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Volume - Volume in thermodynamics

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. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law.

Volume - Volume in calculus

In calculus, a branch of mathematics, the volume of a region D in R 3 is given by a triple integral of the constant function f(x,y,z)=1 and is usually written as:

Volume - Volume in calculus

and the volume integral in spherical coordinates (using the convention for angles with \theta as the azimuth and \varphi measured from the polar axis; see more on conventions) has the form

Volume - Volume in calculus

The volume integral in cylindrical coordinates is

Volume fraction - Volume percent

The percentage by volume (vol%) is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and mole fraction (percentage by moles, mol%) are others.

Volume fraction - Volume percent

In the case of a mixture of ethanol and water, which are miscible in all proportions, the designation of solvent and solute is arbitrary. The volume of such a mixture is slightly less than the sum of the volumes of the components. Thus, by the above definition, the term "40% alcohol by volume" refers to a mixture of 40 volume units of ethanol with enough water to make a final volume of 100 units, rather than a mixture of 40 units of ethanol with 60 units of water.

Volume fraction - Volume percent

Volume percent is the concentration of a certain solute, measured by volume, in a solution. It has as a denominator the volume of the mixture itself, as usual for expressions of concentration, rather than the total of all the individual component's volumes prior to mixing:

Volume (thermodynamics) - Specific volume

The specific volume of a substance is equal to the reciprocal of its mass density. Specific volume may be expressed in, , , or. :

Volume (thermodynamics) - Partial volume

The partial volume of a particular gas is the volume which the gas would have if it alone occupied the volume, with unchanged pressure and temperature, and is useful in gas mixtures, e.g. air, to focus on one particular gas component, e.g. oxygen.

Volume fraction - Volume percent

Volume percent is usually used when the solution is made by mixing two fluids, such as liquids or gases. However, percentages are only additive for ideal gases.

Volume (thermodynamics) - Specific volume

Specific volume (\nu) is the volume occupied by a unit of mass of a material. In many cases the specific volume is a useful quantity to determine because, as an intensive property, it can be used to determine the complete state of a system in conjunction with another independent intensive variable. The specific volume also allows systems to be studied without reference to an exact operating volume, which may not be known (nor significant) at some stages of analysis.

Volume (thermodynamics) - Specific volume

Specific volume may also refer to molar volume.

Volume rendering - Volume segmentation

Image segmentation is a manual or automatic procedure that can be used to section out large portions of the volume that one considers uninteresting before rendering, the amount of calculations that have to be made by ray casting or texture blending can be significantly reduced. This reduction can be as much as from O(n) to O(log n) for n sequentially indexed voxels. Volume segmentation also has significant performance benefits for other ray tracing algorithms. Volume segmentation can subsequently be used to highlight structures of interest.

Volume - Volume in differential geometry

In differential geometry, a branch of mathematics, a volume form on a differentiable manifold is a differential form of top degree (i.e., whose degree is equal to the dimension of the manifold) that is nowhere equal to zero. A manifold has a volume form if and only if it is orientable. An orientable manifold has infinitely many volume forms, since multiplying a volume form by a non-vanishing function yields another volume form. On non-orientable manifolds, one may instead define the weaker notion of a density. Integrating the volume form gives the volume of the manifold according to that form.

Volume - Volume in differential geometry

An oriented pseudo-Riemannian manifold has a natural volume form. In local coordinates, it can be expressed as :

Volume (computing) - Volume label and volume serial number

A volume label is the name given to a specific volume in a filesystem. In the FAT filesystem, the volume label was traditionally restricted to 11 characters (reflecting the 8.3 restrictions, but not divided into name and extension fields) even when long file name was enabled, stored as an entry within a disk's root directory with a special volume-label attribute bit set, and also copied to an 11-byte field within the Extended BIOS Parameter Block of the disk's boot sector. The label is always stored as uppercase in FAT and VFAT filesystems, and cannot contain special characters that are also disallowed for regular filenames. In the NTFS filesystem, the length of its volume label is restricted to 32 characters, and can include lowercase characters and even Unicode. The label command is used to change the label in DOS, Windows, and OS/2. For GUI systems like Windows Explorer, can be pressed while the volume is highlighted, or a right-click on the name will bring up a context menu that allows it to be renamed, either of which is the same process as for renaming a file. Changing the label in Windows will also change the volume creation timestamp to the current date and time for FAT filesystems. NTFS partitions have the System Volume Information directory, whose creation timestamp is set when Windows creates the partition, or when it first recognizes a repartitioning (the creation of a new volume) by a separate disk utility.

Volume (computing) - Volume label and volume serial number

In contrast to the label, the volume serial number is generally unique and is not normally changed by the user, and thus acts as a more consistent and reliable identifier of when a volume has been changed (as when a disk is removed and another inserted). Disk formatting changes the serial number, but relabeling does not. The vol command can be used from the command line to display the current label and serial number of a volume.

Logical volume management - Hybrid volume

A hybrid volume is any volume that intentionally and opaquely makes use of two separate physical volumes. For instance, a workload may consist of random seeks so an SSD may be used to permanently store frequently used or recently written data, while using higher-capacity rotational magnetic media for long-term storage of rarely needed data. On Linux, bcache or dm-cache may be used for this purpose, while Fusion Drive may be used on OS X. ZFS also implements this functionality at the file system level, by allowing administrators to configure multi-level read/write caching.

Volume form - Riemannian volume form

Any oriented pseudo-Riemannian (including Riemannian) manifold has a natural volume form. In local coordinates, it can be expressed as :where the dx^i are 1-forms that form a positively oriented basis for the cotangent bundle of the manifold. Here, |g| is the absolute value of the determinant of the matrix representation of the metric tensor on the manifold.

Volume form - Riemannian volume form

The volume form is denoted variously by