Physics:Material properties (thermodynamics)

From HandWiki

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:

  • 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 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]
[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.[1]

The second principle of thermodynamics has implications on the sign of some thermodynamic properties such isothermal compressibility.[1][2]

See also

External links

References

  1. 1.0 1.1 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
  • Thermodynamics and an Introduction to Thermostatistics (2nd ed.). New York: John Wiley & Sons. ISBN 0-471-86256-8.