• Support PF! Buy your school textbooks, materials and every day products Here!

Black body radiation and the derivation of Stefan Boltzman

  • #1

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
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,586
5,473
What did you replace dλ with when converting to x as the variable of integration?
 
  • #3
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
TSny
Homework Helper
Gold Member
12,546
2,959
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
##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
TSny
Homework Helper
Gold Member
12,546
2,959
Ok. Go for it.
 

Related Threads on Black body radiation and the derivation of Stefan Boltzman

Replies
2
Views
994
Replies
1
Views
3K
Replies
1
Views
1K
Replies
4
Views
3K
Replies
3
Views
8K
Replies
10
Views
573
Replies
2
Views
8K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
941
Replies
10
Views
1K
Top