| Date 08/09/2010 |
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| Script S6_2_1A.m | |||
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%=============================================
%planck 1A %Attention! The functions %fplanck and fplancka must be used %============================================= % %Boltzmann and Planck constants in MKS system k=1.381e-023; h=6.626e-034; %temperatures considered in °K T1=300; T2=1000; T3=2400; T4=4500; T5=6000; % %frequencies interval (numin, numax) divided into N parts N=100000; numin=1.0e001; numax=1.0e016; % %Distribution of the spectral intensities % %function arguments are the previous defined values %funtion fplanck gives back an array 2xN: %the first row contains the frequencies %the second one the spectral intensities % f1=fplanck(T1,N,numin,numax); f2=fplanck(T2,N,numin,numax); f3=fplanck(T3,N,numin,numax); f4=fplanck(T4,N,numin,numax); f5=fplanck(T5,N,numin,numax); % %corresponding plots plot(f1(1,:),f1(2,:),'ro-'),title('Spectral intensities versus frequencies for T=300 °K') axis([0 0.90e+014 0 1.7e-011]),figure plot(f2(1,:),f2(2,:),'bd-'),title('Spectral intensities versus frequencies for T=1000°K') axis([0 3.0e+014 0 6.0e-010]),figure plot(f3(1,:),f3(2,:),'g*-'),title('Spectral intensities versus frequencies for T=2400°K') axis([0 6.50e+014 0 8.5e-009]),figure plot(f4(1,:),f4(2,:),'ro-'),title('Spectral intensities versus frequencies for T=4500°K') axis([0 1.2e+015 0 5.5e-008]),figure plot(f5(1,:),f5(2,:),'bd-'),title('Spectral intensities versus frequencies for T=6000°K') axis([0 1.60e+015 0 1.3e-007]) % %============================================================ %Calculus for each temperature % 1.of the maxima of the spectral frequencies contained in each % of second rows of f1, f2, f3, f4 and f5 % 2.of corresponding frequencies contained in the same positions % in each of the first rows of f1, f2, f3, f4 and f5 %Using the function fplancka, for each temperature, a frequency is searched %to the right of position of the maximum of spectral intensity (fmax) %for which the corresponding the spectral intensity is less than fmax/1000 %The corresponding values of the ratio (h*nu.max)/(k*T) (Wien's law) are %determined % %for T=300°K [f1max,col1]=max(f1(2,:)); nu1max=f1(1,col1) nu1min=fplancka(N,col1,f1max,f1) Wien1=(h*nu1max)/(k*T1) % %for T=1000°K [f2max,col2]=max(f2(2,:)); nu2max=f2(1,col2) nu2min=fplancka(N,col2,f2max,f2) Wien2=(h*nu2max)/(k*T2) % %for T=2400°K [f3max,col3]=max(f3(2,:)); nu3max=f3(1,col3) nu3min=fplancka(N,col3,f3max,f3) Wien3=(h*nu3max)/(k*T3) % %for T=4500°K [f4max,col4]=max(f4(2,:)); nu4max=f4(1,col4) nu4min=fplancka(N,col4,f4max,f4) Wien4=(h*nu4max)/(k*T4) % %for T=6000°K [f5max,col5]=max(f5(2,:)); nu5max=f5(1,col5) nu5min=fplancka(N,col5,f5max,f5) Wien5=(h*nu5max)/(k*T5) % %the mean value for Wien's law aWien=[Wien1 Wien2 Wien3 Wien4 Wien5] Wien=mean(aWien) %============================================= % |
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| Script S6_2_1B.m | |||
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%=============================================
%planck 1B %Attention! The function fplanck must be used %============================================= % %temperatures in °K T1=300; T2=1000; T3=2400; T4=4500; T5=6000; % %interval of the frequencies, between numin and numax, divided in N parts N=10000; numin=1.0e001; numax=1.0e016; % %spectral intensities % f1=fplanck(T1,N,numin,numax); f2=fplanck(T2,N,numin,numax); f3=fplanck(T3,N,numin,numax); f4=fplanck(T4,N,numin,numax); f5=fplanck(T5,N,numin,numax); % %corresponding intensities over all frequencies % I1=trapz(f1(1,:),f1(2,:)); I2=trapz(f2(1,:),f2(2,:)); I3=trapz(f3(1,:),f3(2,:)); I4=trapz(f4(1,:),f4(2,:)); I5=trapz(f5(1,:),f5(2,:)); % %spectral intensities in the visible range % %limit frequencies in the visible range nuluxmin=4.3e+014; nuluxmax=7.4e+014; % f11=fplanck(T1,N,nuluxmin,nuluxmax); f22=fplanck(T2,N,nuluxmin,nuluxmax); f33=fplanck(T3,N,nuluxmin,nuluxmax); f44=fplanck(T4,N,nuluxmin,nuluxmax); f55=fplanck(T5,N,nuluxmin,nuluxmax); % %corresponding intensities over all frequencies in the visible range I11=trapz(f11(1,:),f11(2,:)); I22=trapz(f22(1,:),f22(2,:)); I33=trapz(f33(1,:),f33(2,:)); I44=trapz(f44(1,:),f44(2,:)); I55=trapz(f55(1,:),f55(2,:)); % %corresponding percent values I1perc=(I11*100)/I1 I2perc=(I22*100)/I2 I3perc=(I33*100)/I3 I4perc=(I44*100)/I4 I5perc=(I55*100)/I5 % T=[T1 T2 T3 T4 T5]; %their plot Iperc=[I1perc I2perc I3perc I4perc I5perc]; plot(T,Iperc,'ro-') title('Percent intensity in the visible range for T=300, 1000, 2400, 4500 and 6000°K') %============================================= % |
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| Function fplanck.m | |||
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%==============================================
%function fplanck %This function is necessary to run scripts %planck 1A, planck 1B and planck 3A %============================================== % % %function fplanck(T,N,inf,sup) %spectral intensities for the assigned T are evaluated %inf e sup defines interval of the N frequancies %fplanck returns a 2xN array contains %frequencies in the first row %spectral intensities in the second row % function fplanck=f(T,N,inf,sup) %universal constants of Boltzmann,light speed in vacuum and Planck k=1.381e-023; c=2.998e008; h=6.626e-034; %a constant a=(h/k)/T; %another constant b=(2*pi*h)/c^2; %interval of frequencies nu=linspace(inf,sup,N); % nu3=nu.^3; %spectral intensities esp=a.*nu; den=exp(esp)-1; I=b*(nu3./den); %fplanck returns frequencies and the corresponding spectral intensities fplanck=[nu;I]; %============================================== % |
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| Function fplancka.m | |||
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%==================================================
%function fplancka %This function is necessary to run script Planck 1A %================================================== % % %arguments of function fplancka(N,ind,fmax,f) %N is the number of columns of the array f (2xN) %resulting from the function planck %the first row contains the frequencies %the second one the spectral intensities %ind is the position in the first row of f of the frequency %corresponding to the maximum of spectral intensity fmax %contained in the same position of the second row of f % %fplancka gives back the value of the frequency "numin" %corresponding to a spectral frequency less than fmax/1000 %and the position j of the column where "numin" in contained % function fplancka=g(N,ind,fmax,f) %in fa the first row of f fa=f(1,:); %in fb the second row of f fb=f(2,:); %position j is searched j=0; for i=ind:1:N par=fmax/1000; if fb(i)>par j=j+1; end end %numin and j are the elements returned by fplancka numin=fa(j); fplancka=[numin j]; %================================================== % |
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