Blackbody radiation. Plot of spectral energy density vs. wavelength.

Version 0.2
To do:
(i) Develop Stefan-Boltzmann illustration?
(ii) Better illustrate Wien's law.

k_B = 1.381 10^-23 J/K – Boltzmann's constant; h = 6.6261 10^-34 Js - Planck's constant; s = 5.6703 10^-8 W/m^2K^4 – Stefan-Boltzmann constant; b = 2.898 10^-3 mK – Wien's displacement constant; c = 3 10^8 m/s – speed of light.

u – spectral energy density (du/dE); x – wavelength; T – temperature;

h=6.6261*10^(-34),k_B=1.38*10^(-23),c=3*10^8,b=2.898*10^(-3)

T=slider([0,7000])

Planck distribution.

function(u_P,x)=8*pi*h*c/(x^5*[e^(h*c/(x*k_B*T))-1])

Rayleigh-Jeans law.

function(u_(R*J),x)=8*pi*k_B*T/x^4

UV approximation to Planck distribution.

function(u_(P*u*v),x)=8*pi*h*c/x^5*e^([-h]*c/(x*k_B*T))

Express wavelength in nm and energy in J/m^4. m is a scaling factor to bring curve into a reasonable field of view.

function(u_P,10^(-9)*x)*10^(-m),x>0

m=slider([0,6,6])

function(u_(P*u*v),10^(-9)*x)*10^(-m),x>0

function(u_(R*J),10^(-9)*x)*10^(-m),x>0

Wavelength at maximum of spectral density (=b/T):

L_M=1/4.965114232*h*c/(k_B*T)

x=L_M*10^9

x=b/T*10^9

Wien's displacement law (with arbitrary scaling factor for visibility).

y=L_M*T*10^(m+3)

Range of visible spectrum (400-700 nm).

400<x<700

function(H,x)=[if((700-x)/300,400<x<700)]

vector(h,s,v)=vector(function(H,x),1,1)



Author: David Craig <http://web.lemoyne.edu/~craigda/>

Graph of the formula

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