onsdag 7 maj 2014

Is Blackbody Radiation Universal?

In a recent series of articles Pierre-Marie Robitaille questions the idea of universality of blackbody radiation. Let us see what the analysis of the model studied at Computational Blackbody Radiation can say.

The model consists of a wave equation for a vibrating atomic lattice augmented with small damping modeling outgoing radiation. The model is characterized by a lattice temperature $T$ assumed to be the same for all frequencies $\nu$ and a radiative damping coefficient $\gamma$ with corresponding radiance $R(\nu ,T)$ depending on frequency and temperature according to Planck's law (with simplified high-frequency cut-off):
  • $R(\nu ,T)=\gamma T\nu^2$ for $\nu\leq\frac{T}{h}$,
  • $R(\nu ,T)=0$ for $\nu > \frac{T}{h}$,
where the parameter $h$ defines the high-frequency cut-off.  The model will subject to frequency dependent forcing $f_\nu$ reach equilibrium with incoming = outgoing radiation:
  • $R(\nu ,T) =\epsilon f_\nu^2$ for $\nu\leq\frac{T}{h}$,
  • assuming for simplicity that frequencies $\nu >\frac{T}{h}$ are reflected,
where $\epsilon\le 1$ is a coefficient of absorptivity = emissivity. The radiative qualities of a lattice can thus be described by the coefficients $\gamma$, $\epsilon$ and $h$ and the temperature scale $T$. 

Assume now that we have two lattices 1 and 2 with different characteristics $(\gamma_1,\epsilon_1, h_1, T_1)$ and $(\gamma_2,\epsilon_2, h_2, T_2)$ which are brought into radiative equilibrium. We will then have 
  • $\epsilon_1\gamma_1T_1\nu^2 = \epsilon_2\gamma_2T_2\nu^2$ for $\nu\leq\frac{T_2}{h_2}$ 
  • assuming $\frac{T_2}{h_2}\leq \frac{T_1}{h_1}$ 
  • and for simplicity that 2 reflects frequencies $\nu > \frac{T_2}{h_2}$.    
If we choose lattice 1 as reference, to serve as an ideal reference blackbody, defining a reference temperature scale $T_1$, we can then calibrate the temperature scale $T_2$ for lattice 2 so that 
  • $\epsilon_1\gamma_1T_1= \epsilon_2\gamma_2T_2$,
thus effectively assigning temperature $T_1$ to lattice 2 by radiative equilibrium with lattice 1 acting as ideal blackbody, thus effectively using 1 as a reference thermometer, assuming it has maximal cut-off. Any lattice 2 will then mimic the radiation of lattice 1 in radiative equilibrium and a form of universality will be achieved. 

In practice lattice 1 is represented by a small piece of graphite inside a cavity with walls represented by lattice 2 with the effect that the cavity will radiate like graphite independent of its form or wall material. Universality will thus be reached by mimicing of a reference, viewed as an ideal blackbody, which is perfectly understandable, and not by some mysterious deep inherent quality of blackbody radiation. Without the piece of graphite the cavity will possibly radiate with different characteristics and universality may be lost.

The analysis indicates that the critical quality of the reference blackbody is maximal cut-off and equal temperature of all frequencies, and not maximal absorptivity = emissivity = 1, since the effective parameter is the product $\epsilon\gamma$. 

  • All dancers which mimic Fred Astaire, dance like Fred Astaire, but all dancers do not dance like Fred Astaire.     

3 kommentarer:

  1. Claes, maybe off topic but I wondered if something like this http://physicsworld.com/cws/article/news/2014/apr/28/why-an-ultracold-gas-is-like-a-wireless-network could apply for heat transfer at surfaces at any temperature
    ie can a cold surface detect radiation from a hotter surface and so not radiate in all directions as some alarmists hypothesize.
    The second law of thermodynamics is clear that heat only goes in one direction or not all (when a temperatures are the same) but some say surfaces radiate all the time and the 2nd law is applicable to the net heat.
    I think if a surface knows from incoming radiation not to send out energy waves that it fits in with your concept of cut off frequency but maybe a better explanation
    Could you test it with your maths

  2. If you haven't seen it already this is a rather interesting paper which experimentally shows problems with Kirchoff's law and the science of Black Body radiation. I believe you already had doubts about some of this:


  3. http://hockeyschtick.blogspot.co.uk/2014/05/new-paper-questions-basic-physics.html

    "New paper questions the 'basic physics' underlying climate alarm

    A forthcoming paper published in Progress in Physics has important implications for the 'basic physics' of climate change. Physicist Dr. Pierre-Marie Robitaille's paper(s) show the assumption that greenhouse gases and other non-blackbody materials follow the blackbody laws of Kirchhoff, Planck, and Stefan-Boltzmann is incorrect, that the laws and constants of Planck and Boltzmann are not universal and widely vary by material or different gases. Dr. Robitaille demonstrates CO2 and water vapor act in the opposite manner of actual blackbodies [climate scientists falsely assume greenhouse gases act as true blackbodies], demonstrating decreasing emissivity with increases in temperature. True blackbodies instead increase emissivity to the 4th power of temperature, and thus the blackbody laws of Kirchhoff, Planck, and Stefan-Boltzmann only apply to true blackbodies, not greenhouse gases or most other materials. The significance to the radiative 'greenhouse effect' is that the climate is less sensitive to both CO2 and water vapor since both are less 'greenhouse-like' emitters and absorbers of IR radiation as temperatures increase. "