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Definition of specific heat by via entropy

  1. Mar 25, 2012 #1
    In his Statistical Physics book, Landau introduces the specific heat as the quantity of heat which must be gained in order to raise the temperature of a body one by unit.

    I don't understand, how he directly jumps to the conclusion that that has to be (let's just say, for constant volume):
    C_V = T\left(\frac{\partial S}{\partial T}\right)_V

    If I take a process during which I have no change in volume, I think I can write: [itex]\partial Q = T\mathrm{d}S[/itex], is that correct? My next thought was then that I could write [itex]C_V=\left(\frac{\partial Q}{\partial T}\right)_V[/itex]. However, now I am stuck, because I do not understand why this should yield the above definition, without acting on the [itex]T[/itex] part of the the heat-entropy relation.

    EDIT: I would like to add, that I have the same problem with the specific heat's definition via the energy differential [itex]\mathrm{d}E = T\mathrm{d}S - P\mathrm{d}V[/itex]:
    [tex]C_V = \left(\frac{\partial E}{\partial T}\right)_V[/tex]

    Why does [itex]\frac{\partial}{\partial T}[/itex] not act on [itex]T[/itex]?
    Last edited: Mar 25, 2012
  2. jcsd
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