File:BlackbodyEnergies.svg
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![File:BlackbodyEnergies.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/1/1d/BlackbodyEnergies.svg/450px-BlackbodyEnergies.svg.png)
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Summary
DescriptionBlackbodyEnergies.svg |
English: This shows how Planck's model predicts that oscillators with "photon" constrained-energies ε ≡ hν = hc/λ greater than kT get significantly frozen out of the black body mix, thus solving the ultraviolet catastrophe to which the Rayleigh-Jeans model gave birth. This freeze-out may be explained if (for whatever reason) "quantum oscillators" exist only in packets with energy/frequency & momentum/spatial-frequency linked by the constant h = E/ν = p/g = 2πL.
![]() This plot was created with Gnuplot by v. |
Date | |
Source |
https://systemreboot.net/post/black-body-energy-as-a-sum-of-photon-oscillator-energies The probability of an oscillator having The energy contribution of an oscillator with The average black body energy is the sum of contributions from all oscillators. |
Author | Arun Isaac |
gnuplot source InfoField | click to expand
#! /usr/bin/env gnuplot
# This work is in the public domain.
#
# It was completed by Arun I in 2016.
#
# Though you are not legally obliged to do so, I would appreciate it
# if you credit me for this work by not removing this notice, and
# hopefully linking to my blog post at
# https://systemreboot.net/post/black-body-energy-as-a-sum-of-photon-oscillator-energies
# Base filename for output files
filename='blackbody-energies'
# Set terminal and output file
set term epslatex color colortext standalone
set output sprintf('%s.tex', filename)
# Axes' properties, title and key
set xrange [-0.01:5]
set yrange [0:1.05]
set mxtics 5
set ytics 0.2
set mytics 4
set xlabel '$ h\nu/kT $'
set ylabel 'Average oscillator energy (in units of $ kT $)'
set title "Planck's solution as a freeze-out of\nphoton oscillator-energies as $ h\\nu/kT \\to \\infty $"
unset key
# Line styles
set style line 1 lc 'blue' dt 4
set style line 2 lc 'red' dt 4
set style line 3 lc 'dark-yellow' dt 4
set style line 4 lc 'forest-green' dt 4
# Labels
set arrow from graph 0, first 1 to graph 1, first 1 nohead lc 'black' dt 6
set label '$ E_{\textrm{\tiny avg}}^{\textrm{\tiny Rayleigh}} = kT $' at graph 1, first 1 right offset graph -0.05, -0.05
set label '\footnotesize $ h\nu $' at 1.4, 0.15 tc ls 1
set label '\footnotesize $ 2h\nu $' at 1, 0.33 tc ls 2
set label '\footnotesize $ 3h\nu $' at 0.8, 0.45 tc ls 3
set label '\footnotesize $ 4h\nu $' at 0.65, 0.53 tc ls 4
set label '$ E_{\textrm{\tiny avg}}^{\textrm{\tiny Planck}} $' at 0.6, 0.8
# Expressions to plot
En(x,n) = n*x*exp(-n*x)*(1-exp(-x))
yN(x,N) = sum [n=1:N] En(x,n)
plot x/(exp(x) - 1) with lines lc 'black', \
for [N=1:4] yN(x,N) with lines ls N
# Convert tex -> pdf -> svg
set output
system(sprintf('pdflatex %s.tex && pdf2svg %s.pdf %s.svg', filename, filename, filename))
|
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31 October 2016
image/svg+xml
a107f33620eb01630cdabf881ca491fa531e34a7
111,914 byte
315 pixel
450 pixel
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:58, 31 October 2016 | ![]() | 450 × 315 (109 KB) | Arunisaac | User created page with UploadWizard |
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