- #1
dapias09
- 29
- 0
Hi all,
I'm working with the heat capacities definition and I have got a confusion. I don't understand why we can express them like
Cp = T(∂S/∂T)p
Cv = T(∂S/∂T)v
I know that Cp=(dQ/dT)p = (∂H/∂T)p with H equal to TdS + VdP and Cv=(dQ/dT)v = (∂U/∂T)v with U equal to TdS + PdV,
My guess: If I begin for instance with the enthalpy, H, and I constrain it to constant pressure I get just the TdS term, that is the thermodynamic definition of "Heat (Q)" . So I get the definition of the heat capacity if I derive Q respect to T, or TdS respect to T (is the same thing). Doing it, I get:
dQ/dT = (TdS)/dT = Td^2S/d^2T + dS/dT.
An expression very different of the definition.
Can anyone help me?
Thanks in advance.
I'm working with the heat capacities definition and I have got a confusion. I don't understand why we can express them like
Cp = T(∂S/∂T)p
Cv = T(∂S/∂T)v
I know that Cp=(dQ/dT)p = (∂H/∂T)p with H equal to TdS + VdP and Cv=(dQ/dT)v = (∂U/∂T)v with U equal to TdS + PdV,
My guess: If I begin for instance with the enthalpy, H, and I constrain it to constant pressure I get just the TdS term, that is the thermodynamic definition of "Heat (Q)" . So I get the definition of the heat capacity if I derive Q respect to T, or TdS respect to T (is the same thing). Doing it, I get:
dQ/dT = (TdS)/dT = Td^2S/d^2T + dS/dT.
An expression very different of the definition.
Can anyone help me?
Thanks in advance.