Freethought & Rationalism Archive

Shadow Wraith · 05-23-2003, 12:57 PM

I tried figuring this one out a while back. Here's my work:

http://www.angelfire.com/anime4/keyser_soze/planck.html

Did I do okay, and did I get the right formula?

Abacus · 05-23-2003, 01:05 PM

In your list of symbols, you have 2*pi=approx. 3.1416

Actually, it should be pi = approx. 3.1416

Shadow Wraith · 05-23-2003, 01:16 PM

Yikes. That's a typo. I'll go fix it real quick. I meant to put "2pi = 6.2832". Thanks for pointing that out.

Shadowy Man · 05-23-2003, 01:31 PM

Shouldn't it be 8*pi, since you are integrating over 4*pi steradians?

You said power per area per wavelength.

Shadow Wraith · 05-23-2003, 01:50 PM

I dunno. I just got the formula and what the symbols and all in it mean off of a webpage and tried out a random wavelength and temperature. Did my source make an error?

Shadowy Man · 05-23-2003, 02:19 PM

From Radiative Processes in Astrophysics by Rybicki & Lightman.

Page 22 (the derivation is shown on pages 20 thru 22):

B_lam(T) = 2hc^2/lam^5/[exp(hc/lam kT)-1]

in units of energy/time/area/wavelength/steradian.

If you want it in power/area/wavelength as you have, then you need to integrate over 4*pi steradians.

From what webpage did you get the original formula?

edit: Ah, I see where the confusion might lie. Page 19 of Rybicki & Lightman says that "the emergent flux from an istropically emitting surface is pi * Brightness", so that

Flux = pi * B(T)

That definition would account for your pi.

Shadow Wraith · 05-23-2003, 06:19 PM

I can't remember exactly where I got that particular image from, but an identical formula with the same explanations for the symbols can be found here:

http://www.imsa.edu/edu/geophysics/a...y/planck1.html

Is there a mistake in this source? If so, could you give me a source to the actual formula? I like figuring out things that I won't get actually taught until I go to college.

05-23-2003, 12:57 PM	#1
Shadow Wraith Regular Member Join Date: Oct 2001 Location: North Augusta, SC; Aiken-Augusta metro area Posts: 283	Did I figure this out correctly (Planck's energy distribution formula). I tried figuring this one out a while back. Here's my work: http://www.angelfire.com/anime4/keyser_soze/planck.html Did I do okay, and did I get the right formula?

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05-23-2003, 01:05 PM	#2
Abacus Veteran Member Join Date: Mar 2002 Location: South Dakota Posts: 2,214	In your list of symbols, you have 2*pi=approx. 3.1416 Actually, it should be pi = approx. 3.1416

05-23-2003, 01:16 PM	#3
Shadow Wraith Regular Member Join Date: Oct 2001 Location: North Augusta, SC; Aiken-Augusta metro area Posts: 283	Yikes. That's a typo. I'll go fix it real quick. I meant to put "2pi = 6.2832". Thanks for pointing that out.

05-23-2003, 01:31 PM	#4
Shadowy Man Veteran Member Join Date: Jun 2002 Location: A Shadowy Planet Posts: 7,585	Shouldn't it be 8pi, since you are integrating over 4pi steradians? You said power per area per wavelength.

05-23-2003, 01:50 PM	#5
Shadow Wraith Regular Member Join Date: Oct 2001 Location: North Augusta, SC; Aiken-Augusta metro area Posts: 283	I dunno. I just got the formula and what the symbols and all in it mean off of a webpage and tried out a random wavelength and temperature. Did my source make an error?

05-23-2003, 02:19 PM	#6
Shadowy Man Veteran Member Join Date: Jun 2002 Location: A Shadowy Planet Posts: 7,585	From Radiative Processes in Astrophysics by Rybicki & Lightman. Page 22 (the derivation is shown on pages 20 thru 22): B_lam(T) = 2hc^2/lam^5/[exp(hc/lam kT)-1] in units of energy/time/area/wavelength/steradian. If you want it in power/area/wavelength as you have, then you need to integrate over 4pi steradians. From what webpage did you get the original formula? edit: Ah, I see where the confusion might lie. Page 19 of Rybicki & Lightman says that "the emergent flux from an istropically emitting surface is pi Brightness", so that Flux = pi * B(T) That definition would account for your pi.

05-23-2003, 06:19 PM	#7
Shadow Wraith Regular Member Join Date: Oct 2001 Location: North Augusta, SC; Aiken-Augusta metro area Posts: 283	I can't remember exactly where I got that particular image from, but an identical formula with the same explanations for the symbols can be found here: http://www.imsa.edu/edu/geophysics/a...y/planck1.html Is there a mistake in this source? If so, could you give me a source to the actual formula? I like figuring out things that I won't get actually taught until I go to college.

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