Thermodynamic Derivation of Wien's Law?

Click For Summary
SUMMARY

The discussion focuses on deriving Wien's Law, expressed as \(\lambda_{max} T = \text{constant}\), through thermodynamic principles rather than Planck's formula. The key equation referenced is \(P = \frac{U^{*}}{3}\), where \(P\) represents radiation pressure and \(U^{*}\) is energy density. A thermodynamic derivation is suggested from the book "Heat and Thermodynamics" by Roberts and Miller, which involves concepts such as the slow expansion of a cavity and the Doppler shift of reflected radiation. The discussion emphasizes the rarity of such derivations in contemporary textbooks, which typically rely on Planck's law.

PREREQUISITES
  • Understanding of thermodynamics, specifically the first law of thermodynamics.
  • Familiarity with radiation pressure and its relation to energy density.
  • Knowledge of black body radiation concepts.
  • Basic grasp of Doppler effects in physics.
NEXT STEPS
  • Study the derivation of Wien's Law from thermodynamic principles in "Heat and Thermodynamics" by Roberts and Miller.
  • Explore the relationship between radiation pressure and energy density in thermodynamic systems.
  • Investigate the implications of the Doppler shift in the context of black body radiation.
  • Review contemporary derivations of Wien's Law using Planck's law for comparative analysis.
USEFUL FOR

Physicists, thermodynamics students, and researchers interested in the foundational principles of black body radiation and thermodynamic laws.

Collisionman
Messages
36
Reaction score
0
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!
 
Science news on Phys.org
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.
 

Similar threads

Undergrad Minimization of the Gibbs energy when number of molecules varies
  • · Replies 16 ·
Replies
16
Views
3K
Graduate Thermodynamics Derivative Reduction Problems
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How Does Temperature Affect Wire Tension at Constant Length?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Question about the first law of thermodynamics
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Partial derivatives of thermodynamic state functions
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Change of Variables in Thermodynamics
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Partial derivatives and thermodynamics
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Thermodynamics: Partial derivatives
  • · Replies 4 ·
Replies
4
Views
5K
Graduate Thermodynamics: calculate thermodynamic derivative from data?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Vacuum Flask Thermodynamic Equation
  • · Replies 2 ·
Replies
2
Views
2K