- #1
mSSM
- 31
- 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):
<br /> C_V = T\left(\frac{\partial S}{\partial T}\right)_V<br />
If I take a process during which I have no change in volume, I think I can write: \partial Q = T\mathrm{d}S, is that correct? My next thought was then that I could write C_V=\left(\frac{\partial Q}{\partial T}\right)_V. However, now I am stuck, because I do not understand why this should yield the above definition, without acting on the T 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 \mathrm{d}E = T\mathrm{d}S - P\mathrm{d}V:
C_V = \left(\frac{\partial E}{\partial T}\right)_V
Why does \frac{\partial}{\partial T} not act on T?
I don't understand, how he directly jumps to the conclusion that that has to be (let's just say, for constant volume):
<br /> C_V = T\left(\frac{\partial S}{\partial T}\right)_V<br />
If I take a process during which I have no change in volume, I think I can write: \partial Q = T\mathrm{d}S, is that correct? My next thought was then that I could write C_V=\left(\frac{\partial Q}{\partial T}\right)_V. However, now I am stuck, because I do not understand why this should yield the above definition, without acting on the T 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 \mathrm{d}E = T\mathrm{d}S - P\mathrm{d}V:
C_V = \left(\frac{\partial E}{\partial T}\right)_V
Why does \frac{\partial}{\partial T} not act on T?
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