## Angular acceleration

**SI Base Unit:**Radian per second squared**Units:**Radian per second squared

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**SI Base Unit:**Radian per second squared**Units:**Radian per second squared

Angular acceleration is the rate of change of angular velocity. In SI units, it is measured in radians per second squared (rad/s), and is usually denoted by the Greek letter alpha (α).
The angular acceleration can be defined as either:
where is the angular velocity, is the linear tangential acceleration, and r(usually defined as the radius of the circular path of which a point moving along) is the distance from the origin of the coordinate system that defines and to the point of interest.
For two-dimensional rotational motion, Newton's second law can be adapted to describe the relation between torque and angular acceleration:
where is the total torque exerted on the body, and is the mass moment of inertia of the body.
For all constant values of the torque, , of an object, the angular acceleration will also be constant. For this special case of constant angular acceleration, the above equation will produce a definitive, constant value for the angular acceleration:
For any non-constant torque, the angular acceleration of an object will change with time. The equation becomes a differential equation instead of a constant value. This differential equation is known as the equation

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**SI Base Unit:**Cubic metre per mole**Units:**Cubic metre per mole

The molar volume, symbol Vm, is the volume occupied by one mole of a substance (chemical element or chemical compound) at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ). It has the SI unit cubic metres per mole (m/mol), although it is more practical to use the units cubic decimetres per mole (dm/mol) for gases and cubic centimetres per mole (cm/mol) for liquids and solids.
The molar volume of a substance can be found by measuring its molar mass and density then applying the relation
If the sample is a mixture containing N components, the molar volume is calculated using:
For ideal gases, the molar volume is given by the ideal gas equation: this is a good approximation for many common gases at standard temperature and pressure. For crystalline solids, the molar volume can be measured by X-ray crystallography.
The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas:
Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is known to the same precision as the gas constant: R = 8.314 4621(75) J mol K, that is a relative standard uncertainty of

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**SI Base Unit:**Joule per kilogram per kelvin**Units:**Joule per kilogram per kelvin

Specific heat capacity (often shortened to specific heat) is the measure of heat or thermal energy required to increase the temperature of a unit quantity of a substance by one unit. For example, at a temperature of 15 °C, the heat required to raise the temperature of 1 kg of water by 1 K (equivalent to 1 °C) is 4186 joules, meaning that the specific heat of water is 4.186 kJ·kg·K. This measure was originally determined by mechanical means.
More heat is required to increase the temperature of a substance with high specific heat capacity than one with low specific heat capacity. For instance, eight times the energy is required to increase the temperature of a magnesium ingot (1.030 kJ·kg·K at 25 °C) as is required for a lead ingot (130 J·kg·K at 25 °C) of the same mass. The specific heat capacity of virtually any substance can be measured, including chemical elements, compounds, alloys, solutions, and composites. The term originated primarily through the work of 18th-century medical doctor and professor of Medicine at Glasgow University, Joseph Black, who conducted various measurements and used the phrase capacity for heat.
Temperature is the result of the average total kinetic

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**SI Base Unit:**Watt per meter per kelvin**Units:**Watt per meter per kelvin

Thermal resistance is a heat property and a measure of a temperature difference by which an object or material resists a heat flow (heat per time unit or thermal resistance). Thermal resistance is the reciprocal of thermal conductance.
Absolute thermal resistance is the temperature difference across a structure when a unit of heat energy flows through it in unit time. It is the reciprocal of thermal conductance. The SI units of thermal resistance are kelvins per watt or the equivalent degrees Celsius per watt (the two are the same since as intervals 1 K = 1 °C).
The thermal resistance of materials is of great interest to electronic engineers because most electrical components generate heat and need to be cooled. Electronic components malfunction or fail if they overheat, and some parts routinely need measures taken in the design stage to prevent this.
The heat flow can be modelled by analogy to an electrical circuit where heat flow is represented by current, temperatures are represented by voltages, heat sources are represented by constant current sources, absolute thermal resistances are represented by resistors and thermal capacitances by capacitors.
The diagram shows an

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**Instruments:**Hygrometer

Relative humidity is the amount of water vapor in a mixture of air and water vapor. It is defined as the ratio of the partial pressure of water vapor in an air-water mixture to the saturated vapor pressure of water at a prescribed temperature. The relative humidity of air depends not only on temperature but also on the pressure of the system of interest.
The relative humidity of an air-water mixture is defined as the ratio of the partial pressure of water vapor (H2O) in the mixture to the saturated vapor pressure of water at a prescribed temperature.
Relative humidity is normally expressed as a percentage and is calculated by using the following equation:
The humidity of an air-water vapor mixture is determined through the use of psychrometric charts if both the dry bulb temperature (T) and the wet bulb temperature (Tw) of the mixture are known. These quantities are readily estimated by using a sling psychrometer.
There are several empirical correlations that can be used to estimate the saturated vapor pressure of water vapor as a function of temperature. The Antoine equation is among the least complex of these formulas, having only three parameters (A, B, and C). Other

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**Instruments:**Hydrometer

Specific gravity is the ratio of the density (mass of a unit volume) of a substance to the density (mass of the same unit volume) of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance is nearly always water for liquids or air for gases. Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 atm equal to 101.325 kPa. Temperatures for both sample and reference vary from industry to industry. In British brewing practice the specific gravity as specified above is multiplied by 1000. Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, hydrocarbons, sugar solutions (syrups, juices, honeys, brewers wort, must etc.) and acids.
Specific gravity, as it is the ratio of densities, is a dimensionless quantity. Specific gravity varies with temperature; reference and sample must be compared at the same temperature, or corrected to a standard reference temperature. Substances with a specific

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**SI Base Unit:**Mole per cubic metre**Units:**Mole per cubic metre

In chemistry, the molar concentration, is defined as the amount of a constituent divided by the volume of the mixture :
It is also called molarity, amount-of-substance concentration, amount concentration, substance concentration, or simply concentration. The volume in the definition refers to the volume of the solution, not the volume of the solvent. One litre of a solution usually contains either slightly more or slightly less than 1 litre of solvent because the process of dissolution causes volume of liquid to increase or decrease.
The SI unit is mol/m. However, more commonly the unit mol/L is used. A solution of concentration 1 mol/L is also denoted as "1 molar" (1 M).
An SI prefix is often used to denote concentrations. Commonly used units are listed in the table hereafter:
The conversion to number concentration is given by:
where is the Avogadro constant, approximately 6.022×10 mol.
The conversion to mass concentration is given by:
where is the molar mass of constituent .
The conversion to mole fraction is given by:
where is the average molar mass of the solution and is the density of the solution.
The conversion to mass fraction is given by:
The conversion to

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**SI Base Unit:**Candela**Units:**Candela

In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.
Photometry deals with the measurement of visible light as perceived by human eyes. The human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions (photopic vision), the eye is most sensitive to greenish-yellow light at 555 nm. Light with the same radiant intensity at other wavelengths has a lower luminous intensity. The curve which measures the response of the human eye to light is a defined standard, known as the luminosity function. This curve, denoted V(λ) or , is based on an average of widely differing experimental data from scientists using different measurement techniques. For instance, the measured responses of the eye to violet light varied by a factor of ten.
Luminous intensity should not be confused with another photometric unit, luminous flux,

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**SI Base Unit:**Coulomb per cubic metre**Units:**Coulomb per cubic metre

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**SI Base Unit:**Pascal second**Units:**Pascal second

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress. In everyday terms (and for fluids only), viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement (fluidity).
Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction. For example, high-viscosity felsic magma will create a tall, steep stratovolcano, because it cannot flow far before it cools, while low-viscosity mafic lava will create a wide, shallow-sloped shield volcano.
With the exception of superfluids, all real fluids have some resistance to stress and therefore are viscous. A fluid which has no resistance to shear stress is known as an ideal fluid or inviscid fluid. In common usage, a liquid with the viscosity less than water is known as a mobile liquid, while a substance with a viscosity substantially greater than water is simply called a viscous liquid.
The study of flowing matter is known as rheology, which includes viscosity and related

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**SI Base Unit:**Volt**Units:**Volt

In the physics of electrical circuits, the term potential difference or p.d. is sometimes used as an old-fashioned synonym for the modern quantity known as "the voltage (difference) between two positions in an electrical circuit". Following the discovery of the electron by J.J. Thomson in 1897, and later discoveries about electron behaviour and the role of electrons in the conduction of electricity in metals, it is now known that a "voltage difference" (as measured with a voltmeter) is not the same scientific quantity as the pre-atomic-era physical quantity "electric potential difference" (discussed, for example, by Maxwell in the 1891 edition of textbook. A treatise on electricity and magnetism (Vol. 1). Oxford: Clarendon. first printed 1891, reprinted 1998. ISBN 0-19-850373-3. In the context of electrical circuits, use of the term "potential difference" as a synonym for voltage (difference) is dropping out of use. This may be partly because science has no name (other than voltage) for the potential concerned, partly because of the possibility of confusion between the terms "potential difference" and "electric potential difference", which nowadays refer to different physical

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**Instruments:**Anemometer

Wind speed, or wind velocity, is a fundamental atmospheric rate.
Wind speed affects weather forecasting, aircraft and maritime operations, construction projects, growth and metabolism rate of many plant species, and countless other implications.
Wind speed is now commonly measured with an anemometer but can also be classified using the older Beaufort scale which is based on people's observation of specifically defined wind effects.
Wind speed is affected by a number of factors and situations, operating on varying scales (from micro to macro scales). These include the pressure gradient, Rossby waves and jet streams, and local weather conditions. There are also links to be found between wind speed and wind direction, notably with the pressure gradient and surfaces over which the air is found.
Pressure gradient is a term to describe the difference in air pressure between two points in the atmosphere or on the surface of the Earth. It is vital to wind speed, because the greater the difference in pressure, the faster the wind flows (from the high to low pressure) to balance out the variation. The pressure gradient, when combined with the Coriolis Effect and friction, also influences

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**SI Base Unit:**Ampere per square metre**Units:**Ampere per square metre

In physics, current density in general is a measure of the density of flow of a conserved charge, in other words flux of the charge (sometimes used synonymously). As such the term "current density" can also be applied to other conserved quantities, like mass, energy, chemical concentration, etc.
In the context of electromagnetism, and related fields in solid state physics, condensed matter physics etc., the charge is electric charge, in which case the associated current density is the electric current per unit area of cross section. It is defined as a vector whose magnitude is the electric current per cross-sectional area. In SI units, the electric current density is measured in amperes per square metre.
Electric current density J is simply the electric current I (SI unit: A) per unit area A (SI unit: m). Its magnitude is given by the limit:
For current density as a vector J, the surface integral over a surface S, followed by an integral over the time duration t1 to t2, gives the total amount of charge flowing through the surface in that time (t2 − t1):
The area required to calculate the flux is real or imaginary, flat or curved, either as a cross-sectional area or a surface. For

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**SI Base Unit:**Radian per second**Units:**Radian per second

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector is sometimes used as a synonym for the vector quantity angular velocity.
One revolution is equal to 2π radians, hence
where
In SI units, angular frequency is normally presented in radians per second, even when it does not express a rotational value. From the perspective of dimensional analysis, the unit Hertz (Hz) is also correct, but in practice it is only used for ordinary frequency f, and almost never for ω. This convention helps avoid confusion.
In digital signal processing, the angular frequency may be normalized by the sampling rate, yielding the normalized frequency.
For example
where x is displacement from an equilibrium position.
Using 'ordinary' revolutions-per-second frequency, this equation would be
Another often encountered expression when dealing with small oscillations or where damping is negligible is:
where
This is referred to as the natural

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**SI Base Unit:**Hertz**Units:**Hertz

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example, if a newborn baby's heart beats at a frequency of 120 times a minute, its period (the interval between beats) is half a second.
For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu).
In SI units, the unit of frequency is the hertz (Hz), named after the German physicist Heinrich Hertz: 1 Hz means that an event repeats once per second. A previous name for this unit was cycles per second.
A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated RPM. 60 RPM equals one hertz.
The period, usually denoted by T, is the length of time taken by one cycle, and is the reciprocal of the frequency f:
The SI unit for period is the second.
Calculating the frequency of a repeating event

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**SI Base Unit:**Kelvin**Units:**Kelvin**Instruments:**Thermometer

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot. When a heat transfer path between them is open, heat spontaneously flows from bodies of a higher temperature to bodies of lower temperature. The flow rate increases with the temperature difference, while no heat will be exchanged between bodies of the same temperature, which are then said to be in "thermal equilibrium".
In thermodynamics, in a system of which the entropy is considered as an independent externally controlled variable, absolute, or thermodynamic, temperature is defined as the derivative of the internal energy with respect to the entropy.
In an ideal gas, the constituent molecules do not show internal excitations. They move according to Newton's first law of motion, freely and independently of one another, except during collisions that last for negligibly short times. The temperature of an ideal gas is proportional to the mean translational kinetic energy of its molecules.
Quantitatively, temperature is measured with thermometers, which may be

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**SI Base Unit:**Coulomb per square metre**Units:**Coulomb per square metre

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**SI Base Unit:**Candela per square metre**Units:**Candela per square metre

Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square metre (cd/m). A non-SI term for the same unit is the "nit". The CGS unit of luminance is the stilb, which is equal to one candela per square centimetre or 10 kcd/m.
Luminance is often used to characterize emission or reflection from flat, diffuse surfaces. The luminance indicates how much luminous power will be detected by an eye looking at the surface from a particular angle of view. Luminance is thus an indicator of how bright the surface will appear. In this case, the solid angle of interest is the solid angle subtended by the eye's pupil. Luminance is used in the video industry to characterize the brightness of displays. A typical computer display emits between 50 and 300 cd/m. The sun has luminance of about 1.6×10 cd/m at noon.
Luminance is invariant in geometric optics. This means that for an ideal optical system, the luminance at the output is the same as the input luminance. For real,

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**SI Base Unit:**Joule per kilogram**Units:**Joule per kilogram

Specific energy is defined as the energy per unit mass. Common metric units are J/kg. It is an intensive property. Contrast this with energy, which is an extensive property. There are two main types of specific energy: potential energy and specific kinetic energy. Others are the gray and sievert, measures for the absorption of radiation. The concept of specific energy applies to a particular or theoretical way of extracting useful energy from the material considered that is usually implied by context.
Thermodynamic properties related to specific energy include specific internal energy, specific enthalpy, specific Gibbs free energy, and specific Helmholtz free energy, all of which use units of energy per mass such as J/kg. These intensive properties are each symbolized by using the lower case letter of the symbol for the corresponding extensive property, which is symbolized by a capital letter. For example, the extensive thermodynamic property enthalpy is symbolized by H; specific enthalpy is symbolized by h.
If a defined chemical compound is used which has a definite molar mass, such intensive thermodynamic properties can be expressed on a per mole basis instead of a per mass

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**Instruments:**Gravimeter

In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). In its original concept, gravity was a force between point masses. Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms of a field model, rather than a point attraction.
In a field model, rather than two particles attracting each other, the particles distort spacetime via their mass, and this distortion is what is perceived and measured as a "force". In such a model one states that matter moves in certain ways in response to the curvature of spacetime, and that there is either no gravitational force, or that gravity is a fictitious force.
In classical mechanics as in physics, the field is not real, but merely a model describing the effects of gravity. The field can be determined using Newton's law of universal gravitation. Determined in this way, the gravitational

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**SI Base Unit:**Watt per steradian**Units:**Watt per steradian

In radiometry, radiant intensity is a measure of the intensity of electromagnetic radiation. It is defined as power per unit solid angle. The SI unit of radiant intensity is watts per steradian (W·sr). Radiant intensity is distinct from irradiance and radiant exitance, which are often called intensity in branches of physics other than radiometry.

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**Instruments:**Sphygmomanometer

Blood pressure (BP), sometimes referred to as arterial blood pressure, is the pressure exerted by circulating blood upon the walls of blood vessels, and is one of the principal vital signs. When used without further specification, "blood pressure" usually refers to the arterial pressure of the systemic circulation. During each heartbeat, blood pressure varies between a maximum (systolic) and a minimum (diastolic) pressure. The blood pressure in the circulation is principally due to the pumping action of the heart. Differences in mean blood pressure are responsible for blood flow from one location to another in the circulation. The rate of mean blood flow depends on the resistance to flow presented by the blood vessels. Mean blood pressure decreases as the circulating blood moves away from the heart through arteries and capillaries due to viscous losses of energy. Mean blood pressure drops over the whole circulation, although most of the fall occurs along the small arteries and arterioles. Gravity affects blood pressure via hydrostatic forces (e.g., during standing) and valves in veins, breathing, and pumping from contraction of skeletal muscles also influence blood pressure in

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**SI Base Unit:**Ohm**Units:**Ohm

The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical notion of friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).
An object of uniform cross section has a resistance proportional to its resistivity and length and inversely proportional to its cross-sectional area. All materials show some resistance, except for superconductors, which have a resistance of zero.
The resistance (R) of an object is defined as the ratio of voltage across it (V) to current through it (I), while the conductance (G) is the inverse:
For a wide variety of materials and conditions, V and I are directly proportional to each other, and therefore R and G are constant (although they can depend on other factors like temperature or strain). This proportionality is called Ohm's law, and materials that satisfy it are called "Ohmic" materials.
In other cases, such as a diode or battery, V and I are not directly

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**SI Base Unit:**Newton**Units:**Newton

In physics, a force is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. It is measured with the SI unit of newtons and represented by the symbol F. In other words, a force is that which can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. Force can also be described by intuitive concepts such as a push or pull. A force has both magnitude and direction, making it a vector quantity.
The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes. This law is further given to mean that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional the mass of the object. As a formula, this is expressed as:
Related concepts to force include: thrust, which increases the velocity of an object; drag, which decreases the velocity of an object; and torque which produces changes in rotational speed of an object.

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**SI Base Unit:**Coulomb per kilogram**Units:**Coulomb per kilogram

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**Units:**International unit

In pharmacology, biological activity or pharmacological activity describes the beneficial or adverse effects of a drug on living matter. When a drug is a complex chemical mixture, this activity is exerted by the substance's active ingredient or pharmacophore but can be modified by the other constituents. Activity is generally dosage-dependent and it is not uncommon to have effects ranging from beneficial to adverse for one substance when going from low to high doses. Activity depends critically on fulfillment of the ADME criteria.
Whereas a material is considered bioactive if it has interaction with or effect on any cell tissue in the human body, pharmacological activity is usually taken to describe beneficial effects, i.e. the effects of drug candidates. The main kind of biological activity is a substance's toxicity.
In the study of biomineralisation, bioactivity is often meant as the formation of calcium phosphate deposits on the surface of objects placed in simulated body fluid, a buffer solution with ion content similar to blood.

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**SI Base Unit:**Weber**Units:**Weber

In physics, specifically electromagnetism, the magnetic flux (often denoted Φ or ΦB) through a surface is the component of the B field passing through that surface. The SI unit of magnetic flux is the weber (Wb) (in derived units: volt-seconds), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics that evaluates the change of voltage in the measuring coils to calculate the magnetic flux.
The magnetic interaction is described in terms of a vector field, where each point in space (and time) is associated with a vector that determines what force a moving charge would experience at that point (see Lorentz force). Since a vector field is quite difficult to visualize at first, in elementary physics one may instead visualize this field with field lines. The magnetic flux through some surface, in this simplified picture, is proportional to the number of field lines passing through that surface (in some contexts, the flux may be defined to be precisely the number of field lines passing through that surface; although technically misleading, this distinction is not important). Note that the magnetic flux is the net

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**SI Base Unit:**Second**Units:**Second**Instruments:**Clock

Time is a dimension in which events can be ordered from the past through the present into the future, and also the measure of durations of events and the intervals between them. Time has long been a major subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, music, dance, and the live theater all incorporate some notion of time into their respective measuring systems. Some simple, relatively uncontroversial definitions of time include "time is what clocks measure" and "time is what keeps everything from happening at once".
Two contrasting viewpoints on time divide many prominent philosophers. One view is that time is part of the fundamental structure of the universe—a dimension independent of events, in which events occur in sequence. Sir Isaac Newton subscribed to this realist view, and hence it is sometimes referred to as Newtonian time. The opposing view is that time does not refer to any kind of "container" that events and objects "move through", nor to any entity that "flows", but that it is

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**SI Base Unit:**Gray**Units:**Gray

Absorbed dose (also known as total ionizing dose, TID) is a measure of the energy deposited in a medium by ionizing radiation per unit mass. It is equal to the energy deposited per unit mass of medium, which may be measured as joules per kilogram and represented by the equivalent SI unit, gray (Gy), or the antiquated CGS units, rad and rep. The absorbed dose depends not only on the incident radiation but also on the absorbing material: a soft X-ray beam may deposit four times more dose in bone than in air, or none at all in a vacuum.
Absorbed dose is used to rate the survivability of electronic components to nuclear environments, to gauge the risk of acute radiation syndrome, and as an intermediate figure in dosimetry calculations. The absorbed dose alone is not an adequate indicator of the likely health effects in humans. Consideration must also be given to the type of radiation, the dose rate, the affected tissues, and other factors. For example, 1 Gy of alpha radiation would carry a much greater risk of cancer than 1 Gy of photon radiation. Further calculation can be performed to find the equivalent dose for whole body external exposure, the effective dose for partial body

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The litre (American spelling: liter; SI symbol L or l) is a non-SI metric system unit of volume equal to 1 cubic decimetre (dm), 1,000 cubic centimetres (cm) or 1/1,000 cubic metre. If the lower case L is used as the symbol, it is sometimes rendered as a cursive ℓ to help distinguish it from the capital "I", although this usage has no official approval by any international bureau.
The word litre is derived from an older French unit, the litron, whose name came from Greek via Latin. The original French metric system used the litre as a base unit, and it has been used in several subsequent versions of the metric system and is accepted for use with the SI, although not an official SI unit — the SI unit of volume is the cubic metre (m). The spelling of the word used by the International Bureau of Weights and Measures is "litre" and this is also the usual one in most English-speaking countries, but in American English the official spelling is "liter".
One litre of liquid water has a mass of almost exactly one kilogram, due to the gram being defined in 1795 as one cubic centimetre of water at the temperature of melting ice.
A litre is defined as a special name for a cubic decimetre or 10

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**Units:**Metre squared per second

In physics, angular momentum, moment of momentum, or rotational momentum is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis. The angular momentum of a system of particles (e.g. a rigid body) is the sum of angular momenta of the individual particles. For a rigid body rotating around an axis of symmetry (e.g. the blades of a ceiling fan), the angular momentum can be expressed as the product of the body's moment of inertia, I, (i.e. a measure of an object's resistance to changes in its rotation rate) and its angular velocity ω:
In this way, angular momentum is sometimes described as the rotational analog of linear momentum.
For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum, mv, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is
Angular momentum is conserved in a system where there is no net external torque, and its conservation helps

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**SI Base Unit:**Cubic metres per second**Units:**Cubic metres per second

In physics and engineering, in particular fluid dynamics and hydrometry, the volumetric flow rate, (also known as volume flow rate, rate of fluid flow or volume velocity) is the volume of fluid which passes through a given surface per unit time. The SI unit is m s (cubic meters per second). In US Customary Units and British Imperial Units, volumetric flow rate is often expressed as ft/s (cubic feet per second). It is usually represented by the symbol Q.
Volumetric flow rate should not be confused with volumetric flux, as defined by Darcy's law and represented by the symbol q, with units of m/(m s), that is, m s. The integration of a flux over an area gives the volumetric flow rate.
Volume flow rate is defined by the limit:
i.e. the flow of volume of fluid V through a surface per unit time t.
Since this is only the time derivative of volume, a scalar quantity, the volumetric flow rate is also a scalar quantity. The change in volume is the amount that flows after crossing the boundary for some time duration, not simply the initial amount of volume at the boundary minus the final amount at the boundary, since the change in volume flowing through the area would be zero for steady flow

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**SI Base Unit:**Kilogram per cubic metre**Units:**Kilogram per cubic metre

The mass density or density of a material is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho). 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 also defined as its weight per unit volume, although this quantity is more properly called specific weight.
Different materials usually have different densities, so density is an important concept regarding buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but not the densest materials.
Less dense fluids float on more dense fluids if they do not mix. This concept can be extended, with some care, to less dense solids floating on more dense fluids. If the average density (including any air below the waterline) of an object is less than water it will float in water and if it is more than water's it will sink in water.
In some cases density is expressed as the dimensionless quantities specific gravity or relative density, in which case it is expressed in

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**SI Base Unit:**Coulomb**Units:**Coulomb

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. There exist two types of electric charges, called positive and negative. Positively-charged substances are repelled from other positively-charged substances, but attracted to negatively-charged substances; negatively-charged substances are repelled from negative and attracted to positive. The SI unit of electric charge is the coulomb (C), although in electrical engineering it is also common to use the ampere-hour (Ah), and in chemistry it is common to use the elementary charge (e) as a unit. The symbol Q is often used to denote a charge. The study of how charged substances interact is classical electrodynamics, which is accurate insofar as quantum effects can be ignored.
The electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces (See also:

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**Units:**Star

A five-star scale for rating products, services, films, music, etc.

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**SI Base Unit:**Katal**Units:**Katal

Catalysis is the change in rate of a chemical reaction due to the participation of a substance called a catalyst. Unlike other reagents that participate in the chemical reaction, a catalyst is not consumed by the reaction itself. A catalyst may participate in multiple chemical transformations. Catalysts that speed the reaction are called positive catalysts. Substances that slow a catalyst's effect in a chemical reaction are called inhibitors. Substances that increase the activity of catalysts are called promoters, and substances that deactivate catalysts are called catalytic poisons.
Catalytic reactions have a lower rate-limiting free energy of activation than the corresponding uncatalyzed reaction, resulting in higher reaction rate at the same temperature. However, the mechanistic explanation of catalysis is complex. Catalysts may affect the reaction environment favorably, or bind to the reagents to polarize bonds, e.g. acid catalysts for reactions of carbonyl compounds, or form specific intermediates that are not produced naturally, such as osmate esters in osmium tetroxide-catalyzed dihydroxylation of alkenes, or cause lysis of reagents to reactive forms, such as atomic hydrogen

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**SI Base Unit:**Ampere**Units:**Ampere**Instruments:**Ammeter

Electric current is a flow of electric charge through a conductive medium.
In electric circuits this charge is often carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in a plasma.
The SI unit for measuring the rate of flow of electric charge is the ampere, which is charge flowing through some surface at the rate of one coulomb per second. Electric current is measured using an ammeter.
The conventional symbol for current is , which originates from the French phrase intensité de courant, or in English current intensity. This phrase is frequently used when discussing the value of an electric current, especially in older texts; modern practice often shortens this to simply current but current intensity is still used in many recent textbooks. The symbol was used by André-Marie Ampère, after whom the unit of electric current is named, in formulating the eponymous Ampère's force law which he discovered in 1820. The notation travelled from France to Britain, where it became standard, although at least one journal did not change from using to until 1896.
In metallic solids, electric charge flows by means of

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42

**SI Base Unit:**Joule per cubic metre**Units:**Joule per cubic metre

Energy density is the amount of energy stored in a given system or region of space per unit mass. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored. Quantified energy is energy that has some sort of, as the name suggests, quantified magnitude with related units.
For fuels, the energy per unit volume is sometimes a useful parameter. Comparing, for example, the effectiveness of hydrogen fuel to gasoline, hydrogen has a higher specific energy (energy per unit mass) than gasoline does, but, even in liquid form, a much lower volumetric energy density.
Energy per unit volume has the same physical units as pressure, and in many circumstances is an exact synonym: for example, the energy density of the magnetic field may be expressed as (and behaves as) a physical pressure, and the energy required to compress a compressed gas a little more may be determined by multiplying the difference between the gas pressure and the pressure outside by the change in volume. In short, pressure is a measure of the volumetric enthalpy of a system, that is, the enthalpy per unit volume. A pressure gradient has a

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**SI Base Unit:**Lumen**Units:**Lumen

In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of light emitted, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of light.
The SI unit of luminous flux is the lumen (lm). One lumen is defined as the luminous flux of light produced by a light source that emits one candela of luminous intensity over a solid angle of one steradian. In other systems of units, luminous flux may have units of power.
The luminous flux accounts for the sensitivity of the eye by weighting the power at each wavelength with the luminosity function, which represents the eye's response to different wavelengths. The luminous flux is a weighted sum of the power at all wavelengths in the visible band. Light outside the visible band does not contribute. The ratio of the total luminous flux to the radiant flux is called the luminous efficacy.
Luminous flux is often used as an objective measure of the useful power emitted by a light source, and is typically reported on the packaging for light bulbs, although it is not always prominent. Energy

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**SI Base Unit:**Becquerel**Units:**Becquerel

Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). There are many different types of radioactive decay (see table below). A decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide, transforms to an atom with a nucleus in a different state, or to a different nucleus containing different numbers of protons and neutrons. Either of these products is named the daughter nuclide. In some decays the parent and daughter are different chemical elements, and thus the decay process results in nuclear transmutation (creation of an atom of a new element).
The first decay processes to be discovered were alpha decay, beta decay, and gamma decay. Alpha decay occurs when the nucleus ejects an alpha particle (helium nucleus). This is the most common process of emitting nucleons, but in rarer types of decays, nuclei can eject protons, or specific nuclei of other elements (in the process called cluster decay). Beta decay occurs when the nucleus emits an electron or positron and a type of neutrino, in a process that changes a proton to a neutron or the other way

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45

**SI Base Unit:**Metre per second squared**Units:**Metre per second squared

In physics, acceleration is the rate at which the velocity of a body changes with time. In general, velocity and acceleration are vector quantities, with magnitude and direction, though in many cases only magnitude is considered (sometimes with negative values for deceleration). Acceleration is accompanied by a force, as described by Newton's Second Law; the force, as a vector, is the product of the mass of the object being accelerated and the acceleration (vector). The SI unit of acceleration is the meter per second squared (m/s).
For example, an object such as a car that starts from standstill, then travels in a straight line at increasing speed, is accelerating in the direction of travel. If the car changes direction at constant speedometer reading, there is strictly speaking an acceleration although it is often not so described; passengers in the car will experience a force pushing them back into their seats in linear acceleration, and a sideways force on changing direction. If the speed of the car decreases, it is usual and meaningful to speak of deceleration; mathematically it is acceleration in the opposite direction to that of motion.
Mathematically, instantaneous

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**SI Base Unit:**Watt**Units:**Watt

In physics, power is the rate at which energy is transferred, used, or transformed. The unit of power is the joule per second (J/s), known as the watt (in honor of James Watt, the eighteenth-century developer of the steam engine). For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit time.
Energy transfer can be used to do work, so power is also the rate at which this work is performed. The same amount of work is done when carrying a load up a flight of stairs whether the person carrying it walks or runs, but more power is expended during the running because the work is done in a shorter amount of time. The output power of an electric motor is the product of the torque the motor generates and the angular velocity of its output shaft. The power expended to move a vehicle is the product of the traction force of the wheels and the velocity of the vehicle.
The integral of power over time defines the work done. Because this integral depends on the trajectory of the point of application of the force and torque, this calculation of work

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**SI Base Unit:**Cubic metre**Units:**Cubic metre

Volume is the quantity of three-dimensional space enclosed by some closed boundary, 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. The volumes of more complicated shapes can be calculated by integral calculus if a formula exists for the shape's boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.
The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater

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**Units:**Scoville Unit

Pungency (pronounced /ˈpʌndʒənsi/) or, in some cases, Piquance (/ˈpikəns/), is the condition of having a strong, sharp smell or taste which is often so strong that it is unpleasant. Pungency is the technical term used by scientists to refer to the characteristic of food commonly referred to as spiciness or hotness and sometimes heat which is found in foods such as chili peppers.
Pungency is associated with the sense of taste, and in various Asian countries it has traditionally been considered a basic taste.
The terms "pungent" (/pʌndʒət/) and "pungency" are rarely used in colloquial speech but are preferred by scientists as they eliminate the potential ambiguity arising from use of the words "hot" and "spicy", which can also refer to temperature and the presence of spices, respectively.
For instance, a pumpkin pie can be both hot (out of the oven) and spicy (due to the common inclusion of spices such as cinnamon, nutmeg, allspice, mace, and cloves), but it is not pungent. (A food critic may nevertheless use the word "piquant" to describe such a pie, especially if it is exceptionally well seasoned.) Conversely, pure capsaicin is pungent, yet it is not naturally accompanied by a hot

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**SI Base Unit:**Square meter**Units:**Square meter

Area is a quantity that expresses the extent of a two-dimensional surface or shape, or planar lamina, in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).
The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.
There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is

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**SI Base Unit:**Reciprocal metre**Units:**Reciprocal metre

In the physical sciences, the wavenumber is a property of a wave, its spatial frequency, that is equal to the reciprocal of the wavelength. It is also the magnitude of the wave vector. Its usual symbols are , , σ or k, the first three used for one definition, the last for another. The wavenumber has dimensions of reciprocal length, so its SI unit is m and cgs unit cm (in this context formerly called the kayser, after Heinrich Kayser).
It can be defined as either
For electromagnetic radiation in vacuum, wavenumber is proportional to frequency and to photon energy. Because of this, wavenumbers are used as a unit of energy in spectroscopy. In the SI units, wavenumber is expressed in units of reciprocal meters (m), but in spectroscopy it is usual to give wavenumbers in reciprocal centimeters (cm). The angular wavenumber is expressed in radians per meter (rad·m).
In general, the angular wavenumber k, the magnitude of the wave vector, is given by
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and vp is the phase velocity of the wave.
For the special case of an electromagnetic wave in vacuum, where vp = c, k is given by
where E is

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53

**SI Base Unit:**Metre per second**Units:**Metre per second

In kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.
Like velocity, speed has the dimensions of a length divided by a time; the SI unit of speed is the meter per second, but the most usual unit of speed in everyday usage is the kilometer per hour or, in the USA and the UK, miles per hour. For air and marine travel the knot is commonly used.
The fastest possible speed at which energy or information can travel, according to special relativity, is the speed of light in a vacuum c = 299,792,458 meters per second, approximately 1079 million kilometers per hour (671,000,000 mph). Matter cannot quite reach the speed of light, as this would require an infinite amount of energy. In relativity physics, the concept of rapidity replaces the classical idea of speed. In day-to-day athletics, it is proper to say that a teenager can achieve at least 20 km/h (or 12.43 mph)

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**SI Base Unit:**Joule**Units:**Joule

In physics, energy (Ancient Greek: ἐνέργεια energeia "activity, operation") is an indirectly observed quantity that is often understood as the ability of a physical system to do work on other physical systems. Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.
The total energy contained in an object is identified with its mass, and energy cannot be created or destroyed. When matter (ordinary material particles) is changed into energy (such as energy of motion, or into radiation), the mass of the system does not change through the transformation process. However, there may be mechanistic limits as to how much of the matter in an object may be changed into other types of energy and thus into work, on other systems. Energy, like mass, is a scalar physical quantity. In the International System of Units (SI), energy is measured in joules, but in many fields other units, such as kilowatt-hours and kilocalories, are customary. All of these units translate to units of work, which is always defined in terms of forces and the

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56

**SI Base Unit:**Joule per mole per kelvin**Units:**Joule per mole per kelvin

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Albedo ( /ælˈbiːdoʊ/), or reflection coefficient, derived from Latin albedo "whiteness" (or reflected sunlight), in turn from albus "white", is the diffuse reflectivity or reflecting power of a surface. It is defined as the ratio of reflected radiation from the surface to incident radiation upon it. Being a dimensionless fraction, it may also be expressed as a percentage, and is measured on a scale from zero for no reflecting power of a perfectly black surface, to 1 for perfect reflection of a white surface.
Albedo depends on the frequency of the radiation. When quoted unqualified, it usually refers to some appropriate average across the spectrum of visible light. In general, the albedo depends on the directional distribution of incoming radiation. Exceptions are Lambertian surfaces, which scatter radiation in all directions according to a cosine function, so their albedo does not depend on the incident distribution. In practice, a bidirectional reflectance distribution function (BRDF) may be required to characterize the scattering properties of a surface accurately, although the albedo is a very useful first approximation.
The albedo is an important concept in climatology and

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58

**SI Base Unit:**Farad**Units:**Farad

Capacitance is the ability of a body to store an electrical charge. Any body or structure that is capable of being charged, either with static electricity or by an electric current exhibits capacitance. A common form of energy storage device is a parallel-plate capacitor. In a parallel plate capacitor, capacitance is directly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates. If the charges on the plates are +q and −q, and V gives the voltage between the plates, then the capacitance C is given by
The capacitance is a function only of the physical dimensions (geometry) of the conductors and the permittivity of the dielectric. It is independent of the potential difference between the conductors and the total charge on them.
The SI unit of capacitance is the farad (named after the English physicist Michael Faraday); a 1 farad capacitor when charged with 1 coulomb of electrical charge will have a potential difference of 1 volt between its plates. Historically, a farad was regarded as an inconveniently large unit, both electrically and physically. Its subdivisions were invariably used, namely the microfarad,

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59

**SI Base Unit:**Lux**Units:**Lux

In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelength-weighted by the luminosity function to correlate with human brightness perception. Similarly, luminous emittance is the luminous flux per unit area emitted from a surface. Luminous emittance is also known as luminous exitance.
In SI derived units these are measured in lux (lx) or lumens per square metre (cd·sr·m). In the CGS system, the unit of illuminance is the phot, which is equal to 10,000 lux. The foot-candle is a non-metric unit of illuminance that is used in photography.
Illuminance was formerly often called brightness, but this leads to confusion with other uses of the word. "Brightness" should never be used for quantitative description, but only for nonquantitative references to physiological sensations and perceptions of light.
The human eye is capable of seeing somewhat more than a 2 trillion-fold range: The presence of white objects is somewhat discernible under starlight, at 5×10 lux, while at the bright end, it is possible to read large text at 10 lux, or about 1,000 times that of direct

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60

**Units:**Percentage

Proportion is the relation between elements and a whole.
In architecture the whole is not just a building but the set and setting of the site. The things that make a building and its site "well shaped" include the orientation of the site and the buildings on it to the features of the grounds on which it is situated. Light, shade, wind, elevation, choice of materials, all should relate to a standard and say what is it that makes it what it is, and what is it that makes it not something else.
Vitruvius thought of proportion in terms of unit fractions such as those used in the Greek Orders of Architecture.
Scribes had been using unit fractions for their calculations at least since the time of the Egyptian Mathematical Leather Roll and Rhind Mathematical Papyrus in Egypt and the Epic of Gilgamesh in Mesopotamia.
One example of symmetry might be found in the inscription grids of the Egyptians which were based on parts of the body and their symmetrical relation to each other, fingers, palms, hands, feet, cubits, etc.; Multiples of body proportions would be found in the arrangements of fields and in the buildings people lived in.
A cubit could be divided into fingers, palms, hands and so

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61

**SI Base Unit:**Cubic metre per kilogram**Units:**Cubic metre per kilogram

In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass. It is the reciprocal of density and is an intrinsic property of matter:
Specific volume is commonly applied to:
Imagine a variable-volume, airtight chamber containing a certain number of atoms of oxygen gas. Consider the following four examples:
Specific volume is a property of materials, defined as the number of cubic meters occupied by one kilogram of a particular substance. The standard unit is the meter cubed per kilogram (m/kg or m·kg).
Sometimes specific volume is expressed in terms of the number of cubic centimeters occupied by one gram of a substance. In this case, the unit is the centimeter cubed per gram (cm/g or cm·g). To convert m/kg to cm/g, multiply by 1000; conversely, multiply by 0.001.
Specific volume is inversely proportional to density. If the density of a substance doubles, its specific volume, as expressed in the same base units, is cut in half. If the density drops to 1/10 its former value, the specific volume, as expressed in the same base units, increases by a factor of 10.

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**SI Base Unit:**Grams per joule**Units:**Grams per kilowatt-hour

Brake Specific Fuel Consumption (BSFC) is a measure of fuel efficiency within a shaft reciprocating engine. It is the rate of fuel consumption divided by the power produced. It may also be thought of as power-specific fuel consumption, for this reason. BSFC allows the fuel efficiency of different reciprocating engines to be directly compared.
To calculate this rate, use the formula
Where:
The resulting units of BSFC are grams per joule (g/J)
Commonly BSFC is expressed in units of grams per kilowatt-hour (g/(kW·h)). The conversion factor is as follows:
The conversion between metric and imperial units is:
To calculate the actual efficiency of an engine requires the energy density of the fuel being used.
Different fuels have different energy densities defined by the fuel's heating value. The lower heating value (LHV) is used for internal combustion engine efficiency calculations because the heat at temperatures below 150 °C (300 °F) cannot be put to use.
Some examples of lower heating values for vehicle fuels are:
Thus a diesel engine's efficiency = 1/(BSFC*0.0119531)
and a gasoline engine's efficiency = 1/(BSFC*0.0122225)
Any engine will have different BSFC values at different

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63

**SI Base Unit:**Henry**Units:**Henry

In electromagnetism and electronics, inductance is that property of a conductor by which a change in current in the conductor "induces" (creates) a voltage (electromotive force) in both the conductor itself (self-inductance) and any nearby conductors (mutual inductance). This effect derives from two fundamental observations of physics: First, that a steady current creates a steady magnetic field (Oersted's law) and second, that a time-varying magnetic field induces a voltage in a nearby conductor (Faraday's law of induction). From Lenz's law, in an electric circuit, a changing electric current through a circuit that has inductance induces a proportional voltage which opposes the change in current (self inductance). The varying field in this circuit may also induce an e.m.f. in a neighbouring circuit (mutual inductance).
The term 'inductance' was coined by Oliver Heaviside in February 1886. It is customary to use the symbol L for inductance, in honour of the physicist Heinrich Lenz. In the SI system the unit of inductance is the henry.
To add inductance to a circuit, electronic components called inductors are used, typically consisting of coils of wire to concentrate the magnetic

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**Instruments:**Declinometer

Magnetic declination is the angle between magnetic north (the direction the north end of a compass needle points) and true north. The declination is positive when the magnetic north is east of true north. The term magnetic variation is a synonym, and is more often used in navigation. Isogonic lines are where the declination has the same value, and the lines where the declination is zero are called agonic lines.
Somewhat more formally, Bowditch defines variation as “the angle between the magnetic and geographic meridians at any place, expressed in degrees and minutes east or west to indicate the direction of magnetic north from true north. The angle between magnetic and grid meridians is called grid magnetic angle, grid variation, or grivation. Called magnetic variation when a distinction is needed to prevent possible ambiguity. Also called magnetic declination.”
Magnetic declination varies both from place to place and with the passage of time. As a traveller cruises the east coast of the United States, for example, the declination varies from 20 degrees west (in Maine) to zero (in Florida), to 10 degrees east (in Texas), meaning a compass adjusted at the beginning of the journey

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66

**SI Base Unit:**Joule per kelvin**Units:**Joule per kelvin

Heat capacity (usually denoted by a capital C, often with subscripts), or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount. In the International System of Units (SI), heat capacity is expressed in units of joule(s) (J) per kelvin (K).
Derived quantities that specify heat capacity as an intensive property, i.e., independent of the size of a sample, are the molar heat capacity, which is the heat capacity per mole of a pure substance, and the specific heat capacity, often simply called specific heat, which is the heat capacity per unit mass of a material. Occasionally, in engineering contexts, a volumetric heat capacity is used. Because heat capacities of materials tend to mirror the number of atoms or particles they contain, when intensive heat capacities of various substances are expressed directly or indirectly per particle number, they tend to vary within a much more narrow range.
Temperature reflects the average kinetic energy of particles in matter while heat is the transfer of thermal energy from high to low temperature regions. Thermal energy transmitted by heat is stored

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**SI Base Unit:**Radian**Units:**Radian**Instruments:**Protractor

In geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles are usually presumed to be in a Euclidean plane, but are also defined in non-Euclidean geometry.
Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc by its radius. In the case of an angle (figure), the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any point and its image by the rotation.
The word angle comes from the Latin word angulus, meaning "a corner". The word angulus is a diminutive, of which the primitive form, angus, does not occur in Latin. Cognate words are the Greek ἀγκύλος (ankylοs), meaning "crooked, curved," and the English word "ankle". Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow".
Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a

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68

**SI Base Unit:**Meter**Units:**Meter

In geometric measurements, length most commonly refers to the longest dimension of an object.
In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire thickness. Another example is FET transistors, in which the channel width may be larger than channel length.
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.
Length is a measure of one dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed). In most systems of measurement, the unit of length is a fundamental unit, from which other units are defined.
Measurement has been important ever since man settled from his nomadic lifestyle and started using building materials; occupying land and trading with his neighbours. As society has become more technologically oriented much higher accuracies of measurement are required in an increasingly diverse set of fields, from

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**SI Base Unit:**Farad per metre**Units:**Farad per metre

In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how much electric field (more correctly, flux) is 'generated' per unit charge in that medium. More electric flux exists in a medium with a high permittivity (per unit charge) because of polarization effects. Permittivity is directly related to electric susceptibility, which is a measure of how easily a dielectric polarizes in response to an electric field. Thus, permittivity relates to a material's ability to transmit (or "permit") an electric field.
In SI units, permittivity ε is measured in farads per meter (F/m); electric susceptibility χ is dimensionless. They are related to each other through
where εr is the relative permittivity of the material, and ε0 = 8.85… × 10 F/m is the vacuum permittivity.
In electromagnetism, the electric displacement field D represents how an electric field E influences the organization of electrical charges in a given medium, including charge migration and

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71

A Gram is a unit of measurement for mass (or weight). It is 1/1000th of a Kilogram.

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**SI Base Unit:**Watt per square metre per steradian**Units:**Watt per square metre per steradian

Radiance and spectral radiance are measures of the quantity of radiation that passes through or is emitted from a surface and falls within a given solid angle in a specified direction. They are used in radiometry to characterize diffuse emission and reflection of electromagnetic radiation. In astrophysics, radiance is also used to quantify emission of neutrinos and other particles. The SI unit of radiance is watts per steradian per square metre (W·sr·m), while that of spectral radiance is W·sr·m·Hz.
Radiance characterizes total emission or reflection. Radiance is useful because it indicates how much of the power emitted by an emitting or reflecting surface will be received by an optical system looking at the surface from some angle of view. In this case, the solid angle of interest is the solid angle subtended by the optical system's entrance pupil. Since the eye is an optical system, radiance and its cousin luminance are good indicators of how bright an object will appear. For this reason, radiance and luminance are both sometimes called "brightness". This usage is now discouraged – see Brightness for a discussion. The nonstandard usage of "brightness" for "radiance" persists in

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In mathematics, a ratio is a relationship between two numbers of the same kind (e.g., objects, persons, students, spoonfuls, units of whatever identical dimension), usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second (not necessarily an integer).
In layman's terms a ratio represents, simply, for every amount of one thing, how much there is of another thing. For example, supposing one has 8 oranges and 6 lemons in a bowl of fruit, the ratio of oranges to lemons would be 4:3 (which is equivalent to 8:6) and the ratio of lemons to oranges would be would be 3:4. Additionally, the ratio of oranges to the total amount of fruit is 4:7 (equivalent to 8:14). The 4:7 ratio can be further converted to a fraction of 4/7 to represent how much of the fruit is an orange.
The ratio of numbers A and B can be expressed as:
The numbers A and B are sometimes called terms with A being the antecedent and B being the consequent.
The proportion expressing the equality of the ratios A:B and C:D is written A:B=C:D or A:B::C:D. this latter form, when spoken or written in

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**SI Base Unit:**Steradian**Units:**Steradian

In geometry, a solid angle (symbol: Ω) is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the object appears to an observer looking from that point. In the International System of Units (SI), a solid angle is a dimensionless unit of measurement called a steradian ( symbol: sr).
A small object nearby may subtend the same solid angle as a larger object farther away. For example, although the Moon is much smaller than the Sun, it is also much closer to Earth. Therefore, as viewed from any point on Earth, both objects have approximately the same solid angle as well as apparent size. This is most easily observed during a solar eclipse.
An object's solid angle is equal to the area of the segment of a unit sphere, centered at the angle's vertex, that the object covers. A solid angle equals the area of a segment of unit sphere in the same way a planar angle equals the length of an arc of a unit circle.
The solid angle of a sphere measured from a point in its interior is 4π sr, and the solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2π/3 sr. Solid angles can also be measured in

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**Units:**Grams per mole

In chemistry, the molar mass is a physical property. It is defined as the mass of a given substance (chemical element or chemical compound) divided by its 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.
As an example, the molar mass of water is approximately: M(H2O) ≈ 18 g·mol
The molar mass of atoms of an element is given by the atomic weight of the element multiplied by the molar mass constant, M
u = 1×10 kg/mol = 1 g/mol:
Multiplying by the molar mass constant ensures that the calculation is dimensionally correct: atomic weights are dimensionless quantities(i.e., pure numbers) whereas molar masses have units (in this case, grams/mole).
Some elements are usually encountered as molecules, e.g. hydrogen (H
2), sulfur (S
8), chlorine (Cl
2). The molar mass of molecules of these elements is the molar mass of the atoms multiplied by the number of atoms in each molecule:
The molar mass of a compound is given by the sum of the standard atomic weights of the atoms which form the compound multiplied by the molar mass constant, M
u:
An average molar mass may be defined for mixtures of

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**Units:**Bit

Data ( /ˈdeɪtə/ DAY-tə or /ˈdætə/) are the quantities, characters, or symbols on which operations are performed by a computer, being stored and transmitted in the form of electrical signals and recorded on magnetic, optical, or mechanical recording media. A program is a set of data that consists of a series of coded software instructions to control the operation of a computer or other machine. Physical computer memory elements consist of an address and a byte/word of data storage. Digital data can be reduced to key/value pair combinations. Supersets of this idea, where keys are derived, and values are arranged, relatively, are called data structures. They are also used in peripheral devices.
In an alternate usage, binary files (which are not human-readable) are sometimes called "data" as distinguished from human-readable "text". The total amount of digital data in 2007 was estimated to be 281 billion gigabytes (= 281 exabytes).
Fundamentally, computers follow the instructions they are given. A set of instructions to perform a given task (or tasks) is called a "program". In the nominal case, the program, as executed by the computer, will consist of binary machine code. The elements

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**SI Base Unit:**Katal per cubic metre**Units:**Katal per cubic metre

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**Instruments:**Accelerometer

In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from (accelerate from). A corollary is that all inertial observers always have a proper acceleration of zero.
Proper acceleration contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers.
In the standard inertial coordinates of special relativity, for unidirectional motion, proper acceleration is the rate of change of proper velocity with respect to coordinate time.
The proper acceleration 3-vector, combined with a null time-component, yields the object's four-acceleration, which makes proper-acceleration's magnitude Lorentz-invariant. Thus the concept is useful: (i) with accelerated coordinate systems, (ii) at relativistic speeds, and (iii) in curved spacetime.
In an accelerating rocket

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The reaction rate (rate of reaction) or speed of reaction for a reactant or product in a particular reaction is intuitively defined as how fast or slow a reaction takes place. For example, the oxidation of iron under the atmosphere is a slow reaction that can take many years, but the combustion of butane in a fire is a reaction that takes place in fractions of a second.
Chemical kinetics is the part of physical chemistry that studies reaction rates. The concepts of chemical kinetics are applied in many disciplines, such as chemical engineering, enzymology and environmental engineering.
Consider a typical chemical reaction:
The lowercase letters (a, b, p, and q) represent stoichiometric coefficients, while the capital letters represent the reactants (A and B) and the products (P and Q).
According to IUPAC's Gold Book definition the reaction rate r for a chemical reaction occurring in a closed system under constant-volume conditions, without a build-up of reaction intermediates, is defined as:
where [X] denotes the concentration(Molarity, mol/L) of the substance X. (NOTE: Rate of a reaction is always positive. '-' sign is present in the reactant involving terms because the reactant

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The specific weight (also known as the unit weight) is the weight per unit volume of a material. The symbol of specific weight is γ (the Greek letter Gamma).
A commonly used value is the specific weight of water on Earth at 5°C which is 62.43 lbf/ft or 9807 N/m.
The terms specific gravity, and less often specific weight, are also used for relative density.
where
Unlike density, specific weight is not absolute. It depends upon the value of the gravitational acceleration, which varies with location. A significant influence upon the value of specific gravity is the temperature of the material. Pressure may also affect values, depending upon the bulk modulus of the material, but generally, at moderate pressures, has a less significant effect than the other factors.
In fluid mechanics, specific weight represents the force exerted by gravity on a unit volume of a fluid. For this reason, units are expressed as force per unit volume (e.g., lb/ft or N/m). Specific weight can be used as a characteristic property of a fluid.
Specific weight is used as a property of soil often used to solve earthwork problems.
In soil mechanics, specific weight may refer to:
where
The formula for dry unit

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81

**SI Base Unit:**Siemens**Units:**Siemens

Electrical conductance measures how easily electricity flows along a certain path through an electrical element. The SI derived unit of conductance is the siemens. Because it is the reciprocal of electrical resistance (measured in ohms), historically, this unit was referred to as the mho. Oliver Heaviside coined the term conductivity in September 1885.
Electrical conductance is related to but should not be confused with conduction, the mechanism by which charge flows, or with conductivity, a property of a material.
For purely resistive circuits conductance is related to resistance by:
where R is the electrical resistance (Note: this is not true where the impedance is non-real)
Furthermore, conductance is related to susceptance and admittance by the equation:
or
where:
The conductance G of an object of cross-sectional area A and length can be determined from the material's conductivity σ by the formula,
From Kirchhoff's circuit laws we can deduce the rules for combining conductances. For two conductances G1 and G2 in parallel the voltage across them is the same and from Kirchoff's Current Law the total current is
Substituting Ohm's law for conductances gives
and the equivalent

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83

**Units:**Nuclear magneton

The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it. A loop of electric current, a bar magnet, an electron, a molecule, and a planet all have magnetic moments.
Both the magnetic moment and magnetic field may be considered to be vectors having a magnitude and direction. The direction of the magnetic moment points from the south to north pole of a magnet. The magnetic field produced by a magnet is proportional to its magnetic moment as well. More precisely, the term magnetic moment normally refers to a system's magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.
The preferred definition of a magnetic moment has changed over time. Before the 1930s, textbooks defined the moment using magnetic poles. Since then, most have defined it in terms of Ampèrian currents.
The sources of magnetic moments in materials can be represented by

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84

**SI Base Unit:**Kilogram**Units:**Kilogram

In physics, mass (from Greek μᾶζα "barley cake, lump (of dough)"), more specifically inertial mass, is a quantitative measure of an object's resistance to acceleration. In addition to this, gravitational mass is a measure of magnitude of the gravitational force which is
when interacting with a second object. The SI unit of mass is the kilogram (kg).
In everyday usage, mass is referred to as "weight", the units of which may be pounds or kilograms (for instance, a person's weight may be stated as 75 kg). In scientific use, however, the term "weight" refers to a different, yet related, property of matter. Weight is the gravitational force acting on a given body—which differs depending on the gravitational pull of the opposing body (e.g. a person's weight on Earth vs on the Moon) — while mass is an intrinsic property of that body that never changes. In other words, an object's weight depends on its environment, while its mass does not. On the surface of the Earth, an object with a mass of 50 kilograms weighs 491 Newtons; on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 Newtons. Restated in mathematical terms, on the surface of the Earth,

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85

**SI Base Unit:**Henry per metre**Units:**Henry per metre

In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the Greek letter μ. The term was coined in September, 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity.
In SI units, permeability is measured in henrys per meter (H·m), or newtons per ampere squared (N·A). The permeability constant (μ0), also known as the magnetic constant or the permeability of free space, is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum. The magnetic constant has the exact (defined) value µ0 = 4π×10 ≈ 1.2566370614…×10 H·m or N·A).
A closely related property of materials is magnetic susceptibility, which is a measure of the magnetization of a material in addition to the magnetization of the space occupied by the material.
In electromagnetism, the auxiliary magnetic field H represents how a magnetic field B influences the organization of magnetic dipoles in a given

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86

**SI Base Unit:**Ohm meter**Units:**Ohm centimeter

Electrical resistivity (also known as resistivity, specific electrical resistance, or volume resistivity) is a property of a material; it quantifies how strongly the material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm⋅metre (Ω⋅m). It is commonly represented by the Greek letter ρ (rho).
Electrical conductivity or specific conductance is the reciprocal quantity, and measures a material's ability to conduct an electric current. It is commonly represented by the Greek letter σ (sigma), but κ (kappa) (especially in electrical engineering) or γ (gamma) are also occasionally used. Its SI unit is siemens per metre (S⋅m) and CGSE unit is reciprocal second (s).
Many resistors and conductors have a uniform cross section with a uniform flow of electric current and are made of one material. (See the diagram to the right.) In this case, the electrical resistivity ρ (Greek: rho) is defined as:
where
The reason resistivity is defined this way is that it makes resistivity a material property, unlike resistance. All copper wires, irrespective of their shape and

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87

**Units:**Grams per kilonewton second

Thrust specific fuel consumption (TSFC) or sometimes simply specific fuel consumption, SFC, is an engineering term that is used to describe the fuel efficiency of an engine design with respect to thrust output. It allows the efficiency of different sized engines to be directly compared.
TSFC may also be thought of as fuel consumption (grams/second) per unit of thrust (kilonewtons, or kN). It is thus thrust-specific, meaning that the fuel consumption is divided by the thrust.
TSFC or SFC for thrust engines (e.g. turbojets, turbofans, ramjets, rocket engines, etc.) is the mass of fuel needed to provide the net thrust for a given period e.g. lb/(h·lbf) (pounds of fuel per hour-pound of thrust) or g/(s·kN) (grams of fuel per second-kilonewton). Mass of fuel is used rather than volume (gallons or litres) for the fuel measure since it is independent of temperature.
Specific fuel consumption of air-breathing jet engines at their maximum efficiency vary more or less inversely with speed, which in turn means that the fuel consumption per mile or km can be a more appropriate comparison metric for aircraft that travel at very different speeds.
This figure is inversely proportional to specific

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**SI Base Unit:**Kilogram per square metre**Units:**Kilogram per square metre

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**SI Base Unit:**Watt per square metre**Units:**Watt per square metre

Irradiance is the power of electromagnetic radiation per unit area (radiative flux) incident on a surface. Radiant emittance or radiant exitance is the power per unit area radiated by a surface. The SI units for all of these quantities are watts per square meter (W/m), while the cgs units are ergs per square centimeter per second (erg·cm·s, often used in astronomy). These quantities are sometimes called intensity, but this usage leads to confusion with radiant intensity, which has different units.
All of these quantities characterize the total amount of radiation present, at all frequencies. It is also common to consider each frequency in the spectrum separately. When this is done for radiation incident on a surface, it is called spectral irradiance, and has SI units W/m, or commonly W·m·nm.
If a point source radiates light uniformly in all directions through a non-absorptive medium, then the irradiance decreases in proportion to the square of the distance from the object.
The irradiance of a monochromatic light wave in matter is given in terms of its electric field by
where E is the complex amplitude of the wave's electric field, n is the refractive index of the medium, is the

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In chemistry, the mass concentration (or ) is defined as the mass of a constituent divided by the volume of the mixture :
For a pure chemical the mass concentration equals its density, thus the mass concentration can be called density of a component in a mixture.
The volume in the definition refers to the volume of the solution, not the volume of the solvent. One liter of a solution usually contains either slightly more or slightly less than 1 liter of solvent because the process of dissolution causes volume of liquid to increase or decrease. Sometimes the mass concentration is called titer.
The notation common with mass density underlines the connection between the two quantities (the mass concentration being the mass density of a component in the solution), but it can be a source of confusion especially when they appear in the same formula undifferentiated by an additional symbol (like a star superscript, a bolded symbol or varrho).
Mass concentration depends on the variation of the volume of the solution due mainly to thermal expansion. On small intervals of temperature the dependence is :
where is the mass concentration at a reference temperature, is the thermal expansion

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**SI Base Unit:**Mole**Units:**Mole

Amount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units (SI) defines the amount of substance to be proportional to the number of elementary entities present. The SI unit for amount of substance is the mole. It has the unit symbol mol. The mole is defined as the amount of substance that contains an equal number of elementary entities as there are atoms in 0.012kg of the isotope carbon-12. This number is called Avogadro's number and has the value 6.02214179(30)×10. It is the numerical value of the Avogadro constant which has the unit 1/mol, and relates the molar mass of an amount of substance to its mass.
Amount of substance appears in thermodynamic relations such as the ideal gas law, and in stoichiometric relations between reacting molecules as in the law of multiple proportions.
The only other unit of amount of substance in current use is the pound-mole with the symbol lb-mol, which is sometimes used in chemical engineering in the United States. One pound-mole is exactly 453.59237 mol.

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**SI Base Unit:**Siemens per meter**Units:**Siemens per meter**Instruments:**EC meter

The conductivity (or specific conductance) of an electrolyte solution is a measure of its ability to conduct electricity. The SI unit of conductivity is siemens per meter (S/m).
Conductivity measurements are used routinely in many industrial and environmental applications as a fast, inexpensive and reliable way of measuring the ionic content in a solution. For example, the measurement of product conductivity is a typical way to monitor and continuously trend the performance of the water purification systems.
In many cases, conductivity is linked directly to the total dissolved solids (T.D.S.). High quality deionized water has a conductivity of about 5.5 μS/m, typical drinking water in the range of 5-50 mS/m, while sea water about 5 S/m (i.e., sea water's conductivity is one million times higher than deionized water).
Conductivity is traditionally determined by measuring the AC resistance of the solution between two electrodes. Dilute solutions follow Kohlrausch's Laws of concentration dependence and additivity of ionic contributions. Onsager gave a theoretical explanation of Kohlrausch's law by extending Debye–Hückel theory.
The SI unit of conductivity is S/m and, unless otherwise

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93

**SI Base Unit:**Kilobit per second**Units:**bit per second

In telecommunications and computing, bit rate (sometimes written bitrate, data rate or as a variable R) is the number of bits that are conveyed or processed per unit of time.
The bit rate is quantified using the bits per second (bit/s) unit, often in conjunction with an SI prefix such as kilo- (kbit/s), mega- (Mbit/s), giga- (Gbit/s) or tera- (Tbit/s). Note that, unlike many other computer-related units, 1 kbit/s is traditionally defined as 1,000-bit/s, not 1,024-bit/s, etc., also before 1999 when SI prefixes were introduced for units of information in the standard IEC 60027-2. Uppercase K as in Kbit/s should never be used.
The formal abbreviation for "bits per second" is "bit/s" (not "bits/s", see writing style for SI units). In less formal contexts the abbreviations "b/s" or "bps" are sometimes used, though this risks confusion with "bytes per second" ("B/s", "Bps"), and the use of the abbreviation ps is also inconsistent with the SI symbol for picosecond.
1 Byte/s (B/s) corresponds to 8-bit/s (bit/s).
In digital communication systems, the physical layer gross bitrate, raw bitrate, data signaling rate, gross data transfer rate or uncoded transmission rate (sometimes written as a

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94

**Units:**micro per degree C

The inverse temperature is given by
where k is the Boltzmann constant and T is the temperature. The inverse temperature is actually more fundamental than temperature. The inverse temperature is used in many equations including the Wick Rotation.

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**SI Base Unit:**Pascal**Units:**Pascal

Pressure (the symbol: p) is the ratio of force to the area over which that force is distributed. In other words, pressure is force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure (also spelled gage pressure) is the pressure relative to the local atmospheric or ambient pressure. While pressure may be measured in any unit of force divided by any unit of area, the SI unit of pressure (the newton per square metre) is called the pascal (Pa) after the seventeenth-century philosopher and scientist Blaise Pascal. A pressure of 1 Pa is small; it approximately equals the pressure exerted by a dollar bill resting flat on a table. Everyday pressures are often stated in kilopascals (1 kPa = 1000 Pa).
Pressure is the effect of a force applied to a surface. Pressure is the amount of force acting per unit area. The symbol of pressure is p.
Mathematically:
where:
For liquid, the formula can be:
where:
Pressure is a scalar quantity. It relates the vector surface element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:
The minus(-) sign comes from

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**Units:**Baud

In digital communications, symbol rate (also known as baud or modulation rate) is the number of symbol changes (waveform changes or signalling events) made to the transmission medium per second using a digitally modulated signal or a line code. The Symbol rate is measured in baud (Bd) or symbols/second. In the case of a line code, the symbol rate is the pulse rate in pulses/second. Each symbol can represent or convey one or several bits of data. The symbol rate is related to, but should not be confused with, the gross bitrate expressed in bit/second.
A symbol can be described as either a pulse (in digital baseband transmission) or a "tone" (in passband transmission using modems) representing an integer number of bits. A theoretical definition of a symbol is a waveform, a state or a significant condition of the communication channel that persists for a fixed period of time. A sending device places symbols on the channel at a fixed and known symbol rate, and the receiving device has the job of detecting the sequence of symbols in order to reconstruct the transmitted data. There may be a direct correspondence between a symbol and a small unit of data (for example, each symbol may

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The temperature coefficient is the relative change of a physical property when the temperature is changed by 1 Kelvin.
In the following formula, let R be the physical property to be measured and T be the temperature at which the property is measured. T0 is the reference temperature, and ΔT is the difference between T and T0. Finally, α is the (linear) temperature coefficient. Given these definitions, the physical property is:
Here α has the dimensions of an inverse temperature (1/K or K).
This equation is linear with respect to temperature. For quantities that vary polynomially or logarithmically with temperature, it may be possible to calculate a temperature coefficient that is a useful approximation for a certain range of temperatures. For quantities that vary exponentially with temperature, such as the rate of a chemical reaction, any temperature coefficient would be valid only over a very small temperature range.
Different temperature coefficients are specified for various applications, including nuclear, electrical and magnetic.
A negative temperature coefficient (NTC) occurs when a physical property (such as thermal conductivity or electrical conductivity) of a material

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98

**Units:**Twenty-foot equivalent unit

Cargo capacity measures the capacity of container ships and terminals.

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**SI Base Unit:**Sievert**Units:**Sievert

The equivalent absorbed radiation dose, usually shortened to equivalent dose, but not to be confused with the American dose equivalent, is a computed average measure of the radiation absorbed by a fixed mass of biological tissue, that attempts to account for the different biological damage potential of different types of ionizing radiation. It is therefore a less fundamental quantity than the total radiation energy absorbed per mass (the absorbed dose), but is a more significant quantity for assessing the health risk of radiation exposure. It is adequate for assessing risk due to external radiation fields that penetrate uniformly through the whole body, but needs further corrections when the field is applied only to part(s) of the body or when it is due to an internal source. A further quantity called effective dose can be calculated if the fractionation of radiation to different parts of the body is known, to take into account the varying sensitivity of different organs to radiation. Another quantity called committed dose is used when the radiation source is internal to the body.
Equivalent dose is dimensionally a quantity of energy per unit of mass, and is usually measured in

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**SI Base Unit:**Newton per metre**Units:**Newton per metre

Surface tension is a contractive tendency of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in the floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects (e.g. water striders) to run on the water surface. This property is caused by cohesion of similar molecules, and is responsible for many of the behaviors of liquids.
Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy—which is a more general term in the sense that it applies also to solids and not just liquids.
In materials science, surface tension is used for either surface stress or surface free energy.
The cohesive forces among liquid molecules are responsible for the phenomenon of surface tension. In the bulk of the liquid, each molecule is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have other molecules on all sides of them and therefore are pulled inwards. This creates some

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101

**SI Base Unit:**Newton metre**Units:**Newton metre**Instruments:**De Prony brake

Torque, moment or moment of force (see the terminology below), is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist to an object. Mathematically, torque is defined as the cross product of force and the lever-arm distance, which tends to produce rotation.
Loosely speaking, torque is a measure of the turning force on an object such as a bolt or a flywheel. For example, pushing or pulling the handle of a wrench connected to a nut or bolt produces a torque (turning force) that loosens or tightens the nut or bolt.
The symbol for torque is typically τ, the Greek letter tau. When it is called moment, it is commonly denoted M.
The magnitude of torque depends on three quantities: the force applied, the length of the lever arm connecting the axis to the point of force application, and the angle between the force vector and the lever arm. In symbols:
where
The length of the lever arm is particularly important; choosing this length appropriately lies behind the operation of levers, pulleys, gears, and most other simple machines involving a mechanical advantage.
The SI unit for torque is the

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102

**SI Base Unit:**Joule per cubic metre per kelvin**Units:**Joule per cubic metre per kelvin

Volumetric heat capacity (VHC), also termed volume-specific heat capacity, describes the ability of a given volume of a substance to store internal energy while undergoing a given temperature change, but without undergoing a phase transition. It is different from specific heat capacity in that the VHC is a 'per unit volume' measure of the relationship between thermal energy and temperature of a material, while the specific heat is a 'per unit mass' measure (or occasionally per molar quantity of the material). If given a specific heat value of a substance, one can convert it to the VHC by multiplying the specific heat by the density of the substance.
Dulong and Petit predicted in 1818 that the product of solid substance density and specific heat capacity (ρcp) would be constant for all solids. This amounted to a prediction that volumetric heat capacity in solids would be constant. In 1819 they found that volumetric heat capacities were not quite constant, but that the most constant quantity was the heat capacity of solids adjusted by the presumed weight of the atoms of the substance, as defined by Dalton (the Dulong–Petit law). This quantity was proportional to the heat capacity per

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