Black body radiation and the derivation of Stefan Boltzman

  • #1
dcarmichael
17
2
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)
20191102_144741.jpg
20191102_144734.jpg
 
Physics news on Phys.org
  • #2
What did you replace dλ with when converting to x as the variable of integration?
 
  • #3
haruspex said:
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
 
  • #4
dcarmichael said:
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?
 
  • #5
TSny said:
##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
 
  • #6
Ok. Go for it.
 
Back
Top