1. The problem statement, all variables and given/known data The energy and pressure of black body radiation depend on T and V as Eq(1) & Eq(2). Suppose that the temperature and volume of a box of radiation change adiabatically. Find the relation between dE and dT in this process. Next, using Eq(1), show that T ∝V^-1/3 2. Relevant equations Eq(1): E = σVT^4; Eq(2): p = 1/3σT^4; ΔE = Q - W; Since Q = 0; ΔE = -W 3. The attempt at a solution To begin with we've (a few people working together) have tried what appears to be an overly simple method. E = σ V T^4 dE/dT = 4 σ V T^3 dE = 4 σ V T^3 dT V = dE/(4 σ T^3 dT) ∴ V∝T^-1/3 But this seems overly simplistic, especially since volume is changing too. Any formulae/approaches we're missing?