Solve this equation for u to obtain Stephan Boltzmann's law. In the big-bang theory, the radiation energy

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Question:

Solve this equation for u to obtain Stephan Boltzmann's law.

Tdu 1u 3dT 3

In the big-bang theory, the radiation energy which is initially confined in a small region adiabatically expands in a spherically symmetric way. Based on thermodynamic considerations together with results from part (b), find a relation between the temperature and the radius of the volume of radiation. How does the temperature changes as the radiation expands?

Find the entropy of the electromagnetic radiation as a function of T and V.