The power delivered in narrow spectrum range near 10 µm from black body source with temperature 1000 K is 10 µW.
a) What power would be delivered in narrow spectrum range near 1 µm?
b) At what wavelength the power delivered takes its maximum?
c) Find this maximum value.
For b and c, you are using:
λpeak = 2.898 x 10-3/T
That aspect of this problem is easy and was solvable.
For a, I would assume that one would use:
P = σAT4
Problem is that the question doesn't give surface area at all, only λ. Plugging what was given doesn't produce the relationship at all (even squaring the given λ = 10 µm only produces 5.6 µW). I don't know if it is a bad question or missing something obvious.
I also tried E = σT4 and got 5.7 W/cm2. I would assume that I would have to calculate per 1 µm?
The other alternative solution I tried was using Radiant flux density (Planck’s law):
W = 2hc2/λ5 x 1/(e(hc/λkT)-1) and the numbers still seem off.
The Attempt at a Solution
Also, based on the information above and solving part b and c that moving closer to the black body (2.898 µm) will produce the highest power and would dip off after as we approach 1 µm, but it feels like there is something missing in part a.