Material properties (thermodynamics) - Alchetron, the free social encyclopedia

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

Adiabatic compressibility

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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