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

$\beta_T=-\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)_T \quad = -\frac{1}{V}\,\frac{\partial^2 G}{\partial P^2}$

• Adiabatic compressibility

$\beta_S=-\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)_S \quad = -\frac{1}{V}\,\frac{\partial^2 H}{\partial P^2}$

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

• Specific heat at constant pressure

$c_P=\frac{T}{N}\left(\frac{\partial S}{\partial T}\right)_P \quad = -\frac{T}{N}\,\frac{\partial^2 G}{\partial T^2}$

• Specific heat at constant volume

$c_V=\frac{T}{N}\left(\frac{\partial S}{\partial T}\right)_V \quad = -\frac{T}{N}\,\frac{\partial^2 A}{\partial T^2}$

• Coefficient of thermal expansion

$\alpha=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_P \quad = \frac{1}{V}\,\frac{\partial^2 G}{\partial P\partial T}$

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 $\beta _{T}$, the specific heat at constant pressure $c_{P}$, and the coefficient of thermal expansion $\alpha$.

For example, the following equations are true:

$c_P=c_V+\frac{TV\alpha^2}{N\beta_T}$

$\beta_T=\beta_S+\frac{TV\alpha^2}{Nc_P}$

The three "standard" properties are in fact the three possible second derivatives of the Gibbs free energy with respect to temperature and pressure.

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.
• thermodynamic databases for pure substances.

References

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