Material properties (thermodynamics) explained

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

\kappa _{T =- (1)/(V)} \left( (\partial V)/(\partial P) \right) _{T} =- (1)/(V) (\partial ^{2} G)/(\partial P ^{2})

• Adiabatic compressibility

\kappa _{S =- (1)/(V)} \left( (\partial V)/(\partial P) \right) _{S} =- (1)/(V) (\partial ^{2} H)/(\partial P ^{2})

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

• Specific heat at constant pressure

c _{P = (T)/(N)} \left( (\partial S)/(\partial T) \right) _{P} =- (T)/(N) (\partial ^{2} G)/(\partial T ^{2})

• Specific heat at constant volume

c _{V = (T)/(N)} \left( (\partial S)/(\partial T) \right) _{V} =- (T)/(N) (\partial ^{2} A)/(\partial T ^{2})

• Coefficient of thermal expansion

\alpha = (1)/(\left( V) (\partial V)/(\partial T) \right) _{P} = (1)/(V) (\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

\kappa _{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 + (TV\alpha ^{2})/(N\kappa _{T})} \kappa _{T=\kappa} ^{S + (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. Moreover, considering derivatives such as

(\partial ^{3} G)/(\partial P \partial T ^{2}) 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

• 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.

References

• Book: Callen, Herbert B. . Herbert Callen

. Herbert Callen . 1985 . Thermodynamics and an Introduction to Thermostatistics . 2nd . John Wiley & Sons . New York . 0-471-86256-8 .

Notes and References

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: PrincetonUniversity Press. doi:10.2307/j.ctt13x1c8g