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 Date 08/09/2010
Script S6_2_2.m
Download Script S6_2_2.m
%=============================================
%planck 2
%=============================================
%
%universal constants of Boltzmann,light speed in vacuum and Planck
k=1.381e-023;
c=2.998e008;
h=6.626e-034;
%constants
a=k/h
T1=300;
T2=1000;
T3=2400;
T4=4500;
T5=6000;
%
a1=(a*T1)^3;
a2=(a*T2)^3;
a3=(a*T3)^3;
a4=(a*T4)^3;
a5=(a*T5)^3;
%
%frequencies between nu1 and nu2 in Hz
nu1=1.0e+06;
nu2=1.0e+016;
%
%integral constant called phot for T = 300
%
cost=h/k
xa1=(h*nu1)/(k*T1)
xb1=(h*nu2)/(k*T1)
x1=linspace(xa1,xb1,10000);
xq1=x1.^2;
xexp1=exp(x1);
den1=xexp1-1;
f1=xq1./den1;
phot1=trapz(x1,f1)
plot(x1,f1,'r-')
title('Integral constant called phot for T = 300°K varying frequency')
axis([0 11 0 0.7])
figure
%
%integral constant called phot for T = 1000°K
%
xa2=(h*nu1)/(k*T2)
xb2=(h*nu2)/(k*T2)
x2=linspace(xa2,xb2,10000);
xq2=x2.^2;
xexp2=exp(x2);
den2=xexp2-1;
f2=xq2./den2;
phot2=trapz(x2,f2);
plot(x2,f2,'r-')
title('Integral constant called phot for T = 1000°K varying frequency')
axis([0 11 0 0.7])
figure
%
%integral constant called phot for T = 2400°K
%
xa3=(h*nu1)/(k*T3)
xb3=(h*nu2)/(k*T3)
x3=linspace(xa3,xb3,10000);
xq3=x3.^2;
xexp3=exp(x3);
den3=xexp3-1;
f3=xq3./den3;
phot3=trapz(x3,f3);
plot(x3,f3,'r-')
title('Integral constant called phot for T = 2400°K varying frequency')
axis([0 11 0 0.7])
figure
%
%integral constant called phot for T = 4500°K
%
xa4=(h*nu1)/(k*T4)
xb4=(h*nu2)/(k*T4)
x4=linspace(xa4,xb4,10000);
xq4=x4.^2;
xexp4=exp(x4);
den4=xexp4-1;
f4=xq4./den4;
phot4=trapz(x4,f4);
plot(x4,f4,'r-')
title('Integral constant called phot for T = 4500°K varying frequency')
axis([0 11 0 0.7])
figure
%
%integral constant called phot for T = 6000°K
%
xa5=(h*nu1)/(k*T5)
xb5=(h*nu2)/(k*T5)
x5=linspace(xa5,xb5,10000);
xq5=x5.^2;
xexp5=exp(x5);
den5=xexp5-1;
f5=xq5./den5;
phot5=trapz(x5,f5);
plot(x5,f5,'r-')
title('Integral constant called phot for T = 6000°K varying frequency')
axis([0 11 0 0.7])
%
%mean value of phot
phot=[phot1 phot2 phot3 phot4 phot5]
phot_m=mean(phot)
%
A=(2*pi)/c^2;
%
%constants
coef1=A*a1;
coef2=A*a2;
coef3=A*a3;
coef4=A*a4;
coef5=A*a5;
%
%number of photons per unit time and surface
flux1=coef1*phot1
flux2=coef2*phot2
flux3=coef3*phot3
flux4=coef4*phot4
flux5=coef5*phot5
%constant multiplying the third power of T to obtain flux
%(see the problem, pag. 249)
%for example for flux5
const5=flux5/(T5^3)
%=============================================
%
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