Consider the gas of photons of the thermal equilibrium radiation in a cube of volume V at
Question:
(a) Assume that the temperature of the cosmic black-body radiation was decoupled from the temperature of the matter when both were at 3000 K. What was the radius of the universe at that time, compared to now? If the radius has increased linearly with time, at what fraction of the present age of the universe did the decoupling take place?
(b) Show that the work done by the photons during the expansion is
W = (π2/15h3c3)Viτi3(τi – τf)
The subscripts i and f refer to the initial and final states.
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