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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