- #1
RedMech
- 13
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1. The problem statement:
Using Wien's law ρ(λ,T)=f(λ,T)/λ^5, show the following:
(a) The total emissive power is given by R = aT4 (the Stefan-Boltzmann law),
where a is a constant.
(b) The wavelength λmax at which ρ(λ,T) - or R(λ,T) - has its maximum is such that λ*T = b (Wien's displacement law), where b is a constant.
2. Homework Equations :
Wien's radiation law:
ρ(λ,T)=f(λ,T)/λ^5
ρ(λ,T)=c1/(λ^5*exp{c2/λT})
3. The Attempt at a Solution :
So I tried integrating Wien's equation from zero to infinity
ρ(total)dλ=c/4∫ρ(λ,T)dλ=c/4∫[f(λ,T)/λ^5]dλ. But I got nowhere.
Then I used the full expression of wien's law and tried the integration again
ρ(total)dλ=c/4∫[c1/(λ^5*exp{c2/λT})]dλ
I still didn't know what to do. So please help.
Using Wien's law ρ(λ,T)=f(λ,T)/λ^5, show the following:
(a) The total emissive power is given by R = aT4 (the Stefan-Boltzmann law),
where a is a constant.
(b) The wavelength λmax at which ρ(λ,T) - or R(λ,T) - has its maximum is such that λ*T = b (Wien's displacement law), where b is a constant.
2. Homework Equations :
Wien's radiation law:
ρ(λ,T)=f(λ,T)/λ^5
ρ(λ,T)=c1/(λ^5*exp{c2/λT})
3. The Attempt at a Solution :
So I tried integrating Wien's equation from zero to infinity
ρ(total)dλ=c/4∫ρ(λ,T)dλ=c/4∫[f(λ,T)/λ^5]dλ. But I got nowhere.
Then I used the full expression of wien's law and tried the integration again
ρ(total)dλ=c/4∫[c1/(λ^5*exp{c2/λT})]dλ
I still didn't know what to do. So please help.
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