Physics:Material properties (thermodynamics)

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

[math]\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} }[/math]

• Adiabatic compressibility

[math]\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} }[/math]

• Specific heat (Note - the extensive analog is the heat capacity)

• Specific heat at constant pressure

[math]\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} }[/math]

• Specific heat at constant volume

[math]\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} }[/math]

• Coefficient of thermal expansion

[math]\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} }[/math]

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 [math]\displaystyle{ \kappa_T }[/math], the specific heat at constant pressure [math]\displaystyle{ c_P }[/math], and the coefficient of thermal expansion [math]\displaystyle{ \alpha }[/math].

For example, the following equations are true:

[math]\displaystyle{ c_P=c_V+\frac{TV\alpha^2}{N\kappa_T} }[/math]

[math]\displaystyle{ \kappa_T=\kappa_S+\frac{TV\alpha^2}{Nc_P} }[/math]

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 [math]\displaystyle{ \frac{\partial^3 G}{\partial P \partial T^2} }[/math] 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

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