Blackbody Radiation Test Question

[cstang52]

Homework Statement

The blackbody radiation equations of state are E/V=aT^(4) and P=(1/3)(E/V). From the fundamental state derive a quantity involving only P and V that remains constant when this radiation undergoes a reversible adiabatic transformation.

Homework Equations

Maybe dE=TdS-PdV being the fundamental state?

The Attempt at a Solution

 

[Oxvillian]

I suggest starting with
$$dE = -p \; dV$$
since for an adiabatic process dS = 0. Then try to eliminate dE in favor of dp and dV.