- #1
Chronum
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Homework Statement
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
Homework Equations
Eq(1): E = σVT^4;
Eq(2): p = 1/3σT^4;
ΔE = Q - W;
Since Q = 0;
ΔE = -W
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?