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September 8, 2013
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blackbody radiation / Planck's law

  • September 8, 2013
  • 1 reply
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Hello,

I am just trying to integrate the planck's law with the wavelenght as variable, but I do not get anything I can make sense of.

The task is the calculation of a photon density.

I am using Mathcad 15.

I looked around and there is quite a few old documents available but actually I can not reproduce them.

I am missing something.

I would appreciate a clarification on the right way to do it.

My files is "Planck radiation".

Integrations with density vs. E fails

Integration with density vs. lamdba give an odd number which does not seem right.

Planck.mcad (and pdf) is a legacy document from the internet

It shows that the integration is doable, but I can not reproduce it.

I look in the PTC discussion, but it seems that the attachments are no longer available.

Thanks,

Pierre

Best answer by Werner_E

Beginning with Mathcad 14 the symbolic engine was changed. In older versions its was Maple but now its muPad. Many people consider Maple being more efficient and capable. Anyhow, thats the reason the integral in the old file you posted does not evaluate as it should and as it is shown in the pdf of that file. The "assume" does not work as shown in the sheet, you would first have to clear those four variables for symbolic evaluation and then put the assume ine the symbolic eval - but unfortunately even then muPad does not find a solution for the integral.

planck1.png

Concerning your file and the integral in your formula 1. When I simplify the integrand I get

planck2.png

The denominator in the range of exp(E*10^19) gets really big for positive values of E. Mathcads symbolic interprets it a infinity and yields 0.0 as result, while the numeric fails for values greater than 10^307.

planck3.png

You may consider to chekc and rewrite your formula.

Concerning the result with formula 2, you misinterpreted the symbolics result. 1.23e4 is mupads way to say 1.23*10^4, no reference to Eulers constant.

You do not need tpo retype the symbolcs result - you may either assign ito a variable wich you can evaluate numerically or use inline evaluation.

planck4.png

When I google for Planck & Mathcad I get a lot of findings. Maybe this random pick (also old and from Maple times, I didn't bother to retype) is of help

https://www.cv.nrao.edu/~demerson/osfholo/Planck3.pdf

1 reply

W
Werner_E25-Diamond IAnswer
25-Diamond I
September 8, 2013

Beginning with Mathcad 14 the symbolic engine was changed. In older versions its was Maple but now its muPad. Many people consider Maple being more efficient and capable. Anyhow, thats the reason the integral in the old file you posted does not evaluate as it should and as it is shown in the pdf of that file. The "assume" does not work as shown in the sheet, you would first have to clear those four variables for symbolic evaluation and then put the assume ine the symbolic eval - but unfortunately even then muPad does not find a solution for the integral.

planck1.png

Concerning your file and the integral in your formula 1. When I simplify the integrand I get

planck2.png

The denominator in the range of exp(E*10^19) gets really big for positive values of E. Mathcads symbolic interprets it a infinity and yields 0.0 as result, while the numeric fails for values greater than 10^307.

planck3.png

You may consider to chekc and rewrite your formula.

Concerning the result with formula 2, you misinterpreted the symbolics result. 1.23e4 is mupads way to say 1.23*10^4, no reference to Eulers constant.

You do not need tpo retype the symbolcs result - you may either assign ito a variable wich you can evaluate numerically or use inline evaluation.

planck4.png

When I google for Planck & Mathcad I get a lot of findings. Maybe this random pick (also old and from Maple times, I didn't bother to retype) is of help

https://www.cv.nrao.edu/~demerson/osfholo/Planck3.pdf

W
Werner_E25-Diamond I
25-Diamond I
September 8, 2013

Does anyone know if there is a limit for the number of pictures you are allowed to insert in a posting? Whatever I try in the above reply, the fourth pic is shown correctly first but when I send/update, all I get is a non working link!

I'll try it again here:

planck4.png

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