- #1

RedMech

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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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