power of blackbody radiation

Question

rabindra khadka 2019-4-22

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编辑： Clinton Edwards 2020-10-4

I need to calculate power of blackbody radiation at given temperature for wavelength ranging from 0 to 20 micrometer. And also need to plot the power vs wavelength.

I have intensity as a function of wavelength (Lam)

I2 =(2*h*c)./((Lam.^5).*(exp((h.*c)./(k.*T.*Lam))-1))

I integrated, but the results shows NaN

Please help me

clear all;
clc;
c=3*10^8; % speed of light in vaccum
h=6.625*10.^-34; %  Planck constant 
k=1.38*10.^-23; %   Boltzmann constant
T= 500; % Temperatures in Kelvin
Lam=(0.0:0.01:20).*1e-6; 
I1 =(2*h*c)./((Lam.^5).*(exp((h.*c)./(k.*T.*Lam))-1))
plot(Lam,I1)
avg_I1 = I1(1:length(Lam)-1)+diff(I1)/2;
% Integrated results
A = sum(diff(Lam).*avg_I1)

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Clinton Edwards 2020-10-4

编辑：Clinton Edwards 2020-10-4

在 MATLAB Online 中打开

There are a few errors and enhancements which would be considered.

1) The most critical error is that the the calculation of I1 is missing a c^2 term and only has c in the first parathetical term. Instead of (2*h*c) is should be I1 =(2*h*c^2).

2) Less critical is that the first four significant figures of "h" are 6.626 not 6.625.

My proposed corrections are implemented in the code below with some axis labels.

Hope this helps! Nice job.

clint

% Physical Constants
c=3*10^8; % Speed of Light
h=6.626*10.^-34; %  Planck constant (m^2*kg/s)
k=1.38*10.^-23; %   Boltzmann constant (m^2*kg)/(s^2*K)
Lam=(Lam1:0.01:Lam2).*1e-6; % meters
dLam = Lam(2) - Lam(1); % Delta Lambda
% Calculate Blackbody Values For Vector Lam
I1 =(2*h*c^2)./((Lam.^5).*(exp((h.*c)./(k.*T.*Lam))-1));
plotI1 = I1*1e-12;
plotLam = Lam/1e-6;
plot(plotLam,plotI1,'linewidth',4)
xlabel('Wavelength (um)')
ylabel('Spectral Radiance (KW/m^/sr/wavelength)')
grid 'on'

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Answer 1

David Goodmanson 2019-4-23

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HI rabindra,

The expression has a problem at the first point, lambda = 0. But I1 is so tiny near the origin that you can safely drop lambda= 0 and start the array at .01.

Things will work better using 2*h*c^2 rather than the incorrect 2*h*c. Also, the integration is correct but you can do the same thing more quickly with A=trapz(Lam,I1)