# Blackbody problem

Code

set term svg set termoption enhanced set encoding utf8 set output 'Black_body.svg' unset key set tics nomirror out set border 3 set xrange [0:6] set yrange [0:15] set ylabel "Spectral radiance (kW • sr⁻¹ • m⁻² • nm⁻¹)" set xlabel "Wavelength (μm)" set label "5000 K" at 0.45,13.1 set label "4000 K" at 0.6,4.55 set label "3000 K" at 0.8,1.4 set label "Classical theory (5000 K)" at 1.55,11 set grid lc rgb "light-blue" # length unit is micrometre c=3e14 # speed of light h=6.626e-22 # Planck constant k=1.38e-11 # Boltzmann constant # Planck curves p1(x)=1e-6*2*h*c**2/(x**5*(exp(h*c/(x*k*3000))-1)) p2(x)=1e-6*2*h*c**2/(x**5*(exp(h*c/(x*k*4000))-1)) p3(x)=1e-6*2*h*c**2/(x**5*(exp(h*c/(x*k*5000))-1)) p4(x)=1e-6*2*h*c**2/(x**5*(exp(h*c/(x*k*6000))-1)) # Rayleigh-Jeans curve rj(x)=1e-6*2*c*k*5000/(x**4) plot p1(x) lw 2, p2(x) lw 2, p3(x) lw 2, p4(x) lw 2 plot rj(x) lw 2 lc rgb "black"

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*Sources:*

Darth Kule. Produced by GNUPLOT 4.4 patchlevel 0, background spectrum based on http://commons.wikimedia.org/wiki/File:Linear_visible_spectrum.svg Dedicated to the public domain by the author.

gnuplot 4.2

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**Copyright (C) 1986 - 1993, 1998, 2004, 2007 Thomas Williams, Colin Kelley**Permission to use, copy, and distribute this software and its documentation for any purpose with or without fee is hereby granted, provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentation.

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