I Estimate the number of CMB photons in 0.25-litre

[rano jojo]

i know that the total energy density of a blackbody radiation is

E= 4 segma/C * T^4

so how i can use this to find the number of the CMB photons in 0.25 litre?

 

[Chalnoth]

This link might help:
https://en.m.wikipedia.org/wiki/Photon_gas

If you want to drive the result yourself, use E=hv for the energy of a photon of a given frequency to do the appropriate integral.

 

[Frimus]

I recommend a textbook by Barbara Ryden https://www.amazon.com/dp/1107154839/?tag=pfamazon01-20. In section "2.5 Cosmic Microwave Background" she makes calculations you are asking about and comes to a conclusion that "...there are about 411 CMB photons per cubic centimeter of the universe at the present day."

 

[rano jojo]

I recommend a textbook by Barbara Ryden https://www.amazon.com/dp/1107154839/?tag=pfamazon01-20. In section "2.5 Cosmic Microwave Background" she makes calculations you are asking about and comes to a conclusion that "...there are about 411 CMB photons per cubic centimeter of the universe at the present day."

many thanks but i don't have the book

 

[rano jojo]

This link might help:
https://en.m.wikipedia.org/wiki/Photon_gas

If you want to drive the result yourself, use E=hv for the energy of a photon of a given frequency to do the appropriate integral.

Thank you, but i how i can get the frequency and then how i can find the number of the photons? just i am confused

 

[Chalnoth]

Thank you, but i how i can get the frequency and then how i can find the number of the photons? just i am confused

I'm not sure what level the question is being asked. The photon gas wiki page has the number of photons per volume as a function of temperature directly. You could just use that formula and get the answer straight away.

If instead you're supposed to find out how to derive the number density, you'd have to derive it by integrating over the distribution of photons in a black body using Planck's Law.

 

[SD das]

i know that the total energy density of a blackbody radiation is

E= 4 segma/C * T^4

so how i can use this to find the number of the CMB photons in 0.25 litre?

Use E=mc^2 n another relation in which uses T of this relation~

N with plank relation E=hv, v=1/T n try[emoji4][emoji4]..