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T vs V for adiabatic processes

  1. Sep 23, 2015 #1
    1. The problem statement, all variables and given/known data

    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?

    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.

    [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.
     
  2. jcsd
  3. Sep 24, 2015 #2

    haruspex

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