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Temperature is a physical property of matter that quantitatively expresses the commonnotions of hot and cold . Objects of low temperature are cold, while various degrees of highertemperatures 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 independentexternally controlled variable, absolute, or thermodynamic, temperature is defined as thederivative of the internal energy with respect to the entropy.

In an ideal gas, the constituent molecules do not show internal excitations. They moveaccording to Newton's first law of motion, freely and independently of one another, exceptduring collisions that last for negligibly short times. The temperature of an ideal gas isproportional to the mean translational kinetic energy of its molecules.

Quantitatively, temperature is measured with thermometers , which may be calibrated to avariety of temperature scales .

Thermal vibration of a segment of protein alpha helix . The amplitude of the vibrationsincreases with temperature.

Temperature plays an important role in all fields of natural science, including physics , geology , chemistry , atmospheric sciences and biology .

Much of the world uses the Celsius scale (C) for most temperature measurements. [citationneeded ] It has the same incremental scaling as the Kelvin scale used by scientists, but fixes itsnull point, at 0C = 273.15K, approximately the freezing point of water (at one atmosphere of pressure) .[note 1] The United States uses the Fahrenheit scale for common purposes, a scale onwhich water freezes at 32 F and boils at 212 F (at one atmosphere of pressure). [citation needed ]

For practical purposes of scientific temperature measurement, the International System of Units (SI) defines a scale and unit for the thermodynamic temperature by using the easily

reproducible temperature of the triple point of water as a second reference point. The reasonfor this choice is that, unlike the freezing and boiling point temperatures, the temperature atthe triple point is independent of pressure (since the triple point is a fixed point on a two-dimensional plot of pressure vs. temperature). For historical reasons, the triple pointtemperature of water is fixed at 273.16 units of the measurement increment, which has beennamed the kelvin in honor of the Scottish physicist who first defined the scale. The unitsymbol of the kelvin is K.

Absolute zero is defined as a temperature of precisely 0 kelvins , which is equal to 273.15 Cor 459.68 F.

As distinct from a quantity of heat , temperature may be viewed as a measure of a quality of abody [1] or of heat .[2][3 ][4][5] The quality is called hotness by some writers .[6][7]
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When two systems are at the same temperature, no net heat transfer occurs spontanteously, byconduction or radiation , between them. When a temperature difference does exist, and thereis a thermally conductive or radiative connection between them, there is spontaneous heattransfer from the warmer system to the colder system, until they are at mutual thermalequilibrium . Heat transfer occurs by conduction or by thermal radiation .[8][9 ][10][11 ][12][13 ][14][15]

Experimental physicists, for example Galileo and Newton ,[16] found that there are indefinitelymany empirical temperature scales .

The kinetic theory of gases uses the model of the ideal gas to relate temperature to theaverage translational kinetic energy of the molecules in a container of gas in thermodynamicequilibrium .[32][33 ][34]

Classical mechanics defines the translational kinetic energy of a gas molecule as follows:

where m is the particle mass and v its speed, the magnitude of its velocity. The distribution of the speeds (which determine the translational kinetic energies) of the particles in a classicalideal gas is called the Maxwell-Boltzmann distribution .[33] The temperature of a classicalideal gas is related to its average kinetic energy per degree of freedom E k via the equation :

[35]

where the Boltzmann constant (n = Avogadro number , R = ideal gas constant ).This relation is valid in the ideal gas regime, i.e. when the particle density is much less than

, where is the thermal de Broglie wavelength . A monoatomic gas has only the threetranslational degrees of freedom.

The zeroth law of thermodynamics implies that any two given systems in thermal equilibriumhave the same temperature. In statistical thermodynamics, it can be deduced from the secondlaw of thermodynamics that they also have the same average kinetic energy per particle.

In a mixture of particles of various masses, lighter particles move faster than do heavierparticles, but have the same average kinetic energy. A neon atom moves slowly relative to ahydrogen molecule of the same kinetic energy. A pollen particle suspended in water moves ina slow Brownian motion among fast-moving water molecules.

Zeroth law of thermodynamics

Main article: Zeroth law of thermodynamics

It has long been recognized that if two bodies of different temperatures are brought intothermal connection, conductive or radiative, they exchange heat accompanied by changes of other state variables. Left isolated from other bodies, the two connected bodies eventuallyreach a state of thermal equilibrium in which no further changes occur. This basic knowledgeis relevant to thermodynamics. Some approaches to thermodynamics take this basicknowledge as axiomatic, other approaches select only one narrow aspect of this basic
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o_Galilei#Technologyhttp://en.wikipedia.org/wiki/Temperature#cite_note-Moran-14http://en.wikipedia.org/wiki/Temperature#cite_note-Moran-14http://en.wikipedia.org/wiki/Temperature#cite_note-dugdale-12http://en.wikipedia.org/wiki/Temperature#cite_note-dugdale-12http://en.wikipedia.org/wiki/Temperature#cite_note-Planck_1897-10http://en.wikipedia.org/wiki/Temperature#cite_note-Planck_1897-10http://en.wikipedia.org/wiki/Temperature#cite_note-Maxwell_1872-8http://en.wikipedia.org/wiki/Temperature#cite_note-Maxwell_1872-8http://en.wikipedia.org/wiki/Thermal_equilibriumhttp://en.wikipedia.org/wiki/Thermal_equilibriumhttp://en.wikipedia.org/wiki/Thermal_radiationhttp://en.wikipedia.org/wiki/Heat_conduction


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knowledge as axiomatic, and use other axioms to justify and express deductively theremaining aspects of it. The one aspect chosen by the latter approaches is often stated intextbooks as the zeroth law of thermodynamics, but other statements of this basic knowledgeare made by various writers.

The usual textbook statement of the zeroth law of thermodynamics is that if two systems areeach in thermal equilibrium with a third system, then they are also in thermal equilibriumwith each other. This statement is taken to justify a statement that all three systems have thesame temperature, but, by itself, it does not justify the idea of temperature as a numericalscale for a concept of hotness which exists on a one-dimensional manifold with a sense of greater hotness. Sometimes the zeroth law is stated to provide the latter justification .[24] Forsuitable systems, an empirical temperature scale may be defined by the variation of one of theother state variables, such as pressure, when all other coordinates are fixed. The second lawof thermodynamics is used to define an absolute thermodynamic temperature scale forsystems in thermal equilibrium.

A temperature scale is based on the properties of some reference system to which otherthermometers may be calibrated. One such reference system is a fixed quantity of gas. Theideal gas law indicates that the product of the pressure ( p) and volume ( V ) of a gas is directlyproportional to the thermodynamic temperature :[36]

where T is temperature, n is the number of moles of gas and R = 8.314472(15) Jmol -1K-1 isthe gas constant . Reformulating the pressure-volume term as the sum of classical mechanicalparticle energies in terms of particle mass, m, and root-mean-square particle speed v, the idealgas law directly provides the relationship between kinetic energy and temperature :[37]

Thus, one can define a scale for temperature based on the corresponding pressure and volumeof the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in acontainer of one cubic metre, divided by the gas constant. In practice, such a gas thermometeris not very convenient, but other thermometers can be calibrated to this scale.

The pressure, volume, and the number of moles of a substance are all inherently greater than

or equal to zero, suggesting that temperature must also be greater than or equal to zero. As apractical matter it is not possible to use a gas thermometer to measure absolute zerotemperature since the gasses tend to condense into a liquid long before the temperaturereaches zero. It is possible, however, to extrapolate to absolute zero by using the ideal gaslaw.

Second law of thermodynamics

Main article: Second law of thermodynamics

In the previous section certain properties of temperature were expressed by the zeroth law of thermodynamics. It is also possible to define temperature in terms of the second law of thermodynamics which deals with entropy . Entropy is often thought of as a measure of the
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disorder in a system. The second law states that any process will result in either no change ora net increase in the entropy of the universe. This can be understood in terms of probability.

For example, in a series of coin tosses, a perfectly ordered system would be one in whicheither every toss comes up heads or every toss comes up tails. This means that for a perfectly

ordered set of coin tosses, there is only one set of toss outcomes possible: the set in which100% of tosses come up the same. On the other hand, there are multiple combinations thatcan result in disordered or mixed systems, where some fraction are heads and the rest tails. Adisordered system can be 90% heads and 10% tails, or it could be 98% heads and 2% tails, etcetera. As the number of coin tosses increases, the number of possible combinationscorresponding to imperfectly ordered systems increases. For a very large number of cointosses, the combinations to ~50% heads and ~50% tails dominates and obtaining an outcomesignificantly different from 50/50 becomes extremely unlikely. Thus the system naturallyprogresses to a state of maximum disorder or entropy.

It has been previously stated that temperature governs the flow of heat between two systemsand it was just shown that the universe tends to progress so as to maximize entropy, which isexpected of any natural system. Thus, it is expected that there is some relationship betweentemperature and entropy. To find this relationship, the relationship between heat, work andtemperature is first considered. A heat engine is a device for converting thermal energy intomechanical energy, resulting in the performance of work, and analysis of the Carnot heatengine provides the necessary relationships. The work from a heat engine corresponds to thedifference between the heat put into the system at the high temperature, q H and the heatejected at the low temperature, qC . The efficiency is the work divided by the heat put into thesystem or:

(2)

where wcy is the work done per cycle. The efficiency depends only on qC / q H . Because qC andq H correspond to heat transfer at the temperatures T C and T H , respectively, qC / q H should besome function of these temperatures:

(3)

Carnot's theorem states that all reversible engines operating between the same heat reservoirsare equally efficient. Thus, a heat engine operating between T 1 and T 3 must have the sameefficiency as one consisting of two cycles, one between T 1 and T 2, and the second between T 2 and T 3. This can only be the case if:

which implies:
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Since the first function is independent of T 2, this temperature must cancel on the right side,meaning f (T 1,T 3) is of the form g(T 1)/ g(T 3) (i.e. f (T 1,T 3) = f (T 1,T 2) f (T 2,T 3) = g(T 1)/ g(T 2)g(T 2)/ g(T 3) = g(T 1)/ g(T 3)), where g is a function of a single temperature. A temperature scalecan now be chosen with the property that:

(4)

Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in termsof temperature:

(5)

Notice that for T C

= 0 K the efficiency is 100% and that efficiency becomes greater than100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact thelowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion andrearranging gives:

where the negative sign indicates heat ejected from the system. This relationship suggests the

existence of a state function, S , defined by:

(6)

where the subscript indicates a reversible process. The change of this state function aroundany cycle is zero, as is necessary for any state function. This function corresponds to theentropy of the system, which was described previously. Rearranging Equation 6 gives a newdefinition for temperature in terms of entropy and heat:

(7)

For a system, where entropy S ( E ) is a function of its energy E , the temperature T is given by:

(8),

i.e. the reciprocal of the temperature is the rate of increase of entropy with respect to energy.

Definition from statistical mechanics


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The previous section elaborated the historical derivation relating entropy and heat. A moderndefinition of temperature is given by statistical mechanics . It is defined in terms of thefundamental degrees of freedom of a system. Eq.(8) of the previous section is taken to be thedefining relation of the temperature. Eq. (7) can be derived from first principles .

Generalized temperature from single particle statistics

It is possible to extend the definition of temperature even to systems of few particles, like in aquantum dot . The generalized temperature is obtained by considering time ensembles insteadof configuration space ensembles given in statistical mechanics in the case of thermal andparticle exchange between a small system of fermions (N even less than 10) with asingle/double occupancy system. The finite quantum grand canonical ensemble ,[38] obtainedunder the hypothesis of ergodicity and orthodicity , allows to express the generalizedtemperature from the ratio of the average time of occupation 1 and 2 of the single/doubleoccupancy system :[39]

where E F is the Fermi energy which tends to the ordinary temperature when N goes toinfinity.

Negative temperature

Main article: Negative temperature

On the empirical temperature scales, which are not referenced to absolute zero, a negativetemperature is one below the zero-point of the scale used. For example, dry ice has asublimation t emperature of 78.5C which is equivalent to 109.3F. On the absolute Kelvinscale, however, this temperature is 194.6 K. On the absolute scale of thermodynamictemperature no material can exhibit a temperature smaller than or equal to 0 K, both of whichare forbidden by the third law of thermodynamics .

In the quantum mechanical description of electron and nuclear spin systems that have alimited number of possible states, and therefore a discrete upper limit of energy they canattain, it is possible to obtain a negative temperature , which is numerically indeed less than

absolute zero. However, this is not the macroscopic temperature of the material, but insteadthe temperature of only very specific degrees of freedom, that are isolated from others and donot exchange energy by virtue of the equipartition theorem .

A negative temperature is experimentally achieved with suitable radio frequency techniquesthat cause a population inversion of spin states from the ground state. As the energy in thesystem increases upon population of the upper states, the entropy increases as well, as thesystem becomes less ordered, but attains a maximum value when the spins are evenlydistributed among ground and excited states, after which it begins to decrease, once againachieving a state of higher order as the upper states begin to fill exclusively. At the point of maximum entropy, the temperature function shows the behavior of a singularity , because the

slope of the entropy function decreases to zero at first and then turns negative. Sincetemperature is the inverse of the derivative of the entropy, the temperature formally goes to
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infinity at this point, and switches to negative infinity as the slope turns negative. At energieshigher than this point, the spin degree of freedom therefore exhibits formally a negativethermodynamic temperature. As the energy increases further by continued population of theexcited state, the negative temperature approaches zero asymptotically .[40] As the energy of the system increases in the population inversion, a system with a negative temperature is not

colder than absolute zero, but rather it has a higher energy than at positive temperature, andmay be said to be in fact hotter at negative temperatures. When brought into contact with asystem at a positive temperature, energy will be transferred from the negative temperatureregime to the positive temperature region.

Pressure (the symbol: p ) is the ratio of force to the area over which that force is distributed. In otherwords, pressure is force per unit area applied in a direction perpendicular to the surface of anobject. Gauge pressure (also spelled gage pressure )[a] is the pressure relative to the localatmospheric or ambient pressure. While pressure may be measured in any unit of force divided byany unit of area, the SI unit of pressure (the newton per square metre ) is called the pascal (Pa) afterthe seventeenth-century philosopher and scientist Blaise Pascal . A pressure of 1 Pa is small; itapproximately equals the pressure exerted by a dollar bill resting flat on a table. Everyday pressuresare 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 unitarea. The symbol of pressure is p

Mathematically:

where:

is the pressure,is the normal force , is the area of the surface on contact.

For liquids , the formula may be written:

where:

is the pressure,is the density of the liquid,
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(the value is equal to the gravitational acceleration ),is the depth of the liquid in metres.

Pressure is a scalar quantity. It relates the vector surface element (a vector normal to thesurface) 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 the fact that the force is considered towards the surfaceelement, while the normal vector points outward.

It is incorrect (although rather usual) to say "the pressure is directed in such or suchdirection". The pressure, as a scalar, has no direction. The force given by the previousrelationship to the quantity has a direction, but the pressure does not. If we change the

orientation of the surface element, the direction of the normal force changes accordingly, butthe pressure remains the same.

Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to theseboundaries or sections at every point. It is a fundamental parameter in thermodynamics , and itis conjugate to volume .

Presently or formerly popular pressure units include the following:

atmosphere (atm) manometric units:

o centimeter, inch, and millimeter of mercury (torr ) o Height of equivalent column of water, including millimeter (mm H 2O),

centimeter (cm H 2O), meter, inch, and foot of water customary units:

o kip , ton -force (short), ton-force (long), pound-force, ounce-force, and poundal per square inch

o ton-force (short), and ton-force (long) per square incho fsw (feet sea water) used in underwater diving , particularly in connection with

diving pressure exposure and decompression non-SI metric units:

o bar , decibar, millibar msw (metres sea water ), used in underwater diving , particularly in

connection with diving pressure exposure and decompression o kilogram-force, or kilopond, per square centimeter (technical atmosphere ) o gram-force and tonne-force (metric ton-force) per square centimetero barye (dyne per square centimeter)o kilogram-force and tonne-force per square metero sthene per square meter (pieze )
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Types

Fluid pressure

Fluid pressure is the pressure at some point within a fluid , such as water or air (for moreinformation specifically about liquid pressure, see section below ).

Fluid pressure occurs in one of two situations:

1. an open condition, called "open channel flow"1. the ocean, or2. swimming pool, or3. the atmosphere.

2. a closed condition, called closed conduits1. water line, or2. gas line.

Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because themotions create only negligible changes in the pressure. Such conditions conform withprinciples of fluid statics . The pressure at any given point of a non-moving (static) fluid iscalled the hydrostatic pressure .

Closed bodies of fluid are either "static", when the fluid is not moving, or "dynamic", whenthe fluid can move as in either a pipe or by compressing an air gap in a closed container. Thepressure in closed conditions conforms with the principles of fluid dynamics .

The concepts of fluid pressure are predominantly attributed to the discoveries of BlaisePascal and Daniel Bernoulli . Bernoulli's equation can be used in almost any situation todetermine the pressure at any point in a fluid. The equation makes some assumptions aboutthe fluid, such as the fluid being idea l[8] and incompressible .[8] An ideal fluid is a fluid inwhich there is no friction, it is inviscid ,[8] zero viscosity .[8] The equation is written betweenany two points in a system that contain the same fluid.

[9]

where:

p = pressure of the fluid

= g = densityacceleration of gravity = specific weight of the fluid .[8]

v = velocity of the fluid

g = acceleration of gravity

z = elevation
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= pressure head

= velocity head

Applications

Artesian well Blood pressure Hydraulic head Plant cell turgidity Pythagorean cup

Explosion or deflagration pressures

Explosion or deflagration pressures are the result of the ignition of explosive gases , mists,dust/air suspensions, in unconfined and confined spaces.

Negative pressures

While pressures are, in general, positive, there are several situations in which negativepressures may be encountered:

When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa maybe described as a gauge pressure of 21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa).

When attractive forces (e.g., van der Waals forces ) between the particles of a fluid exceedrepulsive forces. Such scenarios are generally unstable since the particles will move closertogether until repulsive forces balance attractive forces. Negative pressure exists in thetranspiration pull of plants, and is used to suction water even higher than the ten metersthat it rises in a pure vacuum.

The Casimir effect can create a small attractive force due to interactions with vacuumenergy ; this force is sometimes termed "vacuum pressure" (not to be confused with thenegative gauge pressure of a vacuum).

Depending on how the orientation of a surface is chosen, the same distribution of forcesmay be described either as a positive pressure along one surface normal , or as a negativepressure acting along the opposite surface normal.

In the cosmological constant .

Stagnation pressure

Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving.Consequently, although a fluid moving at higher speed will have a lower static pressure , itmay have a higher stagnation pressure when forced to a standstill. Static pressure andstagnation pressure are related by the Mach number of the fluid. In addition, there can bedifferences in pressure due to differences in the elevation (height) of the fluid. See Bernoulli's

equation (note: Bernoulli's equation only applies for incompressible, inviscid flow).
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The pressure of a moving fluid can be measured using a Pitot tube , or one of its variationssuch as a Kiel probe or Cobra probe , connected to a manometer . Depending on where theinlet holes are located on the probe, it can measure static pressures or stagnation pressures.

Surface pressure

There is a two-dimensional analog of pressure the lateral force per unit length applied on aline perpendicular to the force.

Surface pressure is denoted by and shares many similar properties with three -dimensionalpressure. Properties of surface chemicals can be investigated by measuring pressure/areaisotherms, as the two-dimensional analog of Boyle's law , A = k , at constant temperature.

Pressure of an ideal gas

Main article: Ideal gas law

In an ideal gas , molecules have no volume and do not interact. Pressure varies linearly withtemperature, volume, and quantity according to the ideal gas law ,

where:

P is the absolute pressure of the gas

n is the amount of substance

T is the absolute temperature

V is the volume

R is the ideal gas constant .

Real gases exhibit a more complex dependence on the variables of state .[10]

Vapor pressure

Main article: Vapor pressure

Vapor pressure is the pressure of a vapor in thermodynamic equilibrium with its condensedphases in a closed system. All liquids and solids have a tendency to evaporate into a gaseousform, and all gases have a tendency to condense back to their liquid or solid form.
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Atmospheric pressure pressing on the surface of a liquid must be taken into account whentrying to discover the total pressure acting on a liquid. The total pressure of a liquid, then, isgh + the pressure of the atmosphere. When this distinction is important, the term total

pressure is used. Otherwise, discussions of liquid pressure refer to pressure without regard tothe normally ever-present atmospheric pressure.

It is important to recognize that the pressure does not depend on the amount of liquid present.Volume is not the important factor - depth is. The average water pressure acting against adam depends on the average depth of the water and not on the volume of water held back. Forexample, a large, shallow lake with a height of 3 m exerts only half the average pressure thatthe 6 m-tall small, deep pond does. A person will feel the same pressure whether his/her headis dunked a meter beneath the surface of the water in a small pool or to the same depth in themiddle of a large lake. If four vases contain different amounts of water but are all filled toequal depths, then a fish with its head dunked a few centimeters under the surface will beacted on by water pressure that is the same in any of the vases. If the fish swims a fewcentimeters deeper, the pressure on the fish will increase with depth and be the same nomatter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater,but it makes no difference what vase it is in. All vases are filled to equal depths, so the waterpressure is the same at the bottom of each vase, regardless of its shape or volume. If waterpressure at the bottom of a vase were greater than water pressure at the bottom of aneighboring vase, the greater pressure would force water sideways and then up the narrowervase to a higher level until the pressures at the bottom were equalized. Pressure is depthdependent, not volume dependent, so there is a reason that water seeks its own level.

Direction of liquid pressure

An experimentally determined fact about liquid pressure is that it is exerted equally in alldirections .[11] If someone is submerged in water, no matter which way that person tilts his/herhead, the person will feel the same amount of water pressure on his/her ears. Because a liquidcan flow, this pressure isn't only downward. Pressure is seen acting sideways when waterspurts sideways from a leak in the side of an upright can. Pressure also acts upward, asdemonstrated when someone tries to push a beach ball beneath the surface of the water. Thebottom of a boat is pushed upward by water pressure (buoyancy ).

When a liquid presses against a surface, there is a net force that is perpendicular to thesurface. Although pressure doesn't have a specific direction, force does. A submergedtriangular block has water forced against each point from many directions, but components of

the force that are not perpendicular to the surface cancel each other out, leaving only a netperpendicular point .[11] This is why water spurting from a hole in a bucket initially exits thebucket in a direction at right angles to the surface of the bucket in which the hole islocated.Then it curves downward due to gravity. If there are three holes in a bucket (top,bottom, and middle), then the force vectors perpendicular to the inner container surface willincrease with increasing depth - that is, a greater pressure at the bottom makes it so that thebottom hole will shoot water out the farthest. The force exerted by a fluid on a smooth

surface is always at right angles to the surface. The speed of liquid out of the hole is ,where h is the depth below the free surface .[11] Interestingly, this is the same speed the water(or anything else) would have if freely falling the same vertical distance h.

Kinematic pressure
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is the kinematic pressure, where is the pressure and constant mass density. The SI unitof P is m 2 /s2. Kinematic pressure is used in the same manner as kinematic viscosity in orderto compute Navier-Stokes equation without explicitly showing the density .

Navier-Stokes equation with kinematic quantities

Standard conditions for temperature and pressure are standard sets of conditions forexperimental measurements established to allow comparisons to be made between differentsets of data. The most used standards are those of the International Union of Pure andApplied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST),although these are not universally accepted standards. Other organizations have established avariety of alternative definitions for their standard reference conditions.

In chemistry, IUPAC established standard temperature and pressure (informallyabbreviated as STP ) as a temperature of 273.15 K (0 C, 32 F) and an absolute pressure of

100 kPa (14.504 psi , 0.986 atm , 1 bar ),[1]

An unofficial, but commonly used, standard isstandard ambient temperature and pressure (SATP ) as a temperature of 298.15 K (25 C,77 F) and an absolute pressure of 100 kPa (14.504 psi , 0.986 atm). The STP and the SATP should not be confused with the standard state commonly used in thermodynamic evaluationsof the Gibbs free energy of a reaction.

NIST uses a temperature of 20 C (293.15 K, 68 F) and an absolute pressure of 101.325 kPa(14.696 psi, 1 atm). The International Standard Metric Conditions for natural gas and similarfluids are 288.15 K (59.00 F; 15.00 C) and 101.325 kPa .[2]

In industry and commerce , standard conditions for temperature and pressure are often

necessary to define the standard reference conditions to express the volumes of gases andliquids and related quantities such as the rate of volumetric flow (the volumes of gases varysignificantly with temperature and pressure). However, many technical publications (books,

journals, advertisements for equipment and machinery) simply state "standard conditions"without specifying them, often leading to confusion and errors. Good practice is to alwaysincorporate the reference conditions of temperature and pressure.

It is equally as important to indicate the applicable reference conditions of temperature andpressure when stating the molar volume of a ga s[29] as it is when expressing a gas volume orvolumetric flow rate. Stating the molar volume of a gas without indicating the referenceconditions of temperature and pressure has no meaning and it can cause confusion.
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The molar gas volumes can be calculated with an accuracy that is usually sufficient by usingthe universal gas law for ideal gases. The usual expression is:

...which can be rearranged thus:

where (in SI metric units):

P = the absolute pressure of the gas, in Pa (pascal) n = amount of substance , in mol V = the volume of the gas, in mT = the absolute temperature of the gas, in K

R = the universal gas law constant of 8.3145 m Pa/(molK)

The pressure of a gas is directly proportional to its temperature, if the volume is kept constant(Figure 1 ). When the temperature of a gas increases, so does the energy of the particles. Thiscauses them to move more rapidly and to collide with each other and with the side of thecontainer more often. Since pressure is a measure of these collisions, the pressure of the gasincreases with an increase in temperature. The pressure of the gas will decrease if itstemperature decreases.

Figure 1: The relationship between thetemperature and pressure of a gas

In the same way that we have done for the other gas laws, we can describe the relationshipbetween temperature and pressure using symbols, as follows:

, therefore

We can also say that:

(1)

and that, provided the amount of gas stays the same:
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sensorQualitatively, the temperature of an object isdetermined by the sensation of heat or coldfelt by touching an object. Technically,temperature is a measure of the averagekinetic energy of the particles in a sample of matter, expressed in units of degrees on astandardized scale. You can measuretemperature in many different ways that varyin cost of equipment and accuracy.Thermocouples are one of the most commonsensors used to measure temperature becausethey are relatively inexpensive yet accuratesensors that can operate over a wide range of temperatures.

View a 60-second video on how to take aThermocouple Measurement

The basis of thermocouples was established by Thomas Johann Seebeck in 1821 when hediscovered that a conductor generates a voltage when it is subjected to a temperaturegradient. Measuring this voltage requires the use of a second conductor material thatgenerates a different voltage under the same temperature gradient. If the same material isused for the measurement, the voltage generated by the measuring conductor simply cancelsthat of the first conductor. The voltage difference generated by the two dissimilar materialscan be measured and related to the corresponding temperature gradient. Based on Seebecksprinciple, it is clear that thermocouples can only measure temperature differences and they

need a known reference temperature to yield the absolute readings.

The Seebeck effect describes the voltage or electromotive force (EMF) induced by thetemperature gradient along the wire. The change in material EMF with respect to a change intemperature is called the Seebeck coefficient or thermoelectric sensitivity. This coefficient isusually a nonlinear function of temperature.

However, for small changes in temperature over the length of a conductor, the voltage isapproximately linear, which is represented by the following equation where is the changein voltage, S is the Seebeck coefficient, and is the change in temperature:

(1)
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A thermocouple is created whenever two dissimilar metals touch at one end and are measuredat the other, creating a small open-circuit voltage as a function of the temperature differencebetween the contact point and the measurement point of the metals. The measured voltagefrom the thermocouple is the difference between the Seebeck voltage across each conductor,represented by the above equation. S varies with changes in temperature, which causes the

output voltage of thermocouples to be nonlinear over their operating ranges.

Several types of thermocouples are available, and different types are designated by capitalletters that indicate their composition according to American National Standards Institute(ANSI) conventions.

Pressure is defined as force per unit area that a fluid exerts on its surroundings.[1] Forexample, pressure, P, is a function of force, F, and area, A.

P = F/A

A container full of gas contains innumerable atoms and molecules that are constantlybouncing of its walls. The pressure would be the average force of these atoms and moleculeson its walls per unit of area of the container. Moreover, pressure does not have to bemeasured along the wall of a container but rather can be measured as the force per unit areaalong any plane. Air pressure, for example, is a function of the weight of the air pushingdown on Earth. Thus, as the altitude increases, pressure decreases. Similarly, as a scuba diveror submarine dives deeper into the ocean, the pressure increases.

The SI unit for pressure is the Pascal (N/m2), but other common units of pressure includepounds per square inch (PSI), atmospheres (atm), bars, inches of mercury (in Hg), andmillimeters of mercury (mm Hg).

A pressure measurement can be described as either static or dynamic. The pressure in caseswhere no motion is occurring is referred to as static pressure. Examples of static pressureinclude the pressure of the air inside a balloon or water inside a basin. Often times, themotion of a fluid changes the force applied to its surroundings. Such a pressure measurementis known as dynamic pressure measurement. For example, the pressure inside a balloon or atthe bottom of a water basin would change as air is let out of the balloon or as water is poured

out of the basin.

Head pressure (or pressure head) measures the static pressure of a liquid in a tank or a pipe.Head pressure, P, is a function solely on the height of the liquid, h, and weight density, w, of the liquid being measured as shown in Figure 1 below.


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Figure 1. Head Pressure Measurement

The pressure on a scuba diver swimming in the ocean would be the diver's depth multipliedby the weight of the ocean (64 pounds per cubic foot). A scuba diver diving 33 feet into the

ocean would have 2112 pounds of water on every square foot of his body. That translates to14.7 PSI. Interestingly enough, the atmospheric pressure of the air at sea level is also 14.7PSI or 1 atm. Thus, 33 feet of water create as much pressure as 5 miles of air! The totalpressure on a scuba diver 33 feet deep ocean would be the combined pressure caused by theweight of the air and the water, that would be 29.4 PSI or 2 atm.

A pressure measurement can further be described by the type of measurement beingperformed. There are three types of pressure measurements: absolute, gauge, and differential.Absolute pressure measurement is measured relative to a vacuum (Figure 2). Often times, theabbreviations PAA (Pascals Absolute) or PSIA (Pounds per Square Inch Absolute) are usedto describe absolute pressure.

Figure 2. Absolute Pressure Sensor [3]

Gauge pressure is measured relative to ambient atmospheric pressure (Figure 3). Similar toabsolute pressure, the abbreviations PAG (Pascals Gauge) or PSIG (Pounds per Square InchGauge) are used to describe gauge pressure.


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Figure 4. Cross Section of a Typical Strain Gauge Pressure Sensor [3]

When a change in pressure causes the diaphragm to deflect, a corresponding change inresistance is induced on the strain gauge, which can be measured by a Data Acquisition(DAQ) System. These strain gauge pressure transducers come in several different varieties:the bonded strain gauge, the sputtered strain gauge, and the semiconductor strain gauge.

In the bonded strain gauge pressure sensor, a metal foil strain gauge is actually glued orbonded to the surface where strain is being measured. These bonded foil strain gauges(BFSG) have been the industry standard for years and are continually used because of theirquick 1000 Hz response times to changes in pressure as well as their large operatingtemperature.

Sputtered strain gauge manufacturers sputter a layer of glass onto the diaphragm and thendeposit a thin metal film strain gauge on to the transducers diaphragm. Sputtered straingauge sensors actually form a molecular bond between the strain gauge element, theinsulating layer, and the sensing diaphragm. These gauges are most suitable for long-term useand harsh measurement conditions.

Integrated circuit manufacturers have developed composite pressure sensors that areparticularly easy to use. These devices commonly employ a semiconductor diaphragm ontowhich a semiconductor strain gauge and temperature-compensation sensor have been grown.Appropriate signal conditioning is included in integrated circuit form, providing a dc voltage

or current linearly proportional to pressure over a specified range.


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which results in sensor overload. A classic example of overloading a pressure sensor isknown as the water hammer phenomenon. This occurs when a fast moving fluid is suddenlystopped by the closing of a valve. The fluid has momentum that is suddenly arrested, whichcauses a minute stretching of the vessel in which the fluid is constrained. This stretchinggenerates a pressure spike that can damage a pressure sensor. To reduce the effects of water

hammer, sen sors are often mounted with a snubber between the sensor and the pressure line.A snubber is usually a mesh filter or sintered material that allows pressurized fluid throughbut does not allow large volumes of fluid through and therefore prevents pressure spikes inthe event of water hammer. A snubber is a good choice to protect your sensor in certainapplications, but in many tests the peak impact pressure is the region of interest. In such acase you would want to select a pressure sensor that does not include overprotection. [3]

A pressure sensor measures pressure , typically of gases or liquids . Pressure is an expressionof the force required to stop a fluid from expanding, and is usually stated in terms of force perunit area. A pressure sensor usually acts as a transducer ; it generates a signal as a function of the pressure imposed. For the purposes of this article, such a signal is electrical.

Pressure sensors are used for control and monitoring in thousands of everyday applications.Pressure sensors can also be used to indirectly measure other variables such as fluid/gas flow,speed, water level, and altitude. Pressure sensors can alternatively be called pressuretransducers , pressure transmitters , pressure senders , pressure indicators andpiezometers , manometers , among other names.

Pressure sensors can vary drastically in technology, design, performance, application

suitability and cost. A conservative estimate would be that there may be over 50 technologiesand at least 300 companies making pressure sensors worldwide.

There is also a category of pressure sensors that are designed to measure in a dynamic modefor capturing very high speed changes in pressure. Example applications for this type of sensor wo

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