Thermodynamic compressibility

Compressibility, or the coefficient of compressibility, is a measure of the instantaneous relative volume change of a fluid or solid as a response to pressure or mean stress change.

Notes:

1. This definition is incomplete in the sense that the value of the compressibility coefficient depends on whether the process is isentropic or isothermal, hence the partial derivative should be taken at either constant entropy or constant temperature.

2. For solids the difference between isentropic and isothermal compressibility coefficients is usually negligible.

Links:

1. Wikipedia.

compressibility

thermodynamic_compressibility of the gas.

Symbol:

beta

Latex:

\(\beta\)

Dimension:

1/pressure

pressure

pressure in the gas.

Symbol:

p

Latex:

\(p\)

Dimension:

pressure

parameters

Parameters other than pressure on which the volume function depends.

Symbol:

q

Latex:

\(q\)

Dimension:

any_dimension

volume

volume of the gas as a function of pressure and parameters.

Symbol:

V(p, q)

Latex:

\(V{\left(p,q \right)}\)

Dimension:

volume

definition

beta = -Derivative(V(p, q), p) / V(p, q)

Latex:

\[\beta = - \frac{\frac{\partial}{\partial p} V{\left(p,q \right)}}{V{\left(p,q \right)}}\]