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Strictly speaking, the bulk modulus is a thermodynamic quantity, and in order to specify a bulk modulus it is necessary to specify how the pressure varies during compression: constant- temperature (isothermal ), constant- entropy (isentropic ), and other variations are possible. Such distinctions are especially relevant for gases.
Thermodynamics. In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility[1] or, if the temperature is held constant, the isothermal compressibility[2]) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.
The laws of thermodynamics imply the following relations between these two heat capacities (Gaskell 2003:23): = = Here is the thermal expansion coefficient: = is the isothermal compressibility (the inverse of the bulk modulus):
At high P-T, the pressure for the ideal gas is calculated by the force divided by the area, while the pressure for the solid is calculated from bulk modulus (K, or B) and volume at room temperature, or from Eq (1) at high P-T. A pressure gauge's bulk modulus is known, and its thermal equation of state is well known.
In 1895, [3] [4] the original isothermal Tait equation was replaced by Tammann with an equation of the form = = (+) where is the isothermal mixed bulk modulus. This above equation is popularly known as the Tait equation.
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: where P is pressure, V is volume, T is temperature, S is entropy, and N is the number of ...
Some formulations for the Grüneisen parameter include: = = = = = ( ) where V is volume, and are the principal (i.e. per-mass) heat capacities at constant pressure and volume, E is energy, S is entropy, α is the volume thermal expansion coefficient, and are the adiabatic and isothermal bulk moduli, is the speed of sound in the medium ...
The structure of Maxwell relations is a statement of equality among the second derivatives for continuous functions. It follows directly from the fact that the order of differentiation of an analytic function of two variables is irrelevant (Schwarz theorem). In the case of Maxwell relations the function considered is a thermodynamic potential ...