- #1
AxiomOfChoice
- 533
- 1
My professor did this in lecture, and I can't figure out his logic. Can someone fill in the gaps?
He went from:
[tex]
dS = \left( \frac{\partial S}{\partial P} \right)_T dP + \left( \frac{\partial S}{\partial T} \right)_P dT
[/tex]
(which I totally understand; it just follows from the fact that [itex]S[/itex] is an exact differential) to the following:
[tex]
\left( \frac{\partial S}{\partial T} \right)_V = \left( \frac{\partial S}{\partial P} \right)_T \left( \frac{\partial P}{\partial T}\right)_V + \left( \frac{\partial S}{\partial T} \right)_P
[/tex]
Where the heck does THAT come from? Anyone have any ideas?
He went from:
[tex]
dS = \left( \frac{\partial S}{\partial P} \right)_T dP + \left( \frac{\partial S}{\partial T} \right)_P dT
[/tex]
(which I totally understand; it just follows from the fact that [itex]S[/itex] is an exact differential) to the following:
[tex]
\left( \frac{\partial S}{\partial T} \right)_V = \left( \frac{\partial S}{\partial P} \right)_T \left( \frac{\partial P}{\partial T}\right)_V + \left( \frac{\partial S}{\partial T} \right)_P
[/tex]
Where the heck does THAT come from? Anyone have any ideas?