Plot the Planck's Radiation curves Below

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Tunde Adubi
Tunde Adubi on 18 Sep 2022
Edited: Torsten on 19 Sep 2022
I tried to plot both radiation curves attached using Planck's and wien's equation as shown below.
Can you help correct this?
%---------Black Body Radiation Using Planck's Equation
%---------Black Body Radiation Using Wien's Equation
clc;
close all;
clear all;
%-----------------------------------%
c=3*10^8; % speed of light in vaccum
h=6.625*10.^-34; % Planck constant
k=1.38*10.^-23; % Boltzmann constant
T=(300); % Temperatures in Kelvin
V= (0:5:30).*1e2; %The wavenumber(Hundred)
Lam=1./V; %The wavelength
figure(1)
%------------Wiens equation
I300= ((2*h*c*c*(V.^3))./(exp(h*c.*V)./(k*T))-1);
%------------Plancks equation
I2(:,T)=(2*h*c*c)./((Lam.^5).*(exp((h.*c)./(k*T.*Lam))-1));
%-----------------------------------------------------
plot(V,I300,'k','linewidth',1)
hold on
plot(Lam,I2(:,T),'r','linewidth',1)
xlabel('Wavenumber','fontsize',14)
ylabel('Spectral Irradiance [W m^{-2} sr^{-1} nmm^{-1}]','fontsize',14)
title('Plancks Radiance Law','fontsize',14)
fh = figure(1);
set(fh, 'color', 'white');

Answers (1)

Torsten
Torsten on 18 Sep 2022
x-axis and y-axis for the two plots have very different scales. So there must be an error in your formulae if we compare it to the .png file you attached.
%---------Black Body Radiation Using Planck's Equation
%---------Black Body Radiation Using Wien's Equation
clc;
close all;
clear all;
%-----------------------------------%
c=3*10^8; % speed of light in vaccum
h=6.625*10.^-34; % Planck constant
k=1.38*10.^-23; % Boltzmann constant
T=(300); % Temperatures in Kelvin
V= (0:5:30).*1e2; %The wavenumber(Hundred)
Lam=1./V; %The wavelength
figure(1)
%------------Wiens equation
I300= ((2*h*c*c*(V.^3))./(exp(h*c.*V)./(k*T))-1);
%------------Plancks equation
I2=(2*h*c*c)./((Lam.^5).*(exp((h.*c)./(k*T.*Lam))-1));
%-----------------------------------------------------
figure(1)
plot(V,I300,'k','linewidth',1)
xlabel('Wavenumber','fontsize',14)
ylabel('Spectral Irradiance [W m^{-2} sr^{-1} nmm^{-1}]','fontsize',14)
title('Plancks Radiance Law','fontsize',14)
figure(2)
plot(Lam,I2,'r','linewidth',1)
xlabel('Wavenumber','fontsize',14)
ylabel('Spectral Irradiance [W m^{-2} sr^{-1} nmm^{-1}]','fontsize',14)
title('Plancks Radiance Law','fontsize',14)
%fh = figure(1);
%set(fh, 'color', 'white');
  2 Comments
Tunde Adubi
Tunde Adubi on 19 Sep 2022
Yeah, the result is that attached and should be on the same plot as seen there. Your's is not quite correct.
Torsten
Torsten on 19 Sep 2022
Edited: Torsten on 19 Sep 2022
Your's is not quite correct.
It's not my result, it's yours. The formulae for I300 and I2 you use seem to be wrong.

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