- #1

Chronum

- 21

- 0

## 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?