4.8

The Stefan-Boltzmann law can be employed to estimate the rate of radiation of energy H from a surface, as in
 H =  AeoT^4
where H is in watts, A = the surface area (m^2), e = the emissivity that characterizes the emitting properties of the surface (dimensionless), o = a universal constant called the Stefan-Boltzmann constant (=5.67 x 10^-8 W m^-2 K^-4), and T= absolute temperature (k). Determine the error of H for a steel plate with A = .15 m^2, e = .90, and T = 650 + or - 20. Compare your results with the exact error. Repeat the computation but with T = 650 + or - 40.  Interpret your results.

o = 5.67 *10^-8;

A = 0.15;

e = 0.9;

T = 650 + (-20:20);

%T = 650 + (-40:40);

H = @(T) A* e * o * T.^4;

hold on

plot(T, H(T))

hold off

This code yields the graph of H showing a range of error of approximately 350 degrees with 

T = 650 ± 20

As would stand to reason, when we double the range of uncertainty for T to 40(T=650±40), the range of error about doubles