Heat Capacity
#Physics
Topics
$\displaystyle C_{y}=\left( \frac{ \partial Q }{ \partial T } \right)_{y}$
- $\displaystyle y=V$ or $\displaystyle P$
$\displaystyle C_{V}=\left( \frac{ \mathrm{d}Q }{ \mathrm{d}\tau } \right){P}=\left( \frac{ \partial U }{ \partial \tau } \right){V}=\tau\left( \frac{ \partial \sigma }{ \partial \tau } \right)_{V}$
$\displaystyle C_{V}=\frac{12\pi^{4}Nk_{B}}{5}\left( \frac{T}{\theta} \right)^{3}$
- The Debye low temperature limit of the heat capacity of a dielectric solid
- $\displaystyle \theta$ is the Debye temperature
$\displaystyle C_{P}=\left( \frac{ \mathrm{d}Q }{ \mathrm{d}\tau } \right){P}=\left( \frac{ \partial U }{ \partial \tau } \right){P}=\tau\left( \frac{ \partial \sigma }{ \partial \tau } \right)_{P}=\frac{\mathrm{d}U+P\mathrm{d}V}{\mathrm{d}\tau}$
$\displaystyle C_{P}=C_{V}+N$
$\displaystyle C_{P}=\frac{5}{2}N$
- Heat capacity at constant pressure for an ideal monatomic gas