Can Wien's Law be derived without using Planck's formula?

In summary, the conversation discusses the difference between Wien distribution law and Wien's Displacement Law and the frustration of finding derivations of Wien's law based on Planck's radiation formula. The speaker is looking for a derivation without using a formula that did not exist in 1896 for a research project on Blackbody radiation. They mention the original paper, "On the division of energy in the emission-spectrum of a black body" from 1898 and its incorrectness at long wavelengths. They suggest looking up the original paper for more information.
  • #1
Math Jeans
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Just for clarification, I am referring to the Wien distribution law, and not Wien's Displacement Law.

I understand the fact that the law can easily be derived by treating is as a high-frequency limit of Planck's radiation formula, however, this is incredibly frustrating to me. Why? Wien's law was derived 4 years BEFORE Planck's radiation formula, and all of the derivations of Wien's law that I can find on the internet are based off of Planck's law.

I'm currently doing a research project on Blackbody radiation, and in order to keep a coherent timeline, I really need a derivation without the use of a formula which did not exist in 1896.

Any thoughts/sources?
 
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  • #2
This is old but in case anyone cares...

The original paper is "On the division of energy in the emission-spectrum of a black body", it's written in english, or was translated and is quite clear and very readable, even for modern readers. He assumes that the form black body radiation formula is an exponential, and integrates out to give something proportional T^4. Believe it or not, with not much else he derives his result, the constants are left to experiment to find. This was published june 1898 and by 1899 it was shown to be incorrect at long wavelegnths. Planck's solution is 1900. Look up the original paper.
 
  • #3

1. What is Wien's Law?

Wien's Law is a basic principle in thermodynamics that describes the relationship between the wavelength of thermal radiation emitted by an object and its temperature.

2. What is the true derivation of Wien's Law?

The true derivation of Wien's Law was first proposed by physicist Wilhelm Wien in 1893. It is based on the Planck's law of blackbody radiation and takes into account both the wavelength and temperature of the object.

3. How is Wien's Law used in science?

Wien's Law is used in many areas of science, including astrophysics, thermodynamics, and quantum mechanics. It is commonly used to determine the temperature of stars and other celestial objects based on their emission spectra.

4. What is the mathematical equation for Wien's Law?

The mathematical equation for Wien's Law is λ_max = b/T, where λ_max is the peak wavelength of thermal radiation emitted, b is a constant known as Wien's displacement constant, and T is the temperature of the object in Kelvin.

5. Is Wien's Law applicable to all objects?

No, Wien's Law is only applicable to objects that emit thermal radiation as a result of their temperature. It does not apply to objects that are not in thermal equilibrium or do not emit thermal radiation, such as non-luminous objects or objects at extremely low temperatures.

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