# 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
• β T = 1 V ( V P ) T = 1 V 2 G P 2
• β S = 1 V ( V P ) S = 1 V 2 H 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
• Specific heat at constant volume
• c V = T N ( S T ) V = T N 2 A T 2
• Coefficient of thermal expansion
• 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 β T , the specific heat at constant pressure c P , and the coefficient of thermal expansion α .

For example, the following equations are true:

c P = c V + T V α 2 N β T β T = β S + T V α 2 N c P

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

## References

Material properties (thermodynamics) Wikipedia

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