# T vs V for adiabatic processes

1. Sep 23, 2015

1. The problem statement, all variables and given/known data

The energy and pressure of black body radiation depend on $T$ and $V$ as $E = σV T^4$ , $p=\frac{1}{3}σT^4$ σ = a constant

(1) Suppose that the temperature and volume of a box of radiation change adiabatically, which means that there is no heat flow. First, find the relation between $dE$ and $dT$ in this process. Next using equation (1) show that $T ∝ V^-\frac{1}{3}$

b)Pressureless glop

Suppose that the energy and pressure of a different substance are given by $E = γV T^\frac{2}{3}$ ,$p = 0$ γ = constant

The temperature and volume of a box of this substance are changed adiabatically. What is the relation between T and V during this process?

2. Relevant equations
See problem description

3. The attempt at a solution
I'm not quite sure where to begin with this one. I've solved every other problem in the problem set without a problem, but this one I'm a little confused where to start.

$\Delta E = Q - W$

The processes are adiabatic, so Q = 0. Also, $W = pdV$

Therefore
$\Delta E = -pdV$

Is it asking me to find dE/dT? For part a this would be:
$\frac{dE}{dT} = 4σVT^3$

After I get these pieces, I'm not sure how to assemble them into the answers the problems are asking for.

2. Sep 24, 2015

### haruspex

That would only be true if V is constant with respect to changes in T. Is it?