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!

Finding the equations of state for a system (entropy)

  1. Aug 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Suppose the entropy of a system is given by the relation:

    S(E,V,N) = a(E,V,N)^(1/3)

    Determine three equations of state for this system

    2. Relevant equations

    there were no equations given on the sheet but i'm assuming that this might help.

    dS=(1/T)*dE+(p/T)*dV+Ʃμ*dN for a quasistatic process

    3. The attempt at a solution

    So with this, i was trying to determine the partial derivative of the function a(E,V,N)^(1/3). Similar to the way we can find:

    (∂S(E,V,N)/∂E)*dE+(∂S(E,V,N)/∂V)*dV+Ʃ(∂S(E,V,N)/∂N)*dN

    through partial differentials for S(E,V,N). The only problem is finding the partial differential when there's a power of 1/3 involved. How do i go about obtaining a result like the one above? Also, do i relate it to the equation dS to obtain the equations of state, or am i looking in the wrong direction?

    Thanks for all the help everyone.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 18, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    I think you're on the right track. Use the chain rule. For example, ∂S/∂E =( dS/da)(∂a/∂E)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted