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Entropy of an ideal paramagnet

  1. Mar 22, 2007 #1
    1. The problem statement, all variables and given/known data
    The entropy of an ideal paramagnet is given by

    [tex] S = S_0 - CU^2 [/tex]

    where U is the energy, which can be positive or negative, and C is a positive constant. Determine the equation for U as a funtion of T and sketch your result.

    2. Relevant equations

    [tex] \frac{1}{T} = \left(\frac{\partial S}{\partial U}\right)_V [/tex]

    3. The attempt at a solution
    I differentiated the given equation, treating S0 as not depending on U.

    [tex] \frac{1}{T} = -2CU [/tex]

    [tex] U(T) = -\frac{1}{2CT} [/tex]

    so far so good i hope. But in the question it says U can be positive or negative.. But in my last equation the only way of getting U positive is by having a negative temperature??
    Or should I just answer that the energy is strict negative in this case?

    Any help will do!
  2. jcsd
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