HOME TheInfoList picture info OED2 Volumes 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 circular shapes can be easily calculated using arithmetic formulas. Volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shape's boundary [...More Info...]       [...Related Items...] Volume (other) Volume is the quantity of space an object occupies in a 3D space. Volume may also refer to: picture info Cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices. The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is dual to the octahedron [...More Info...]       [...Related Items...] Invariant (mathematics) In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually indicated by the context in which the term is used. For example, the area of a triangle is an invariant with respect to isometries of the Euclidean plane. The phrases "invariant under" and "invariant to" a transformation are both used. More generally, an invariant with respect to an equivalence relation is a property that is constant on each equivalence class. Invariants are used in diverse areas of mathematics such as geometry, topology and algebra. Some important classes of transformations are defined by an invariant they leave unchanged, for example conformal maps are defined as transformations of the plane that preserve angles [...More Info...]       [...Related Items...] picture info Thermodynamics Thermodynamics is a branch of physics concerned with heat and temperature and their relation to other forms of energy and work. The behavior of these quantities is governed by the four laws of thermodynamics, irrespective of the composition or specific properties of the material or system in question. The laws of thermodynamics are explained in terms of microscopic constituents by statistical mechanics [...More Info...]       [...Related Items...] picture info Gas Volume In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit of mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature [...More Info...]       [...Related Items...] picture info Conjugate Variables (thermodynamics) In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature and entropy or pressure and volume. In fact, all thermodynamic potentials are expressed in terms of conjugate pairs. The product of two quantities that are conjugate has units of energy or sometimes power. For a mechanical system, a small increment of energy is the product of a force times a small displacement. A similar situation exists in thermodynamics. An increment in the energy of a thermodynamic system can be expressed as the sum of the products of certain generalized "forces" that, when unbalanced, cause certain generalized "displacements", and the product of the two is the energy transferred as a result. These forces and their associated displacements are called conjugate variables. The thermodynamic force is always an intensive variable and the displacement is always an extensive variable, yielding an extensive energy transfer [...More Info...]       [...Related Items...] picture info Pressure Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled gage pressure) is the pressure relative to the ambient pressure. Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre; similarly, the pound-force per square inch (psi) is the traditional unit of pressure in the imperial and US customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as ​1--->⁄760 of this [...More Info...]       [...Related Items...] picture info Gill (unit) The gill (pronounced picture info Pint The pint (/ˈpaɪnt/, ; symbol pt, sometimes abbreviated as "p") is a unit of volume or capacity in both the imperial and United States customary measurement systems. In both of those systems it is traditionally one-eighth of a gallon. The British Imperial pint is about 20% larger than the American pint since the two systems are not compatible. Almost all other countries have standardized on the metric system, so the size of what may be called a pint varies depending on local custom. Pints are still commonly used alongside metric labeling for milk in the United Kingdom (2018) The Imperial pint (≈ 568 mL) is used in the United Kingdom and Ireland and to a limited extent in Commonwealth nations. In the United States, two pints are used: a liquid pint (≈ 473 mL) and a less-common dry pint (≈ 551 mL) [...More Info...]       [...Related Items...] picture info Quart The quart (abbreviation qt.) is an English unit of volume equal to a quarter gallon. It is divided into two pints or four cups. Historically, the exact size of the quart has varied with the different values of gallons over time and in reference to different commodities. Presently, three kinds of quarts remain in use: the liquid quart and dry quart of the US customary system and the imperial quart of the British imperial system [...More Info...]       [...Related Items...] picture info Gallon The gallon (/ˈɡælən/) is a unit of measurement for liquid capacity in both the US customary units and the British imperial systems of measurement [...More Info...]       [...Related Items...] picture info Length In geometric measurements, length is the most extended dimension of an object. In the International System of Quantities, length is any quantity with dimension distance. In other contexts, length is a measured dimension of an object. Length may be distinguished from height, which is vertical extent, and width or breadth, which are the distance from side to side, measuring across the object at right angles to the length. For example, it is possible to cut a length of wire shorter than the wire's width [...More Info...]       [...Related Items...] Volume Form In mathematics, a volume form on a differentiable manifold is a top-dimensional form (i.e., a differential form of top degree). Thus on a manifold M of dimension n, a volume form is an n-form, a section of the line bundle Ωn--->(M) = ⋀n--->(T∗--->M). A manifold admits a nonzero volume form if and only if it is orientable. An orientable manifold has infinitely many volume forms, since multiplying a volume form by a function yields another volume form. On non-orientable manifolds, one may instead define the weaker notion of a density. A volume form provides a means to define the integral of a function on a differentiable manifold. In other words, a volume form gives rise to a measure with respect to which functions can be integrated by the appropriate Lebesgue integral. The absolute value of a volume form is a volume element, which is also known variously as a twisted volume form or pseudo-volume form [...More Info...]       [...Related Items...] picture info Centimetre A centimetre (international spelling as used by the International Bureau of Weights and Measures; symbol cm) or centimeter (American spelling) is a unit of length in the metric system, equal to one hundredth of a metre, centi being the SI prefix for a factor of 1/100. The centimetre was the base unit of length in the now deprecated centimetre–gram–second (CGS) system of units. Though for many physical quantities, SI prefixes for factors of 103--->—like milli- and kilo-—are often preferred by technicians, the centimetre remains a practical unit of length for many everyday measurements [...More Info...]       [...Related Items...]