Plot Planck‟s law for Black Body radiation and compare it with Raleigh-Jeans Law at high temperature and low temperature.

 Plot Planck‟s law for Black Body radiation and compare it with Raleigh-Jeans Law at high temperature and low temperature. 

PROGRAM :     In terms of frequency

clf ;clc
h = 6.626e-34 // Planck's Constant in SI unit
k = 1.38e-23 //  Boltzmann Constant in SI unit
c = 3e8 // Speed of light
lambda = linspace(1e-7,1.5e-5,40)' // in (m) unit
lambda_rj = linspace(6e-6,1.5e-5,40)'
nu = linspace(3e6,3e14,40)' // in (Hz) unit
nu_rj = linspace(1e3,3e13,40)' // in (Hz) unit
T = 600:200:1000 // in (K) unit
T0 = 1100
// Planck's law in terms of frequency
function y=Planck_f(nu, T)
    y = (8*%pi*h*(nu^3))/((c^3)*(exp((h*nu)/(k*T))-1))
endfunction
y2 = feval(nu,T,Planck_f)
plot2d(nu,y2,[-1,-4, -3])
legend([string(T)],opt="ur")
xlabel("Frequency (Hz)","font_size",4)
ylabel("Energy Density","font_size",4)
title("Planck''s law for Black-Body radiation","font_size",4)
xgrid
scf()
//Reyleigh-Jeans law in terms of frequency
function y=rj_f(nu, T)
    y = (8*%pi*k*T*(nu^2))/(c^3)
endfunction
y3 = feval(nu_rj,T,rj_f)
plot2d(nu_rj,y3,[-1,-5, -3])
legend([string(T)],2)
xlabel("Frequency (Hz)","font_size",4)
ylabel("Energy Density","font_size",4)
title("Reyleigh-Jeans law for Black-Body radiation","font_size",4)
xgrid
scf()
// Comparison between above two laws
y2 = feval(nu,T0,Planck_f)
y3 = feval(nu_rj,T0,rj_f)
plot2d(nu,y2,-14);plot2d(nu_rj,y3,-8)
legend("Planck''s law","Reyleigh-Jeans Law",opt="ur")
xlabel("Frequency (Hz)","font_size",4)
ylabel("Energy Density","font_size",4)
title("Comparison between Planck''s law and Reyleigh-Jeans law for Black Body radiation at "+string(T0),"font_size",2)
xgrid

output: