- ...pressure
![[*]](http://www.phys.virginia.edu/usr/icons.gif/foot_motif.gif)
- In general, the specific heat is dQ/dT, or TdS/dT. This can be rewritten
using the basic equation of thermodynamics (just energy balance), dE = TdS - pdV.
At constant volume, dE = TdS and
![\begin{displaymath}
C_{V}=T\left( \frac{\partial S}{\partial T}\right) _{V}=\left( \frac{\partial E}{\partial T}\right) _{V}
\end{displaymath}](img25.gif)
At constant pressure, it is convenient to work with the quantity H = E + pV, called the enthalpy.
We find dH = dE + pdV + Vdp = TdS + Vdp, and so
![\begin{displaymath}
C_{p}=T\left( \frac{\partial S}{\partial T}\right) _{p}=\left( \frac{\partial H}{\partial T}\right) _{p}
\end{displaymath}](img26.gif)
In an ideal gas, dE = CVdT and pV = NkBT, so that dH = dE + d(pV) = (CV + NkB)dT and Cp = CV + NkB.
V. Celli, Univ. of Virginia
11/10/1997