body formula question

In summary, the conversation discusses the Planck black body / Johnson-Nyquist resistor temperature formula and the use of $e^{h\nu/kT}-1$ in the denominator. The formula is used for both photons and electrons, which obey different statistics (Bose-Einstein for photons and Fermi-Dirac for electrons). The use of -1 in the denominator is due to the use of Bose-Einstein statistics for photons.
  • #1
telegraphic
3
0
Hi all -- I had a question about the Planck black body / Johnson-Nyquist resistor temperature formula:

[itex]
\[
E_{\nu}^{2}d\nu=\frac{4R_{\nu}hd\nu}{e^{h\nu/kT}-1}\]
[/itex]

I'm just wondering why the formula has [itex]$ exp(h\nu/kT)-1$[/itex] in the denominator? I would have expected [itex]$ exp(h\nu/kT)+1$[/itex] as electrons are fermions...

Cheers
 
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  • #2
Hi,
The formula you write is for radiation (photons).
 
  • #3
Rajini said:
Hi,
The formula you write is for radiation (photons).

Hi Rajini, yeah I definitely agree that it's right for photons (Bose-Einstein statistics), but it apparently also holds for resistor noise -- in fact, I've written it in the form given by Nyquist in 1928 in his "thermal agitation of electric charge in conductors". So I guess my question is: why? Shouldn't electrons obey Fermi-Dirac statistics?
 
  • #4
Hello,
Electrons obey the Fermi-statistics.
For photon Bose-Einstein (BES) statistics.
When you consider for radiation (photons) you use BES. So in the denominator of your formula -1 instead of +1.
 

What is the Planck black body formula?

The Planck black body formula, also known as the Planck radiation law, is a mathematical equation that describes the spectral energy density of electromagnetic radiation emitted by a black body at a given temperature. It was developed by physicist Max Planck in 1900 and is considered one of the cornerstones of modern physics.

What is a black body?

A black body is an idealized object that absorbs all radiation that falls on it and emits radiation at all wavelengths. It is a theoretical concept used to study the behavior of electromagnetic radiation in thermodynamic equilibrium. In reality, no object can be a perfect black body, but many objects, such as stars, can closely approximate black bodies.

How is the Planck black body formula derived?

The Planck black body formula was derived by Max Planck using a combination of classical physics and newly developed quantum mechanics. He assumed that the energy of electromagnetic radiation is quantized, or can only exist in discrete packets called photons. By applying this concept to the laws of thermodynamics, he was able to arrive at the mathematical formula that describes the spectral energy density of a black body.

What is the significance of the Planck black body formula?

The Planck black body formula has significant implications for understanding the behavior of electromagnetic radiation and the relationship between energy and temperature. It has been verified by countless experiments and is used in a wide range of fields, including astrophysics, cosmology, and thermodynamics. It is also a fundamental component of the theory of quantum mechanics.

How is the Planck black body formula used in practical applications?

The Planck black body formula is used in many practical applications, such as in the design of light bulbs and other sources of artificial light, as well as in the study of the cosmic microwave background radiation. It is also used in the field of spectroscopy to analyze the composition of materials and in the development of new technologies, such as solar panels and thermal imaging devices.

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