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The bulk modulus (or or ) of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume .
Generally, at constant temperature, the bulk modulus is defined by: = (). The easiest way to get an equation of state linking P and V is to assume that K is constant, that is to say, independent of pressure and deformation of the solid, then we simply find Hooke's law. In this case, the volume decreases exponentially with pressure.
Physically, volume viscosity represents the irreversible resistance, over and above the reversible resistance caused by isentropic bulk modulus, to a compression or expansion of a fluid. [1] At the molecular level, it stems from the finite time required for energy injected in the system to be distributed among the rotational and vibrational ...
A pressure gauge's bulk modulus is known, and its thermal equation of state is well known. To study a solid with unknown bulk modulus, it has to be loaded with a pressure gauge, and its pressure will be determined from its pressure gauge. The most common pressure gauges are Au, Pt, Cu, and MgO, etc.
The third-order Birch–Murnaghan isothermal equation of state is given by = [() / /] {+ (′) [() /]}. where P is the pressure, V 0 is the reference volume, V is the deformed volume, B 0 is the bulk modulus, and B 0 ' is the derivative of the bulk modulus with respect to pressure. The bulk modulus and its derivative are usually obtained from ...
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.
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 isentropic bulk modulus =, where is the specific heat capacity ratio and p is the fluid pressure. If the fluid obeys the ideal gas law , we have K s = γ p = γ ρ R T = ρ a 2 {\displaystyle K_{s}=\gamma p=\gamma \rho RT=\,\rho a^{2}} ,