The thermodynamic properties of materials are intensive thermodynamic parameters which are specific to a given material. Each is directly related to a second order differential of a thermodynamic potential. Examples for a simple 1-component system are:
Compressibility (or its inverse, the bulk modulus) Isothermal compressibility
κ T = − 1 V ( ∂ V ∂ P ) T = − 1 V ∂ 2 G ∂ P 2 {\displaystyle \kappa _{T}=-{\frac {1}{V}}\left({\frac {\partial V}{\partial P}}\right)_{T}\quad =-{\frac {1}{V}}\,{\frac {\partial ^{2}G}{\partial P^{2}}}}
Adiabatic compressibility
κ S = − 1 V ( ∂ V ∂ P ) S = − 1 V ∂ 2 H ∂ P 2 {\displaystyle \kappa _{S}=-{\frac {1}{V}}\left({\frac {\partial V}{\partial P}}\right)_{S}\quad =-{\frac {1}{V}}\,{\frac {\partial ^{2}H}{\partial P^{2}}}}
Specific heat (Note - the extensive analog is the heat capacity) Specific heat at constant pressure
c P = T N ( ∂ S ∂ T ) P = − T N ∂ 2 G ∂ T 2 {\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}}}}
Specific heat at constant volume
c V = T N ( ∂ S ∂ T ) V = − T N ∂ 2 A ∂ T 2 {\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}}}}
Coefficient of thermal expansion
α = 1 V ( ∂ V ∂ T ) P = 1 V ∂ 2 G ∂ P ∂ T {\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}}}
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