T vs V for adiabatic processes

[RadiumBlue]

Homework Statement

[/B]
a) Black body radiation:

The energy and pressure of black body radiation depend on [itex]T[/itex] and [itex]V[/itex] as [itex] E = σV T^4 [/itex] , [itex]p=\frac{1}{3}σT^4 [/itex] 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 [itex]dE[/itex] and [itex]dT[/itex] in this process. Next using equation (1) show that [itex]T ∝ V^-\frac{1}{3}[/itex]

b)Pressureless glop

Suppose that the energy and pressure of a different substance are given by [itex] E = γV T^\frac{2}{3}[/itex] ,[itex] p = 0 [/itex] 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?

Homework Equations

See problem description

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.

[itex] \Delta E = Q - W [/itex]

The processes are adiabatic, so Q = 0. Also, [itex]W = pdV[/itex]

Therefore
[itex] \Delta E = -pdV [/itex]

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

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

 

[haruspex]

##\frac{dE}{dT} = 4σVT^3##

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