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PhysicsItHertz
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Homework Statement
Derive Stefan-Boltzmann Law from Wien's Law.
Hint: You can use (without proof) R(T)=∫(-∞ to ∞) R(λ,T)dλ, p(λ,T)= 4/c R(λ,T).
Homework Equations
Stefan-Boltzmann Law:P=AσT^4
Wien's Law: λmax=(2.898*10^-3 m*K)/T.
The Attempt at a Solution
Let λmax=(2.898*10^-3 m*K)/T.
Using cross multiplication gives: T=(2.898*10^-3m*K)/λmax.
Raising both sides to the fourth power gives: T^4=(2.898*10^-3m*K)^4/(λmax)^4.
Multiplying both sides by λmax^4 gives: T^4*(λmax)^4=(2.898*10^-3m*K)^4.
Im not really sure if this going to go anywhere.
My idea was to just algebraically manipulate Wien's Law to equate to Stefan-Boltzmann Law.
The issue I have with doing this is that I am not sure what the hint even means (physically).