Kirchhoff's Law: Detailed Mathematical Deduction (Proof)

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Discussion Overview

The discussion revolves around the mathematical deduction or proof of Kirchhoff's Law of Radiation, with participants expressing varying levels of understanding and seeking detailed explanations. The scope includes theoretical aspects of radiation laws and their implications in thermodynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants request a detailed mathematical proof of Kirchhoff's Law of Radiation.
  • One participant suggests that understanding the starting assumptions is crucial for the proof.
  • Another participant provides a logical explanation of Kirchhoff's Current Law and Voltage Law, though it is not directly related to radiation.
  • A participant explains that Kirchhoff's Law of Radiation states that the emissivity of a surface equals its absorptivity, implying conservation of energy between two surfaces at the same temperature.
  • There is a request for a mathematical deduction specifically related to Kirchhoff's Law of Radiation, indicating a desire for clarity beyond general explanations.
  • One participant mentions that existing resources may not provide sufficient depth and suggests that the law may be based on foundational principles of thermodynamics.
  • Links to external resources, including a Wikipedia article and a reference to an original paper, are shared for further exploration.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the existence of a detailed mathematical proof for Kirchhoff's Law of Radiation, with some expressing skepticism about the completeness of available resources.

Contextual Notes

There are indications of varying levels of understanding among participants regarding the law and its implications, as well as differing interpretations of the need for mathematical rigor in the discussion.

koustav
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can anyone give me the detailed mathematical deduction(proof) of kirchhoff's law?
 
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You need to explain the starting assumption that you wish to consider.
 
I can give you a logical "proof" for both laws:

Current law: if the sum of the currents into a node were NOT zero, then there would be current either coming in from, or going to into, nothingness. That would not be science, it would be magic.

Likewise for the sum of voltages around a loop.

:smile:
 
Depending on where your physics is at, you may know that voltage is really potential difference. There is an electric potential field with a scalar value defined for all space (including within your circuit wires) related to the work done to push a unit charge to that point from a pre-agreed point: usually infinity. The voltage between two points is just the difference between the potential at each point. If the potential difference between point a and b is v1 and the potential difference between b and c is v2, the potential difference between a and c is v1 + v2.

As an alternative approach, consider v1 to be the work required to push a unit charge from a to b and v2 the work from b to c. Clearly, the work to go from a to c is the sum of the two numbers.

Hope this helps
 
sorry but i mean kirchhoff's law of radiation
 
koustav said:
sorry but i mean kirchhoff's law of radiation

Afaik, his law of radiation is another conservation law. It says that the emissivity of a surface is the same as its absorptivity. A consequence of this is that two surfaces at the same temperature, facing each other will each absorb the same radiated power at any wavelength as they will emit. So neither surface can heat up at the expense of the other. That would generate free Energy - verboten!
 
ya but want the mathematical deduction of kirchhoff's law of radiation
 
Google?
 
i have already searched but i didn't get
 
  • #10
Is there, precisely, a
detailed mathematical deduction(proof) of kirchhoff's law
?
I have read around what I can find in a couple of textbooks and on the www. It seems as much an article of faith as anything, based on the second law of thermodynamics. You may have to dig further than just what Google has to offer at the first level. And it's not just a matter of a mathematical derivation.


This link refers to the original paper and http://www.ptep-online.com/index_files/2009/PP-19-01.PDF has a lot about the studies at the time. It points out the big error in Kirchoff's approach.
Hope it's of some use.
 
  • #11
Hope this helps you.Detailed derivation.
 

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