1. Not finding help here? Sign up for a free 30min 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!

Statistical physiics Problem 5.5

  1. Mar 12, 2008 #1
    1. The problem statement, all variables and given/known data
    http://ocw.mit.edu/NR/rdonlyres/Phy...5482B93-6A5E-4E2F-ABD2-E34AC245396C/0/ps5.pdf

    I am stuck on Problem 5 part a. They say that the relevant state variables are H,M,T, and U. Obviously the first law of thermodynamics still holds: dU = dW+dQ (does anyone know how to make inexact differentials in latex)? But does dW = -PdV here? P and V were not among the state variables they talked about so does that really make sense? How do I proceed?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 13, 2008 #2
    anyone?
     
  4. Mar 13, 2008 #3

    Mapes

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    [itex]dW=H\,dM[/itex] and [itex]U=TS+MH[/itex]. Work terms always consist of a generalized force (an intensive quantity) and a generalized displacement (an extensive quantity). Examples: force x distance, magnetic field x magnetization, electric field x polarization, surface energy x area, stress x strain, etc.

    In this problem [itex]P\,dV[/itex] work is evidently assumed to be negligible compared to [itex]M\,dH[/itex] work. You can tell because the problem states that there are only two independent variables (recall our earlier discussion on ideal gases).
     
  5. Mar 13, 2008 #4
    OK, I see why [itex]dU = \delta Q +HdM[/itex]. But why is U = TS+MH true? I am trying to express [itex]C_M \equiv \left(\frac{\delta Q}{dT} \right)_M[/tex] as a derivative of the internal energy. Can you give me a hint how to do that?
     
  6. Mar 14, 2008 #5

    Mapes

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    From what you've written, it looks like you can conclude that [itex]
    C_M \equiv \left(\frac{\partial U}{\partial T} \right)_M
    [/itex].

    In general, [itex]
    U=TS-PV+\sum\mu_i N_i +FL+ MH+EP+\gamma A+\sigma V\epsilon\dots
    [/itex] where the terms represent the work terms I listed above. This is called the Euler form of the fundamental relation, if you want to find more information about it. Callen's Thermodynamics is a good reference.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Statistical physiics Problem 5.5
  1. Statistics Problems (Replies: 0)

Loading...