# 材料性质 (热力学)

• 等温压缩率
${\displaystyle \beta _{T}=-{\frac {1}{V}}\left({\frac {\partial V}{\partial P}}\right)_{T}\quad =-{\frac {1}{V}}\,{\frac {\partial ^{2}G}{\partial P^{2}}}}$
• 绝热压缩率
${\displaystyle \beta _{S}=-{\frac {1}{V}}\left({\frac {\partial V}{\partial P}}\right)_{S}\quad =-{\frac {1}{V}}\,{\frac {\partial ^{2}H}{\partial P^{2}}}}$
• 等压摩尔热容
${\displaystyle c_{P}={\frac {T}{N}}\left({\frac {\partial S}{\partial T}}\right)_{P}\quad =-{\frac {T}{N}}\,{\frac {\partial ^{2}G}{\partial T^{2}}}}$
• 等容摩尔热容
${\displaystyle c_{V}={\frac {T}{N}}\left({\frac {\partial S}{\partial T}}\right)_{V}\quad =-{\frac {T}{N}}\,{\frac {\partial ^{2}A}{\partial T^{2}}}}$
${\displaystyle \alpha ={\frac {1}{V}}\left({\frac {\partial V}{\partial T}}\right)_{P}\quad ={\frac {1}{V}}\,{\frac {\partial ^{2}G}{\partial P\partial T}}}$

${\displaystyle c_{P}=c_{V}+{\frac {TV\alpha ^{2}}{N\beta _{T}}}}$
${\displaystyle \beta _{T}=\beta _{S}+{\frac {TV\alpha ^{2}}{Nc_{P}}}}$

## 参考文献

Callen, Herbert B. Thermodynamics and an Introduction to Thermostatistics 2nd Ed. New York: John Wiley & Sons. 1985. ISBN 0-471-86256-8.