Hello. I am trying to study "Introduction to Cosmology" by Barbara Ryden,(adsbygoogle = window.adsbygoogle || []).push({});

but I am stuck with an equation from chapter two, and I have no idea how to figure out this. If you can suggest me a reading material or can explain the equation to me, that would be wonderful.

It is page 20 of the book, chapter 2, equation # 25.

It says:

The energy density of photons in the frequency range f -> f + df is given by the blackbody function

ε(f) df = ((8*∏*h)/(c^3)) ((f^3 * df)/(exp(hf/kT) -1))

and what is that exp?

then it goes...

The peak in the blackbody function occurs at hf_peak =(approx) 2.82kT. Integrated over all frequencies, equation #25 yields a total energy density for blackbody radiation of

ε_γ = α * T^4, ( I wrote "_" to mean subscript).

where

α = ((∏^2)/(15))((k^4)(h^3 * c^3)) <this h is actually h with the dash

the definition of 'α' and the equation#25 just came out of nowhere, and I am very clueless.

And they don't look anything like the blackbody equation that I know:

P_rad = σεAT^4 where ε is emissivity and σ is the Stefan-Boltzmann constant.

Thank you for your help..

Sincerely,

Kyle Lee

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# Blackbody radiation

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