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# Material properties (thermodynamics)

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 Title: Material properties (thermodynamics) Author: World Heritage Encyclopedia Language: English Subject: Collection: Thermodynamic Properties Publisher: World Heritage Encyclopedia Publication Date:

### 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:

• 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}
\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 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}
\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.

## Sources

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