The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is isentropic or isothermal.
Accordingly, isothermal compressibility is defined: where the subscript T indicates that the partial differential is to be taken at constant temperature.
The isothermal compressibility is generally related to the isentropic (or adiabatic) compressibility by a few relations:[3] where γ is the heat capacity ratio, α is the volumetric coefficient of thermal expansion, ρ = N/V is the particle density, and
The deviation from ideal gas behavior tends to become particularly significant (or, equivalently, the compressibility factor strays far from unity) near the critical point, or in the case of high pressure or low temperature.
In these cases, a generalized compressibility chart or an alternative equation of state better suited to the problem must be utilized to produce accurate results.
The Earth sciences use compressibility to quantify the ability of a soil or rock to reduce in volume under applied pressure.
This concept is important for specific storage, when estimating groundwater reserves in confined aquifers.
For example, the construction of high-rise structures over underlying layers of highly compressible bay mud poses a considerable design constraint, and often leads to use of driven piles or other innovative techniques.
At low speeds, the compressibility of air is not significant in relation to aircraft design, but as the airflow nears and exceeds the speed of sound, a host of new aerodynamic effects become important in the design of aircraft.
These effects, often several of them at a time, made it very difficult for World War II era aircraft to reach speeds much beyond 800 km/h (500 mph).
From a strictly aerodynamic point of view, the term should refer only to those side-effects arising as a result of the changes in airflow from an incompressible fluid (similar in effect to water) to a compressible fluid (acting as a gas) as the speed of sound is approached.
One complication occurs in hypersonic aerodynamics, where dissociation causes an increase in the "notional" molar volume because a mole of oxygen, as O2, becomes 2 moles of monatomic oxygen and N2 similarly dissociates to 2 N. Since this occurs dynamically as air flows over the aerospace object, it is convenient to alter the compressibility factor Z, defined for an initial 30 gram moles of air, rather than track the varying mean molecular weight, millisecond by millisecond.
Z for the resulting plasma can similarly be computed for a mole of initial air, producing values between 2 and 4 for partially or singly ionized gas.