- #1

mSSM

- 33

- 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):

[tex]

C_V = T\left(\frac{\partial S}{\partial T}\right)_V

[/tex]

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]?

I don't understand, how he directly jumps to the conclusion that that has to be (let's just say, for constant volume):

[tex]

C_V = T\left(\frac{\partial S}{\partial T}\right)_V

[/tex]

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]?

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