In physics, what is defined as mass per unit volume?
"Density The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ""ρ"" (the lower case Greek letter rho), although the Latin letter ""D"" can also be used. Mathematically, density is defined as mass divided by volume: where ""ρ"" is the density, ""m"" is the mass, and ""V"" is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically"
"Mass Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does"
"volume, area, mass, and force. These may be combined to understand the concept of pressure, which is force per unit area and density, which is mass per unit volume. It has been experimentally determined that, at low enough pressures and densities, all gases behave as ideal gases. The behavior of an ideal gas is given by the ideal gas law: where ""P"" is pressure, ""V"" is volume, ""N"" is the number of particles (total mass divided by mass per particle), ""k"" is Boltzmann's constant, and ""T"" is temperature. In fact, this equation is more than a phenomenological equation, it gives"
"Mass (mass spectrometry) The mass recorded by a mass spectrometer can refer to different physical quantities depending on the characteristics of the instrument and the manner in which the mass spectrum is displayed. The unified atomic mass unit (symbol: u) is the standard unit that is used for indicating mass on an atomic or molecular scale (atomic mass). The dalton (symbol: Da) is equivalent to the unified atomic mass unit. One unified atomic mass unit is approximately the mass of one a single proton or neutron. The unified atomic mass unit has a value of . The ""amu"" without the"
"for use within SI"". SI distinguishes between mass and weight ""mass"" being a measure of the amount of material contained in an object and ""weight"" the gravitational force on that object. We normally ""weigh"" objects by comparing the gravitational force on that object with the gravitational force on an object of known mass (such as a 1 kg ""weight""). Although this concept was understood by ancient scientists (Archimedes' principle is based on it), the wording was only formalised in 1901. The SI base unit of mass is the kilogram which was originally defined in 1795 as the mass of one"
"the extensive quantities such as energy, volume, or entropy (versus intensive quantities of temperature and pressure) are placed on a unit mass basis, and so too are the calculations, making those more general and therefore of more general use. Hence, each term involving an extensive quantity could be divided by the mass, giving the terms units of joules/kg (specific energy), meters/kg (specific volume), or joules/(kelvin·kg) (specific entropy, heat capacity) etc. and would be represented using lower case letters, u, v, s, etc. Equation 1 can now be related to the specific heat equation for constant volume. The specific heats are"
"""V"" is the volume of gas (SI unit cubic metres), ""n"" is the amount of gas (SI unit moles), ""m"" is the mass (SI unit kilograms) contained in ""V"", and ""T"" is the thermodynamic temperature (SI unit kelvins). ""R"" is the molar-weight-specific gas constant, discussed below. The gas constant is expressed in the same physical units as molar entropy and molar heat capacity. From the general equation ""PV"" = ""nRT"" we get: where ""P"" is pressure, ""V"" is volume, ""n"" is number of moles of a given substance, and ""T"" is temperature. As pressure is defined as force per unit"
"Atomic mass unit The unified atomic mass unit or dalton (symbol: u, or Da) is a standard unit of mass that quantifies mass on an atomic or molecular scale (atomic mass). One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1g/mol. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest, and has a value of , or approximately 1.66 yoctograms. The CIPM has categorised it as a non-SI unit"
"Atomic mass The atomic mass (""m"") is the mass of an atom. Its unit is the unified atomic mass units (symbol: u, or Da) where 1 unified atomic mass unit is defined as of the mass of a single carbon-12 atom, at rest. For atoms, the protons and neutrons of the nucleus account for almost all of the mass, and the atomic mass measured in u has nearly the same value as the mass number. When divided by unified atomic mass units or daltons to form a pure numeric ratio, the atomic mass of an atom becomes a dimensionless value"
"is assigned the average of the properties of atoms in a small region nearby. In particular, it has a density and velocity that depend on time and position . The momentum per unit volume is . Consider a column of water in hydrostatic equilibrium. All the forces on the water are in balance and the water is motionless. On any given drop of water, two forces are balanced. The first is gravity, which acts directly on each atom and molecule inside. The gravitational force per unit volume is , where is the gravitational acceleration. The second force is the sum"
"of the hydrogen atom. Mass (mass spectrometry) The mass recorded by a mass spectrometer can refer to different physical quantities depending on the characteristics of the instrument and the manner in which the mass spectrum is displayed. The unified atomic mass unit (symbol: u) is the standard unit that is used for indicating mass on an atomic or molecular scale (atomic mass). The dalton (symbol: Da) is equivalent to the unified atomic mass unit. One unified atomic mass unit is approximately the mass of one a single proton or neutron. The unified atomic mass unit has a value of ."
"gas law. Volume Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is 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 space the container itself displaces. Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular,"
"Mass flow rate In physics and engineering, mass flow rate is the mass of a substance which passes per unit of time. Its unit is kilogram per second in SI units, and slug per second or pound per second in US customary units. The common symbol is formula_1 (ṁ, pronounced ""m-dot""), although sometimes ""μ"" (Greek lowercase mu) is used. Sometimes, mass flow rate is termed ""mass flux"" or ""mass current"", see for example ""Fluid Mechanics, Schaum's et al"". In this article, the (more intuitive) definition is used. Mass flow rate is defined by the limit: The reason for the dot"
"discussed above. When a point particle has an additive property, such as mass or charge, concentrated at a single point in space, this can be represented by a Dirac delta function. Point mass (pointlike mass) is the concept, for example in classical physics, of a physical object (typically matter) that has nonzero mass, and yet explicitly and specifically is (or is being thought of or modeled as) infinitesimal (infinitely small) in its volume or linear dimensions. A common use for point mass lies in the analysis of the gravitational fields. When analyzing the gravitational forces in a system, it becomes"
"Molar mass In chemistry, the molar mass ""M"" is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The base SI unit for molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol. In simple terms, molar mass of a substance is the total weight of that substance (in either kilogram or gram) for one mole of that substance. That is, the weight of a substance for 6.02214076×10^23 molecules or atoms of that substance. As an example, the molar mass of"
"mass unit ""u"" has been defined as 1/12 the mass of C. Before that the atomic mass unit ""amu"" was defined as 1/16 the mass of O (physics) and as 1/16 the mass of O (chemistry). Thus the publication date in literature ought to be heeded when reading about the milli mass unit as its name does not reveal whether it refers to the old amu or the newer u. The mass excess is usually indicated in mu or mmu. In mass spectrometry the mass accuracy of a mass analyzer is often indicated in mu, even though a more correct"
"the other and in such cases the combined volume is not additive. In ""differential geometry"", volume is expressed by means of the volume form, and is an important global Riemannian invariant. In ""thermodynamics"", volume is a fundamental parameter, and is a conjugate variable to pressure. Any unit of length gives a corresponding unit of volume: the volume of a cube whose sides have the given length. For example, a cubic centimetre (cm) is the volume of a cube whose sides are one centimetre (1 cm) in length. In the International System of Units (SI), the standard unit of volume is"
"vacuum, the momentum per unit volume is where is the vacuum permeability and is the speed of light. The momentum density is proportional to the Poynting vector which gives the directional rate of energy transfer per unit area: If momentum is to be conserved over the volume over a region , changes in the momentum of matter through the Lorentz force must be balanced by changes in the momentum of the electromagnetic field and outflow of momentum. If is the momentum of all the particles in , and the particles are treated as a continuum, then Newton's second law gives"
"these is a different concept. In scientific contexts, mass refers loosely to the amount of ""matter"" in an object (though ""matter"" may be difficult to define), whereas weight refers to the force experienced by an object due to gravity. An object with a mass of 1.0 kilogram will weigh approximately 9.81 newtons (newton is the unit of force, while kilogram is the unit of mass) on the surface of the Earth (its mass multiplied by the gravitational field strength). Its weight will be less on Mars (where gravity is weaker), more on Saturn, and negligible in space when far from"
"Another three base units (for temperature, amount of substance and luminous intensity) were added later. The early metric systems defined a unit of weight as a base unit, while the SI defines an analogous unit of mass. In everyday use, these are mostly interchangeable, but in scientific contexts the difference matters. Mass, strictly the inertial mass, represents a quantity of matter. It relates the acceleration of a body to the applied force via Newton's law, : force equals mass times acceleration. A force of 1 N (newton) applied to a mass of 1 kg will accelerate it at 1 m/s."
"including mass in Newtonian mechanics, see the article on mass. The term ""mass"" in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The ""invariant mass"" is another name for the ""rest mass"" of single particles. The more general invariant mass (calculated with a more complicated formula) loosely corresponds to the ""rest mass"" of a ""system"". Thus, invariant mass is a natural unit of mass used for systems which are being viewed from their center of momentum frame (COM frame), as when any"
"determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: formula_2, where formula_3 is an elementary volume at position formula_4. The mass of the body then can be expressed as In practice, bulk materials such as sugar, sand, or snow contain voids. Many materials exist in nature as flakes, pellets, or granules. Voids are regions which contain something other than the considered material. Commonly the void is air, but it could also be vacuum, liquid, solid, or a different gas or"
"particle of mass is a vector field consisting at every point of a vector pointing directly towards the particle. The magnitude of the field at every point is calculated applying the universal law, and represents the force per unit mass on any object at that point in space. Because the force field is conservative, there is a scalar potential energy per unit mass, , at each point in space associated with the force fields; this is called gravitational potential. The gravitational field equation is where is the gravitational force, is the mass of the test particle, is the position of"
"Kendrick mass The Kendrick mass is defined by setting the mass of a chosen molecular fragment, typically CH, to an integer value in atomic mass units. It is different from the IUPAC definition, which is based on setting the mass of C isotope to exactly 12 u. The Kendrick mass is often used to identify homologous compounds differing only by a number of base units in high resolution mass spectra. This definition of mass was first suggested in 1963 by chemist Edward Kendrick, and it has been adopted by scientists working in the area of high-resolution mass spectrometry, environmental analysis,"
", that the Laue scalar could be written: which gives the corresponding Einstein's constant for a tensor with dimension of ""mass per volume"": But another valid choice for writing the form of the stress–energy tensor, is in units of ""energy per volume"": Neglecting the same term orders, the corresponding Laue scalar is: which contains an additional term to convert units of mass density to units of energy density, so the corresponding Einstein's constant in the field equations is then: This is just a question of choice, since for any chosen value unit, the Einstein field equations are the same. The"
"Volume Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is 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 space the container itself displaces. Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and"
"Milli mass unit The milli mass unit or (mmu) is used as a unit of mass by some scientific authors even though this unit is not defined by the IUPAP red book nor by the IUPAC green book. It is a short form of the tongue-breaking but formally more correct ""milli unified atomic mass unit"" (mu) and equivalent to 1/1000 of the unified atomic mass unit (u). A more modern name is the millidalton (mDa) since the ""unified atomic mass unit"" is more and more displaced by the unit dalton. (1 Da = 1 u) Since 1961 the unified atomic"
"for the same mass flow rate. For example, a mass flow rate of 1,000 kg/h of air at 1 atmosphere of absolute pressure is 455 SCFM when defined at but 481 SCFM when defined at . In countries using the SI metric system of units, the term ""normal cubic metre"" (Nm) is very often used to denote gas volumes at some normalized or standard condition. Again, as noted above, there is no universally accepted set of normalized or standard conditions. Actual cubic foot per minute (ACFM) is the volume of gas flowing anywhere in a system, taking into account its"
"volume fraction (percentage by volume, vol%) are others. For elemental analysis, mass fraction (or ""mass percent composition"") can also refer to the ratio of the mass of one element to the total mass of a compound. It can be calculated for any compound using its empirical formula or its chemical formula. ""Percent concentration"" does not refer to this quantity. This improper name persists, especially in elementary textbooks. In biology, the unit ""%"" is sometimes (incorrectly) used to denote mass concentration, also called ""mass/volume percentage."" A solution with 1 g of solute dissolved in a final volume of 100 mL of"
"is an ""extensive property"". The symbol used to represent density in equations is ρ (rho) with SI units of kilograms per cubic meter. This term is the reciprocal of specific volume. Since gas molecules can move freely within a container, their mass is normally characterized by density. Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as compressibility. Like"
"The amount of energy that can be stored in a capacitor per mass of that capacitor is called its specific energy. Specific energy is measured gravimetrically (per unit of mass) in watt-hours per kilogram (Wh/kg). The amount of energy can be stored in a capacitor per volume of that capacitor is called its energy density. Energy density is measured volumetrically (per unit of volume) in watt-hours per litre (Wh/l). Commercial energy density (also called volumetric specific energy in some literature) varies widely but in general range from around 5 to . Units of liters and dm can be used interchangeably."
"pressure, because the resulting numbers are extremely large (on the order of 10). Using the number density of an ideal gas at and as a yardstick: is often introduced as a unit of number density, for any substances at any conditions (not necessarily limited to an ideal gas at and ). Using the number density as a function of spatial coordinates, the total number of objects ""N"" in the entire volume ""V"" can be calculated as where d""V"" = d""x"" d""y"" d""z"" is a volume element. If each object possesses the same mass ""m"", the total mass ""m"" of all"
"where i.e. internal energy per unit volume equals mass density times the sum of: proper energy per unit mass, kinetic energy per unit mass, and gravitational potential energy per unit mass. i.e. change in heat per unit volume (negative divergence of heat flow) equals the divergence of heat conductivity times the gradient of the temperature. i.e. divergence of work done against stress equals flow of material times divergence of stress plus stress times divergence of material flow. i.e. stress times divergence of material flow equals deviatoric stress tensor times divergence of material flow minus pressure times material flow. i.e. enthalpy"