I would like to plot blackbody spectral emissive power against wavelength in different temperatures. For that reason, I assigned a vector variable for wavelength and I used a for loop for the different temperatures. My code is the following:
clcclear% Constants
c0=2.998*10^8; % Speed of Light in vacuum
h=6.626*10^-34; % Planck's constant [J*s]
k=1.387*10^-23; % Boltzmann's constant [J/K]
sigma=5670*10^-8; % Stefan-Boltzmann constant [W/(m^2*K^4)]
lamda=0.1*10^-6:0.001*10^-6:25*10^-6; % Thermal Radiation 0.1-100μm (0.4-0.7μm visible light) [m]
n=1; % refractive index
T(1)=0; % Surface temperature of the sun
c=c0/n; % Speed of light not in vacuum
hta=1./lamda; % wavenumber
v=c./lamda; % frequency
for i=0:2:10 if i<10 T=i*500; else T=5762; end Ev=2*pi*h*v.^3*n^2./(c0^2*(exp(h*v/(k*T))-1)); % Planck's law spectral emissive power function of frequency
Elamda=2*pi*h*c0^2./(n^2*lamda.^5.*(exp(h*c0./(n*lamda*k*T))-1));% Planck's law spectral emissive power funtion of wavelength
Eb=trapz(Elamda) % Total Emissive power
Eb1=n^2*sigma*T^4 hold on set(gca,'XScale','log','YScale', 'log') % set log scaling instead of default linear
axis([0.1 25 100 10^8]) %set axis limits
xlabel('\bf Wavelength \lambda/μm') ylabel('\bf Blackbody Spectral Emissive Power, E_b_\lambda/(W/(m^2*μm))') title('\bf \fontsize{12} Blackbody Emissive Spectrum') plot(lamda*10^6,Elamda./10^6, '-.b') % if loglog is used instead of plot and hold on is also set then matlab plots in linear mode instead of logarithmic
end
First of all, I would like to have a different color for each curve. I tried to create a for loop and assign a string variable, the sort name of each color, which ultimately was set inside the plot command, but without success.
Finally, the *Eb *and *Eb1 *should give more or less the same results. Because Eb is the area under the curve of Elamda (computed with trapz) and the Eb1 is the integration of the Elamda (the integration of spectral emissive power, so the total emissive power). The problem occurs because of the step in lamda (the wavelength). Can you please explain how can I overcome this problem?
Thank you very much, Giorgos
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