Thermodynamic Derivation of Wien's Law?

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Discussion Overview

The discussion centers around the derivation of Wien's law, specifically the relationship between the peak wavelength and absolute temperature of a black body, using thermodynamic principles rather than Planck's formula. Participants are exploring methods to achieve this derivation, focusing on the use of energy density and radiation pressure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests a thermodynamic derivation of Wien's law, specifically avoiding Planck's formula and focusing on the equation involving energy density.
  • Another participant questions the definition of P, seeking clarification on its meaning in the context of the discussion.
  • A third participant mentions a thermodynamic derivation found in a specific textbook, which involves concepts like the slow expansion of a cavity and the Doppler shift of reflected radiation, suggesting that the derivation is complex and may not be commonly used in modern texts.
  • The participant who defined P as radiation pressure connects it to the first law of thermodynamics and expresses a desire to derive Wien's law from this perspective.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the derivation method for Wien's law, with differing views on the complexity and relevance of various approaches. Questions remain about the definitions and implications of key terms.

Contextual Notes

There are unresolved aspects regarding the assumptions underlying the proposed derivations, particularly in relation to the definitions of terms like radiation pressure and energy density.

Collisionman
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Can someone tell me how I can derive Wien's law, i.e.,

\lambda_{max} T = constant

where \lambda_{max} is the peak wavelength and T is the absolute temperature of the black body, using the equation,

P=\frac{U^{*}}{3}

where U^{*} is the energy density.

Note: I'm not looking for the derivation using Plank's formula. I'm looking for a purely thermodynamic derivation.

Thanks in advance!
 
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what is P?
 
There is a thermodynamic derivation of Wien's Law in Heat and Thermodynamics by Roberts and Miller. It invokes considering slow expansion of a cavity, Doppler shift of reflected radiation, and so on. It is long and complicated, Maybe slicker derivations exist.
These day, most textbook writers don't bother with this sort of derivation, but derive it from Planck's law. But I know you don't want this.
 
Last edited:
MikeyW said:
what is P?

P is the Radiation Pressure. It relates to the first law of termodynamics definition of work, PdV. Basically, I'm looking to derive Wien's law from the first law.
 

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