Why does Wien's displacement law predict infinite radiation energy?

In summary, Wein's displacement law, as described in Omnes' book on QM, is represented by the equation E (T,ν) = v3F (v/T). This function was first discovered by Rayleigh in June 1900, using a principle from classical statistical physics that assumes equal distribution of energy among all degrees of freedom. However, this leads to a contradiction as it predicts infinite total radiation energy (E(T,v)dv). Rayleigh did not provide an explanation for this result, but it can be understood by integrating \nu from 0 to infinity, which reveals that the integral diverges due to the increasing nature of E with \nu.
  • #1
g.lemaitre
267
2
Wein's displacement law is

E (T,ν) = = v3F (v/T)

This is from Omnes' book on QM

... Rayleigh, who apparently found the function F in June 1900. He used a standard result from classical statistical physics (the equality, or “equipartition” of energy among all the degrees of freedom) and applied it to the radiation oscillators. He found F to be a constant. The result is perfectly correct from the standpoint of classical physics but at the same time perfectly absurd because his expression predicts that the total radiation energy (E(T,v)dv is infinite.

He doesn't explain why the total radiation is infinite. I'd like to know why.
 
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  • #2
E is increasing with [itex]\nu[/itex], if you integrate [itex]\nu[/itex] from 0 to infinity to get the full energy content (as all frequencies are allowed) you will see that the integral diverges.
 

Related to Why does Wien's displacement law predict infinite radiation energy?

What is Wien's displacement law?

Wien's displacement law is a basic law of physics that describes the relationship between the temperature of an object and the wavelength at which it emits the maximum amount of radiation. It states that objects with higher temperatures emit shorter wavelengths of radiation, while objects with lower temperatures emit longer wavelengths.

How is Wien's displacement law derived?

Wien's displacement law was first derived by Austrian physicist Wilhelm Wien in the late 19th century using theoretical and empirical methods. It was later confirmed by experiments and is now considered a fundamental law of thermal radiation.

What is the mathematical expression for Wien's displacement law?

The mathematical expression for Wien's displacement law is λmax = b/T, where λmax is the wavelength at which an object emits the maximum amount of radiation, b is a constant known as Wien's displacement constant, and T is the temperature of the object in Kelvin.

How does Wien's displacement law relate to blackbody radiation?

Wien's displacement law is closely related to the concept of blackbody radiation, which is the thermal radiation emitted by an object at a given temperature. This law helps us understand the spectrum of radiation emitted by a blackbody at different temperatures, and has applications in fields such as astronomy and thermodynamics.

What are the practical applications of Wien's displacement law?

Wien's displacement law has practical applications in various fields, including astronomy, thermodynamics, and engineering. It helps us understand the behavior of thermal radiation in different environments and can be used to calculate the temperature of objects based on their emitted radiation. It also plays a crucial role in the design of technologies such as infrared sensors and thermal imaging devices.

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