1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Thermodynmaics- Energy equation

  1. Aug 31, 2011 #1
    1. The problem statement, all variables and given/known data

    The equation of state PV= U/3 applies to a photon gas at pressure P, volume V and internal energy U. By using the 'energy equation', show that the internal energy of a phont gas is proportional to the fourth power of temperature (i.e U [itex]\propto[/itex]T[itex]^{4}[/itex]). You can assume that U/V is only a function of temperature.

    2. Relevant equations

    Energy equation: (dU/dvV)[itex]_{T}[/itex] = T (dP/dT)[itex]_{V}[/itex] - P

    3. The attempt at a solution

    U = 3PV
    (dU/dV)[itex]_{T}[/itex] = 3P as (dP/dV)[itex]_{T}[/itex] = 0 as it is only a function of T

    From here.. I'm not sure what to do. Help?
  2. jcsd
  3. Sep 3, 2011 #2


    User Avatar
    Homework Helper

    (typoes corrected)

    There is nothing in what you are told that allows you to state that [itex](\frac{dP}{dV})_{T} = 0 [/itex] . This would lead you to the result 3P = -P .

    What you know is that [itex]P = \frac{U}{3V} [/itex] ; we also know that U must depend on temperature T , particularly since we're being asked to find a proportionality for it. You need to differentiate P implicitly with respect to T , with V held constant; this will give you a relation between [itex]\frac{\partial P}{\partial T}[/itex] and [itex]\frac{\partial U}{\partial T}[/itex] . Use this to replace [itex]\frac{\partial P}{\partial T}[/itex] in your energy relation, bring all the P's to one side, and use the given relation U = 3PV to replace P . You will have a separable differential equation that will lead you to the proportionality you seek.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook