MATLAB: Whenever i use individual value of time (Tv) the output function (F) giving right value but using time in the form of loop ,output function gives wrong result for all.How to fix this

Question

clc

clear all

c1 = 3.742*10.^8;

c2 = 1.43878*10.^4;

sigma = 5.67*10.^-8;

lamda_1 = 8;

lamda_2 = 13;

Tv = -10:5:30;

F = zeros(size(Tv));

count = 1;

for T=Tv

fun = @(lambda) c1./(lambda.^5.*(exp(c2./(lambda * T+273)))-1);

F(count) = integral(fun,lamda_1,lamda_2)./(sigma.*(T+273)^4)

plot(T, F(count), '+', 'MarkerSize', 10, 'LineWidth', 2)

hold on

grid

count = count + 1;

end

xlabel('Temperature')

ylabel('Fraction in atmospheric window)')

title('Fraction of the radiation emitted in the atmospheric window as a function of temperature')

legend('T=-10','T=-5','T=0','T=5','T=10','T=15','T=20','T=25','T=30')

hold off

Answer 1

You missed a set of brackets connecting TV to 273.

c1 = 3.742*10.^8;
c2 = 1.43878*10.^4;
sigma = 5.67*10.^-8;
lamda_1 = 8;
lamda_2 = 13;
Tv = -10:5:30;
F = zeros(size(Tv));
count = 1;
for T=Tv
fun = @(lambda) c1./(lambda.^5.*(exp(c2./(lambda *(T+273))))-1); %%%%%%%
F(count) = integral(fun,lamda_1,lamda_2)./(sigma.*(T+273)^4);
plot(T, F(count), '+', 'MarkerSize', 10, 'LineWidth', 2)
hold on
count = count + 1;
end
grid
xlabel('Temperature')
ylabel('Fraction in atmospheric window)')
title('Fraction of the radiation emitted in the atmospheric window as a function of temperature')
legend('T=-10','T=-5','T=0','T=5','T=10','T=15','T=20','T=25','T=30')
hold off