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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).