Radiation Problem: Black-body Expansion, T_f=xT_i

[neelakash]

Homework Statement

Black-body radiation, at temperature Ti fills a volume V. The system expands adiabatically
and reversibly to a volume 8V. The final temperature T_f = xT_i, where the factor x is equal to
(a) 0.5 (b) 2.8 (c) 0.25 (d) 1

Homework Equations

The Attempt at a Solution

Correct answer should be (d)1 because, photons do not feel attraction or repulsion potential to each other.So, increasing volume adiabatically should not reduce or increase its temperature.

Please check if I am correct.

 

[Mapes]

This is incorrect. The Stefan-Boltzmann Law tells us that the energy and entropy of blackbody radiation in a box are $U=bVT^4$ and $S=\frac{4}{3}bVT^3$, respectively, where $b$ is a constant (reference: Callen's Thermodynamics). I'll leave the rest to you.