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!

Thermodynamics, magnetic system

  1. Jul 20, 2013 #1

    fluidistic

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Hi guys, once again I'm having troubles with a magnetic system problem. Here it is:
    Consider a magnetic system described by the state equation ##M=f(B,T)## where M is the magnetization of the system and B is the applied magnetic field; f is differentiable.
    1)Express the differential of internal energy in funtion of T and M and determine which condition the specific heat at constant magnetization must satisfy in terms of the state equation.
    2)Assume now that the state equation has the form M=f(B/T) where f is continuously differentiable and only depends on the ratio B/T. Verify that under this assumption U and ##C_M## only depend on T.
    3)Assume now that the state function has the particular form ##M=DB/T## (Curie's law) and ##C_M## is constant. Write down the fundamental equation in the entropy representation.


    2. Relevant equations
    Lots I guess.


    3. The attempt at a solution
    I'm stuck at part 1), unfortunately.
    So first, I think it is fair if I consider that U depends only on M, T and n where n is fixed. I don't know if I can make this assumption or start with the fact that U is a function of S, V, M and n; where V and n are fixed.
    Assuming the former, then ##dU=\left ( \frac{\partial U}{\partial M} \right ) _{T,n} dM+ \left ( \frac{\partial U}{\partial T} \right ) _{M,n} dT####=C_MdT+\left [ B-T \left ( \frac{\partial B}{\partial T} \right ) _{M,n} \right ] dM##.
    Using a cyclic relation on the ##\left ( \frac{\partial B}{\partial T} \right ) _{M,n}## term I reach that ##dU=C_MdT+ \left [ B+T \frac{\left ( \frac{\partial M}{\partial T} \right ) _B }{\left ( \frac{\partial M}{\partial B} \right ) _T} \right ] dM##. The ##C_M## bothers me, but I don't think I could rewrite it with M's and T's as they are asking. The partial derivatives also bother me, I don't know if I must rewrite that expression.
    I don't really know the form of the expression they are asking me. Any tip is appreciated. Thank you.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Thermodynamics, magnetic system
Loading...