Black body radiation and the derivation of Stefan Boltzman

[dcarmichael]

Homework Statement

The total intensity i(t) radiated from a blackbody is given by the integral from 0 to infinity of all wavelengths of the Planck distribution.But I keep seem to be getting the wrong answer. Could someone point out where I'm going wrong

Relevant Equations

Let l=lambda I(l,T)=(2Pihc^2)/l^5 *1/(e^(hc/lkT)-1)

 

[haruspex]

What did you replace dλ with when converting to x as the variable of integration?

 

[dcarmichael]

What did you replace dλ with when converting to x as the variable of integration?

I didnt indicate it but dλ is replaced with dx since x is new variable of integration

 

[TSny]

I didnt indicate it but dλ is replaced with dx since x is new variable of integration

$d\lambda \neq dx$

Note that you can write $\lambda = \large \frac{a}{x}$, where $a$ is a constant. Taking the differential of both sides of this relation, you should get $d\lambda = \boxed ?\, dx$. What goes inside the box?

 

[dcarmichael]

$d\lambda \neq dx$

Note that you can write $\lambda = \large \frac{a}{x}$, where $a$ is a constant. Taking the differential of both sides of this relation, you should get $d\lambda = \boxed ?\, dx$. What goes inside the box?

dλ= -(a/x^2)dx

 

[TSny]

Ok. Go for it.