The bulk modulus (K) of a substance measures the substance's resistance to uniform compression. It is defined as the pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure increase needed to cause a given relative decrease in volume Volume is how much three-dimensional space a substance or shape occupies or contains, often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of. Its base unit is the pascal The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength. It is a measure of force per unit area, defined as one newton per square metre. In everyday life, the pascal is perhaps best known from meteorological barometric pressure reports, where it occurs in the form of hectopascals (1 hPa ≡ 100.

As an example, suppose an iron cannon ball with bulk modulus 160 GPa The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength. It is a measure of force per unit area, defined as one newton per square metre. In everyday life, the pascal is perhaps best known from meteorological barometric pressure reports, where it occurs in the form of hectopascals (1 hPa ≡ 100 is to be reduced in volume by 0.5%. This requires a pressure increase of 0.005×160 GPa = 0.8 GPa (116,000 psi The pound per square inch or, more accurately, pound-force per square inch is a unit of pressure or of stress based on avoirdupois units. It is the pressure resulting from a force of one pound-force applied to an area of one square inch:).

Contents

Definition

The bulk modulus K can be formally defined by the equation:

where P is pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure, V is volume, and ∂P/∂V denotes the partial derivative In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant . Partial derivatives are used in vector calculus and differential geometry of pressure with respect to volume. The inverse of the bulk modulus gives a substance's compressibility In thermodynamics and fluid mechanics, compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change.

Other moduli describe the material's response (strain In continuum mechanics, deformation or strain is the change in the metric properties of a continuous body B in the displacement from an initial placement κ0 to a final placement κ(B). A change in the metric properties means that a curve drawn in the initial body placement changes its length when displaced to a curve in the final placement. If) to other kinds of stress In continuum mechanics, stress is a measure of the average force per unit area of a surface within a deformable body on which internal forces act. In other words, it is a measure of the intensity of the internal forces acting between particles of a deformable body across imaginary internal surfaces . These internal forces are produced between the: the shear modulus The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force . In the case of an object that's shaped like a rectangular prism, it will deform into a parallelepiped. Anisotropic materials such as wood and paper exhibit differing describes the response to shear, and Young's modulus In solid mechanics, Young's modulus, also known as the tensile modulus, is a measure of the stiffness of an isotropic elastic material. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. This can be experimentally determined from the slope of a stress-strain curve created describes the response to linear strain. For a fluid A fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids, only the bulk modulus is meaningful. For an anisotropic Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies homogeneity in all directions. It can be defined as a difference, when measured along different axes, in a material's physical property (absorbance, refractive index, density, etc.) An example of anisotropy is the light coming through a polarizer. An solid such as wood Wood is a hard, fibrous tissue found in many plants. It has been used for centuries for both fuel and as a construction material for several types of living areas such as houses. It is an organic material, a natural composite of cellulose fibers embedded in a matrix of lignin which resists compression. In the strict sense wood is produced as or paper Paper is a thin material mainly used for writing upon, printing upon or for packaging. It is produced by pressing together moist fibers, typically cellulose pulp derived from wood, rags or grasses, and drying them into flexible sheets, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit. Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials. Hooke's.

Thermodynamic relation

Strictly speaking, the bulk modulus is a thermodynamic In physics and chemistry, thermodynamics is the study of energy conversion between heat and mechanical work, and subsequently the macroscopic variables such as temperature, volume and pressure. Its progenitor, based on statistical predictions of the collective motion of particles from their microscopic behavior, is the field of statistical quantity, and it is necessary to specify how the temperature varies in order to specify a bulk modulus: constant-temperature Historically, two equivalent concepts of temperature have developed, the thermodynamic description and a microscopic explanation based on statistical physics. Since thermodynamics deals entirely with macroscopic measurements, the thermodynamic definition of temperature, first stated by Lord Kelvin, is stated entirely in empirical, measurable (KT), constant-entropy Entropy is a measure of how disorganized a system is. It is an important part of the second law of thermodynamics. Thermodynamic systems consist of objects, e.g. atoms or molecules, which "carry" energy. In applied thermodynamics, as a matter of convention, entropy is measured in units of energy per temperature . If thermodynamic systems (adiabatic In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid. The term "adiabatic" literally means impassable, coming from the Greek roots ἀ- , διὰ- ("through"), and βαῖνειν ("to pass"); this etymology corresponds KS), and other variations are possible. In practice, such distinctions are usually only relevant for gases Gas is one of three classical states of matter. Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons are so energized that they leave their parent atoms.

For a gas, the adiabatic bulk modulus KS is approximately given by

and the isothermal bulk modulus KT is approximately given by

where

γ is the adiabatic index The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume (CV). It is sometimes also known as the isentropic expansion factor and is denoted by γ (gamma) or κ (kappa). The latter symbol kappa is primarily used by chemical engineers. Mechanical, sometimes called κ.
P is the pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.

In a fluid A fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids, the bulk modulus K and the density The density of a material is defined as its mass per unit volume. The symbol of density is ρ . In some countries (for instance, in the United States), density is also defined as its weight per unit volume ρ determine the speed of sound The speed of sound is the rate of travel of a sound wave through an elastic medium. In dry air at 20 °C , the speed of sound is 343 metres per second (1,125 ft/s). This equates to 1,236 kilometres per hour (768 mph), or about one kilometre in three seconds and about one mile in five seconds. This figure increases with temperature (equations are c (pressure waves P-waves are type of elastic wave, also called seismic waves, that can travel through gases , solids and liquids, including the Earth. P-waves are produced by earthquakes and recorded by seismometers. The name P-wave stands either for primary wave, as it has the highest velocity and is therefore the first to be recorded, or pressure wave, as it is), according to the formula

Solids can also sustain transverse waves A transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer. If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y-z plane: for these materials one additional elastic modulus An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region:, for example the shear modulus The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force . In the case of an object that's shaped like a rectangular prism, it will deform into a parallelepiped. Anisotropic materials such as wood and paper exhibit differing, is needed to determine wave speeds.

Measurement

It is possible to measure the bulk modulus using powder diffraction under applied pressure.

Selected values

Approximate bulk modulus (K) for common materials
Material Bulk modulus in G The Oxford English Dictionary reports the earliest written use of giga in this sense to be in the Reports of the IUPAC 14th Conference in 1947: "The following prefixes to abbreviations for the names of units should be used: G giga 109×" Pa The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength. It is a measure of force per unit area, defined as one newton per square metre. In everyday life, the pascal is perhaps best known from meteorological barometric pressure reports, where it occurs in the form of hectopascals (1 hPa ≡ 100 Bulk modulus in psi The pound per square inch or, more accurately, pound-force per square inch is a unit of pressure or of stress based on avoirdupois units. It is the pressure resulting from a force of one pound-force applied to an area of one square inch:
Glass Glass is an amorphous solid material. Glasses are typically brittle, and often optically transparent. Glass is commonly used for windows, bottles, and eyewear; examples of glassy materials include soda-lime glass, borosilicate glass, acrylic glass, sugar glass, Muscovy-glass, and aluminium oxynitride. The term glass developed in the late Roman (see also diagram below table) 35 to 55 5.8×106
Steel Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten. Carbon and other elements act as a hardening agent, preventing 160 23×106
Diamond In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions. Diamond is renowned as a material with superlative[1] 442 64×106
Influences of selected glass Glass is an amorphous solid material. Glasses are typically brittle, and often optically transparent. Glass is commonly used for windows, bottles, and eyewear; examples of glassy materials include soda-lime glass, borosilicate glass, acrylic glass, sugar glass, Muscovy-glass, and aluminium oxynitride. The term glass developed in the late Roman component additions on the bulk modulus of a specific base glass.[2]
Approximate bulk modulus (K) for other substances
Water Water is a chemical substance with the chemical formula H2O. Its molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state, water vapor or steam 2.2×109 Pa (value increases at higher pressures)
Air 1.42×105 Pa (adiabatic bulk modulus)
Air 1.01×105 Pa (constant temperature bulk modulus)
Solid helium Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert monatomic gas that heads the noble gas group in the periodic table. Its boiling and melting points are the lowest among the elements and it exists only as a gas except 5×107 Pa (approximate)

References

  1. ^ Phys. Rev. B 32, 7988 - 7991 (1985), Calculation of bulk moduli of diamond and zinc-blende solids
  2. ^ Bulk modulus calculation of glasses
Elastic moduli An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region: for homogeneous isotropic Isotropy is uniformity in all directions. Precise definitions depend on the subject area. The word is made up from Greek iso and tropos (direction). Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, dependent on direction materials
Bulk modulus (K) • Young's modulus In solid mechanics, Young's modulus, also known as the tensile modulus, is a measure of the stiffness of an isotropic elastic material. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. This can be experimentally determined from the slope of a stress-strain curve created (E) • Lamé's first parameter where σ is the stress, ε the strain tensor, the the identity matrix and the trace function (λ) • Shear modulus The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force . In the case of an object that's shaped like a rectangular prism, it will deform into a parallelepiped. Anisotropic materials such as wood and paper exhibit differing (G) • Poisson's ratio Poisson's ratio , named after Siméon Poisson, is the ratio, when a sample object is stretched, of the contraction or transverse strain (perpendicular to the applied load), to the extension or axial strain (in the direction of the applied load) (ν) • P-wave modulus In linear elasticity, the P-wave modulus M, also known as the longitudinal modulus, is one of the elastic moduli available to describe isotropic homogeneous materials (M)
Conversion formulas
Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these, thus given any two, any other of the elastic moduli can be calculated according to these formulas.

Categories: Elasticity (physics) | Physical quantities This category identifies Physical quantities which are necessary defined quantities, measured, manipulated, generally used by Physicists, Engineers, Chemists, etc

Personal tools
Namespaces
">
Variants
Views
">
Actions
Search">
The Central London Railway was a railway company established in 1889 to construct a deep-level underground "tube" railway in London. Funding for construction was obtained in 1895 through a syndicate of financiers and construction work took place from 1896 to 1900. When opened in 1900, the railway served 13 stations and ran completely
Navigation
Interaction
Toolbox
Print/export
Languages

 

The above information uses material from Wikipedia and is licensed under the GNU Free Documentation License.
Some facts may not have been fully verified for accuracy. [Disclaimers]
This page was last archived by our server on Wed Jul 14 19:54:37 2010. [ refresh local cache ]
Displaying this page or its contents does not use any Wikimedia Foundation's resources.
The owners of this site proudly support the Wikimedia Foundation.

[Hide]▼
[Hide]▲