Material properties (thermodynamics)

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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}}}

where P  is pressure, V  is volume, T  is temperature, S  is entropy, and N  is the number of particles.

For a single component system, only three second derivatives are needed in order to derive all others, and so only three material properties are needed to derive all others. For a single component system, the "standard" three parameters are the isothermal compressibility κ T {\displaystyle \kappa _{T}} , the specific heat at constant pressure c P {\displaystyle c_{P}} , and the coefficient of thermal expansion α {\displaystyle \alpha } .

For example, the following equations are true:

c P = c V + T V α 2 N κ T {\displaystyle c_{P}=c_{V}+{\frac {TV\alpha ^{2}}{N\kappa _{T}}}} κ T = κ S + T V α 2 N c P {\displaystyle \kappa _{T}=\kappa _{S}+{\frac {TV\alpha ^{2}}{Nc_{P}}}}

The three "standard" properties are in fact the three possible second derivatives of the Gibbs free energy with respect to temperature and pressure. Moreover, considering derivatives such as ∂ 3 G ∂ P ∂ T 2 {\displaystyle {\frac {\partial ^{3}G}{\partial P\partial T^{2}}}} and the related Schwartz relations, shows that the properties triplet is not independent. In fact, one property function can be given as an expression of the two others, up to a reference state value.

The second principle of thermodynamics has implications on the sign of some thermodynamic properties such isothermal compressibility.

See also

• List of materials properties (thermal properties)
• Heat capacity ratio
• Statistical mechanics
• Thermodynamic equations
• Thermodynamic databases for pure substances
• Heat transfer coefficient
• Latent heat
• Specific heat of melting (Enthalpy of fusion)
• Specific heat of vaporization (Enthalpy of vaporization)
• Thermal mass

External links

• The Dortmund Data Bank is a factual data bank for thermodynamic and thermophysical data.

References

1. ^ a b S. Benjelloun, "Thermodynamic identities and thermodynamic consistency of Equation of States", Link to Archiv e-print Link to Hal e-print
2. ^ Israel, R. (1979). Convexity in the Theory of Lattice Gases. Princeton, New Jersey: Princeton University Press. doi:10.2307/j.ctt13x1c8g

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