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Kinetic Theory Of Gases

Kinetic theory of gases

Kinetic theory, or kinetic-molecular theory, or collision theory attempts to explain the macroscopic properties of gases by considering their composition at a molecular level.

Postulates

The fundamental aspects of kinetic theory are given by several postulates:
- Gases are composed of molecules in constant, random motion; the moving particles constantly collide with each other and with the walls of the container containing the gas
- The collisions between gas molecules are elastic
- The collisions of gas particles with the walls of the container holding them are perfectly elastic as well
- The total volume of the gas molecules is negligible compared to the volume of the entire container. This is equivalent to stating that the distance separating the gas particles is relatively large compared to their size.
- The interactions between molecules are negligible
- The gas consists of very small particles, each of which has a mass
- The gas particles are constantly moving rapidly in a random fashion
- The average kinetic energy of a gas particle depends only on the temperature at which the gas particle is present
- The gas particles exert no force on one another The above postulates accurately describe the behavior of ideal gases. Real gases approach ideality under conditions of low density and high temperature.

Pressure

Pressure is explained by kinetic theory as arising from the force exerted by colliding gas molecules onto the walls of the container. Consider a gas of N molecules, each of mass m, enclosed in a cuboidal container of volume V. When a gas molecule collides with the wall of the container perpendicular to the x coordinate axis and bounces off in the opposite direction with the same speed (an elastic collision), then the momentum lost by the particle and gained by the wall is :

2mv_x

where v_x is the x-component of the initial velocity of the particle. Since force is the rate of change of momentum and the particle under consideration impacts with the wall once every 2l/v_x time units (where l is the length of the container), the force due to this particle is :

mv_x \cdot v_x \over l

and the total force acting on the wall is :

m\sum_j v_^2 \over l

where the summation is over all the gas molecules in the container. Since the particles are moving randomly in all directions, and since for each particle :

v^2 = v_x^2 + v_y^2 + v_z^2

the expression for the total force becomes :

m\sum_j v_j^2 \over 3l

This can be written as :

Nmv_^2 \over 3l

where v_rms is the root mean square velocity of the gas. Therefore, pressure, the force per unit area, equals :

Nmv_^2 \over 3Al

where A is the area of the wall. Thus, as cross-sectional area multiplied by length is equal to volume, we have the following expression for the pressure :

P =

where V is the volume. Also, as Nm is the total mass of the gas, and mass divided by volume is density :

P =  \rho\ v_^2

where ρ is the density of the gas. This result is interesting and significant, because it relates pressure, a macroscopic property, to the average (translational) kinetic energy per molecule (1/2mv_rms²), which is a microscopic property. Note that the product of pressure and volume is simply two thirds of the total kinetic energy.

Temperature

The above equation tells us that the product of pressure and volume per mole is proportional to the average molecular kinetic energy. Further, the ideal gas equation tells us that this product is proportional to the absolute temperature. Putting the two together, we arrive at one important result of the kinetic theory: average molecular kinetic energy is proportional to the absolute temperature. The constant of proportionality is 3/2 times Boltzmann's constant, which is the ratio of the gas constant R to Avogadro's number (independent of the gas). This result is related to the equipartition theorem. Thus the kinetic energy per kelvin is:
- per mole: 12.47 J
- per molecule: 20.7 yJ = 129 μeV At standard temperature (273.15 K), we get:
- per mole: 3406 J
- per molecule: 5.65 zJ = 35.2 meV Examples:
- hydrogen (molecular mass = 2): 1703 kJ/kg
- nitrogen (molecular mass = 28): 122 kJ/kg
- oxygen (molecular mass = 32): 106 kJ/kg

RMS speeds of molecules

From the kinetic energy formula it can be shown that :

v_^2

= 24,940 T / molecular mass with v in m/s and T in kelvins. For standard temperature, root mean square speeds are:
- thermal neutrons 2610 m/s
- hydrogen 1846 m/s
- nitrogen 493 m/s
- oxygen 461 m/s The most probable speeds are 81.6% of these (e.g. for thermal neutrons 2131 m/s), and the mean speeds 92.1%, see also distribution of speeds.

External links

- [http://www.ucdsb.on.ca/tiss/stretton/chem1/gases9.html Introduction] to the kinetic molecular theory of gases, from The Upper Canada District School Board
- [http://comp.uark.edu/~jgeabana/mol_dyn/ Java animation] illustrating the kinetic theory from University of Arkansas
- [http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/ktcon.html Flowchart] linking together kinetic theory concepts, from HyperPhysics
- [http://www.ewellcastle.co.uk/science/pages/kinetics.html Interactive Java Applets] allowing high school students to experiment and discover how various factors affect rates of chemical reactions. Category:Gases Category:Thermodynamics

Macroscopic

Macroscopic is commonly used to describe physical objects that are measurable and observable by the naked eye. When applied to phenomena and abstract objects, it describes existence in the world as we perceive it. Lengths scales generally considered macroscopic roughly fall in the range 1 mm - 1 km. The term macroscopic may also refer to a "larger view", namely a view only available from a large perspective. A macroscopic position could be considered the "big picture".

Examples

- A macroscopic view of a ball is just that: a ball. A microscopic view could reveal a thick round skin seemingly composed entirely of puckered cracks and fissures (as viewed through a microscope) or, further down in scale, a collection of molecules in the rough shape of a sphere.

Macroscopy in physics

In physics, macroscopy is can be a physical trait applied relative to what one is observing. If one looks at a galaxy, a star is a microscopic entity, even if it is many, many orders of magnitude larger than us.

Molecule

A molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. The science of molecules is called molecular chemistry or molecular physics, depending on the focus. Molecular chemistry deals with the laws governing the interaction between molecules that results in the formation and breakage of chemical bonds, while molecular physics deals with the laws governing their structure and properties. In practice, however, this distinction is vague. According to the strict definition, molecules can consist of one atom (as in noble gases) or more atoms bonded together. The concept of monatomic (single-atom) molecule is used almost exclusively in the kinetic theory of gases. In molecular sciences, a molecule consists of a stable system (bound state) comprising two or more atoms. The term unstable molecule is used for very reactive species, i.e., short-lived assemblies (resonances) of electrons and nuclei, such as radicals, molecular ions, Rydberg molecules, transition states, Van der Waals complexes, or systems of colliding atoms as in Bose-Einstein condensates. A peculiar use of the term molecular is as a synonym to covalent, which arises from the fact that, unlike molecular covalent compounds, ionic compounds do not yield well-defined smallest particles that would be consistent with the definition above. No typical "smallest particle" can be defined for covalent crystals, or network solids, which are composed of repeating unit cells that extend indefinitely either in a plane (such as in graphite) or three-dimensionally (such as in diamond). Although the concept of molecules was first introduced in 1811 by Avogadro, and was accepted by many chemists as a result of Dalton's laws of Definite and Multiple Proportions (1803-1808), with notable exceptions (Boltzmann, Maxwell, Gibbs), the existence of molecules as anything other than convenient mathematical constructs was still an open debate in the physics community until the work of Perrin (1911), and was strenuously resisted by early positvists such as Mach. The modern theory of molecules makes great use of the many numerical techniques offered by computational chemistry. Dozens of molecules have now been identified in interstellar space by microwave spectroscopy. microwave spectroscopy (right) representations of the terpenoid, atisane. In the 3D model on the left, carbon atoms are represented by gray spheres; white spheres represent the hydrogen atoms and the cylinders represent the bonds. The model is enveloped in a "mesh" representation of the molecular surface, colored by areas of positive (red) and negative (blue) electric charge. In the 3D model (center), the light-blue spheres represent carbon atoms, the white spheres are hydrogen atoms, and the cylinders in between the atoms correspond to single bonds.]]

Chemical bond

:See main article chemical bond In a molecule, the atoms are joined by shared pairs of electrons in a chemical bond. It may consist of atoms of the same chemical element, as with oxygen (O₂), or of different elements, as with water (H₂O).

Size

Most molecules are much too small to be seen with the naked eye, but there are exceptions. DNA, a macromolecule, can reach macroscopic sizes. The smallest molecule is the hydrogen molecule. The interatomic distance is 0.15 nanometres (1.5 Å). But the size of its electron cloud is difficult to define precisely. Under standard conditions molecules have a dimension of a few to a few dozen Å.

Empirical formula

:See main article empirical formula The empirical formula of a molecule is the simplest integer ratio of the chemical elements that constitute the compound. For example, in their pure forms, water is always composed of a 2:1 ratio of hydrogen to oxygen, and ethyl alcohol or ethanol is always composed of carbon, hydrogen, and oxygen in a 2:6:1 ratio. However, this does not determine the kind of molecule uniquely - dimethyl ether has the same ratio as ethanol, for instance. Molecules with the same atoms in different arrangements are called isomers. The empirical formula is often the same as the molecular formula but not always. For example the molecule acetylene has molecular formula C2H2, but the simplest integer ratio of elements is CH.

Chemical formula

:See main article chemical formula The chemical formula reflects the exact number of atoms that compose a molecule. The molecular mass can be calculated from the chemical formula and is expressed in conventional units equal to 1/12 from the mass of a ¹²C isotope atom. For network solids, the term formula unit is used in stoichiometric calculations.

Molecular geometry

:See main article molecular geometry Molecules have fixed equilibrium geometries—bond lengths and angles—. A pure substance is composed of molecules with the same geometrical structure. The chemical formula and the structure of a molecule are the two important factors that determine its properties, particularly its reactivity. Isomers share a chemical formula but normally have very different properties because of their different structures. Stereoisomers, a particular type of isomers, may have very similar physico-chemical properties and at the same time very different biochemical activities.

Molecular spectroscopy

:See main article spectroscopy Molecular spectroscopy is the study of the response (spectrum) of a molecule to a signal of known energy (or frequency, according to Planck's formula). This signal is usually an electromagnetic wave or a beam of electrons, but new molecular spectroscopies, such as the positron spectroscopy, are under development. The molecular response can be signal absorption (absorption spectroscopy), emission of another signal (emission spectroscopy), fragmentation, or a change in its chemical nature. Spectroscopy is recognized as the most powerful tool in the investigation of the microscopic properties of molecules, and, in particular, their energy levels. Nowadays, in order to extract the maximum microscopic information from the experimental results, spectroscopical studies are very often coupled with computational chemical investigations. The theoretical background of spectroscopy is the scattering theory.

Collision

Physical collision

Dynamics

In physics, collision means the action of bodies striking or coming together (touching). Collisions involve forces (there is a change in velocity). Collisions can be elastic, meaning they conserve energy and momentum, inelastic, meaning they conserve momentum but not energy, or totally inelastic (or plastic), meaning they conserve momentum and the two objects stick together. The magnitude of the velocity difference at impact is called the closing speed. The field of dynamics is concerned with moving and colliding objects.

Billiards

In billiards, collisions play an important role. Because the collisions between billiard balls are almost perfectly elastic, and the balls roll on a low-friction surface, their predictable behaviour is often used to illustrate Newton's laws of motion.

Traffic

In traffic such a collision can be between two vehicles, a vehicle and a person, a vehicle and an object, two persons or a person and an object (and more if an animal is involved). It is an accident or even a disaster. At level crossings sometimes a train collides with a vehicle or person. Due to the speed and weight of a train it needs a long distance to stop, typically longer than the train driver can see ahead. When a train collides with a car this is more likely to be deadly for the people in the car than for those in the train, because the train has more mass and momentum.

Attacks by means of a deliberate collision

Attacks by means of a deliberate collision can be:
- with the body: unarmed striking, punching, kicking, martial arts, pugilism
- striking directly with a mêlée weapon, such as a sword, club or axe An attacking collision with a distant object can be achieved by throwing or launching a projectile. Projectiles can be:
- unpowered, thus depending on momentum transferred from the launcher:
- arrow
- catapult
- bullet
- spear
- artillery
- powered in flight:
- rocket
- guided in flight:
- guided missile Rockets and missiles usually carry explosives, in which case they do not need to achieve a direct collision to be effective, if they are detonated at the right moment.

Others

- A "collision" applied for construction work, is hitting a nail with a hammer, etc., and for cleaning a carpet-beater.
- In baseball a ball is hit with a baseball bat, in racquet sports also a ball or other object is hit, in bowling a ball hits a target.
- Supercolliders slam molecules, atoms, and subatomic particles together.
- Collision detection for use in computer games, computational geometry, AI, physical simulations etc.
- Bumper cars are designed to collide for fun.
- In cryptography, a collision is where a cryptographic hash function returns the same hash for two different inputs.
- "A collision" or (3+4=7) is a David Crowder Band cd (2005).

Telecommunications

In telecommunication, the term collision has the following meanings: # In a data transmission system, the situation that occurs when two or more demands are made simultaneously on equipment that can handle only one at any given instant. # In a computer, the situation that occurs when an attempt is made to store simultaneously two different data items at a given memory address that can hold only one of the items. Source: from Federal Standard 1037C and from MIL-STD-188

Volume

Volume, also called capacity, is a quantification of how much space an object occupies. The international unit for volume is the cubic meter. The volume of a solid object is a numerical value given to describe the three-dimensional concept of how much space it occupies. One-dimensional objects (such as lines) and two-dimensional objects (such as squares) are assigned zero volume in the three-dimensional space. Mathematically, volumes are defined by means of integral calculus, by approximating the given body with a large amount of small cubes, and adding the volumes of those cubes. The generalization of volume to arbitrarily many dimensions is called content. In differential geometry, volume is expressed by means of the volume form. Volume and capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in litres or its derived units), and volume being how much space an object displaces (commonly measured in cubic metres or its derived units). Volume is a fundamental parameter in thermodynamics and it is conjugate to pressure.

Volume formula

Common equations for volume: :A cube:

s^3 = s \cdot s \cdot s

(where s is the length of a side) : :A rectangular prism:

l \cdot w \cdot h

(length, width, height) : :A cylinder:

\pi \cdot r^2 h

(r = radius of circular face, h = distance between faces) : :A sphere:

\frac \pi r^3

(r = radius of sphere) : :An ellipsoid:

\frac \pi abc

(a, b, c = semi-axes of ellipsoid) : :A pyramid:

\frac A h

(A = area of base, h = height from base to apex) : :A cone (circular-based pyramid):

\frac \pi r^2 h

(r = radius of circle at base, h = distance from base to tip) : :Any prism that has a constant cross sectional area along the height
- :

A \cdot h

(A = area of the base, h = height) : :Any figure (calculus required) :

\int A(h) dh

where h is any dimension of the figure, and A(h) is the area of the cross-sections perpendicular to h described as a function of the position along h; this will work for any figure (no matter if the prism is slanted or the cross-sections change shape). The volume of a parallelepiped is the absolute value of the scalar triple product of the subtending vectors, or equivalently the absolute value of the determinant of the corresponding matrix. The volume of any tetrahedron, given its vertices a, b, c and d, is (1/6)·|det(a−b, b−c, c−d)|, or any other combination of pairs of vertices that form a simply connected graph.

Volume measures: other metric units

A commonly used metric unit for volume is the litre (American spelling liter), and one thousand litres is the volume of a cubic metre (American spelling cubic meter), which was formerly termed a stere and often called a "cube" in engineering slang. A cubic centimetre (American spelling cubic centimeter) is the same volume as a millilitre.

Volume measures: USA

U.S. customary units of volume:
- U.S. fluid ounce, about 29.6 mL
- U.S. liquid pint = 16 fluid ounces, or about 473 mL
- U.S. dry pint = 1/64 U.S. bushel, or about 551 mL (used for things such as blueberries)
- U.S. liquid quart = 32 fluid ounces or two U.S. pints, or about 946 mL
- U.S. dry quart = 1/32 U.S. bushel, or about 1.101 L
- U.S. gallon = 128 fluid ounces or four U.S. quarts, about 3.785 L
- U.S. dry gallon = 1/8 U.S. bushel, or about 4.405 L
- U.S. (dry level) bushel = 2150.42 cubic inches, or about 35.239 L The acre foot is often used in measuring the volume of water in a reservoir or an aquifer. It is the volume of water that would cover an area of one acre to a depth of one foot. It is equivalent to 43,560 cubic feet or exactly 1233.481 837 547 52 m³.
- cubic inch = 16.387 064 cm³
- cubic foot = 1,728 in³ ≈ 28.317 dm³
- cubic yard = 27 ft³ ≈ 0.7646 m³
- cubic mile = 5,451,776,000 yd³ = 3,379,200 acre-feet ≈ 4.168 km³

Volume measures: UK

Imperial units of volume:
- UK fluid ounce, about 28.4 mL (this equals the volume of an avoirdupois ounce of water under certain conditions)
- UK pint = 20 fluid ounces, or about 568 mL
- UK quart = 40 ounces or two pints, or about 1.137 L
- UK gallon = 160 ounces or four quarts, or exactly 4.546 09 L May it be noted that due to metrication within the UK, the quart is now obsolete and the fluid ounce extremely rare. The gallon is only used for transportation uses, (it is illegal for petrol & diesel to be sold by the gallon). The pint is the only Imperial unit that is in everyday use, for the sale of draught beer & cider (bottled & canned beer is sold in SI units) and for milk (this too is increasingly being sold in SI units).

Volume measures: cooking

Traditional cooking measures for volume also include:
- teaspoon = 1/6 U.S. fluid ounce (about 4.929 mL)
- teaspoon = 1/6 Imperial fluid ounce (about 4.736 mL) (Canada)
- teaspoon = 5 mL (metric)
- tablespoon = 1/2 U.S. fluid ounce or 3 teaspoons (about 14.79 mL)
- tablespoon = 1/2 Imperial fluid ounce or 3 teaspoons (about 14.21 mL) (Canada)
- tablespoon = 15 mL or 3 teaspoons (metric)
- tablespoon = 5 fluidrams (about 17.76 mL) (British)
- cup = 8 U.S. fluid ounces or 1/2 U.S. liquid pint (about 237 mL)
- cup = 8 Imperial fluid ounces or 1/2 fluid pint (about 227 mL) (Canada)
- cup = 250 mL (metric)

Relationship to density

The volume of an object is equal to its mass divided by its average density. This is a rearrangement of the calculation of density as mass per unit volume. The term specific volume is used for volume divided by mass. This is the reciprocal of the mass density, expressed in units such as cubic meters per kilogram (m³/kg).

Volume comparisons

To help compare different volumes, see orders of magnitude (volume)

External links

- [http://www.unitconversion.org/unit_converter/volume.html Online Volume Converter - convert between various units of volume, such as cubic meter, liter, barrel, tablespoon, cup, and so on]
- [http://www.unitconversion.org/unit_converter/volume-v.html Interactive Volume Conversion Table - convert selected unit to all other units of volume]
- [http://www.unitconversion.org/unit_converter/volume-dry-v.html Volume - Dry Online Interactive Unit Converter]
- [http://jumk.de/calc/volume.shtml Volume or capacity conversion of English and American units to metric units]
- [http://calc.skyrocket.de/en/ Online Unit Converter - Conversion of many different units]
- [http://www.ex.ac.uk/trol/scol/ccvol.htm Conversion Calculator for Units of Volume for many units (Cleave Books)]
- ko:부피 ja:体積 simple:Volume

Negligible

Although related to the more mathematical concepts of infinitesimal , the idea of something being negligible is particularly useful in practical disciplines like physics, chemistry, mechanical and electronic engineering, computer programming and in everyday decision-making. A quantity can be said to be negligible when it is safe to ignore (neglect) it in the present case, within the margins for error that have been agreed to be acceptable in this case.

Examples in electronic engineering

In order for electronic circuit designers to be able to think quickly and clearly through complex problems and complex circuitry, they are mentally equipped with a number of ideal circuit concepts that they use. These include the perfect voltage source, the perfect current source, the perfect amplifier, a perfect earth and many others. In none of these cases can the perfect circuit element actually exist in practice. To take one example, consider the perfect voltage source. If a perfect voltage source existed, it would have no internal impedance and would continue to maintain its rated voltage, say 5 V dc, across any load, no matter what current may become necessary to do this. As the load impedance reduced toward zero ohms (a perfect short circuit - which also cannot truly exist) then the current flow and power delivery would approach infinity. This is simultaneously impossible, impractical and undesirable. So,rather than abandon the idea of the 'voltage source' we simply remember that the concept has limitations and work with them. To continue this example, we need to derive a specification for this practical voltage source. Perhaps we can say that the current draw will never exceed 2 amps. Perhaps we can say that input voltages between 4.999 V and 5.001 V will produce errors that in themselves are negligible for the practical purposes of the remaining circuitry. If the output impedance of the voltage source can drop 0.002 V (5.001 - 4.999) at a current of 2 A, it must be no more than 0.001 Ω or one milli-ohm. Now we have a practical case - our voltage source with its negligible 1 mΩ output impedance will produce voltages that only deviate from 5.0 V by negligible amounts, provided the current requirements remain within spec. In another case these discrepancies may be far too much as any voltage less than 4.999999 volts, or more than 5.000001 V, would be unacceptable. This is no problem, we just tighten our specification - there is always a practical limit. In yet another case we may have a good 12.0 V supply available and a requirement that any voltage between 4V and 6V will be acceptable and that no more than 2 mA will ever be drawn. In this case a couple of 2 kΩ resistors in a simple voltage divider may suffice as a voltage source. This is hardly ideal, but it meets the requirements. The important point in the latter example is that, once drawn or soldered in place, the electronic engineer will continue to look upon the voltage divider, to a first approximation, as an ideal voltage source because as far as this requirement is concerned, that is what it is. Its practical discrepancies are negligible compared to the specification at this point. It is an important part of the engineer's skill, however, always to remember the assumptions and simplifications inherent in this thinking and to be able quickly to identify when cost savings can be made by reducing a specification requirement as well as when new requirements invalidate previously acceptable assumptions. Similar examples could be created for any of the 'ideal' circuit elements listed above, and many more, from RF frequency mixers to the simplest switch.

Examples in probability

The continuing success of the global travel industry depends upon the general public's perception that the personal risks involved in airline flight, as well as those involved in visiting foreign countries, are negligible compared to the pleasure to be gained by doing so. Widely publicised stories about terrorism and the future impact of global warming may increase the perception of risk without actually affecting it in reality. Similarly in technical design, there are probabilities, in each case, that an electronic product may be used in the vicinity of a powerful radio transmitter, that mains-borne power surges may occur, that its batteries may go flat while in use etc. The designer has to consider each of these and write some off as outside of the specified requirements, while others clearly are not. There are clearly a very large number of uncontrollable possibilities that any designed product (not just electronic ones) may have to contend with; knowing where to draw each line can become very difficult. Decisions made in this area can easily spell success or failure in a competitive marketplace. Your competitors may have been able to make significant cost savings by not handling cases that really almost never occur, or that do not worry the general public when they do. On the other hand, failures in cases that users see as perfectly normal may quickly give your product an unacceptably bad reputation.

Examples in software engineering

One might expect that a deterministic thing like a piece of software does not suffer from the vagaries of the negligible but this is not the case in at least two areas.

Digital representation of real-world variables

A computer system's internal representation of floating point numbers may normally approximate so closely to real numbers as to produce only negligible errors under most circumstances, but if, one day two very similar such values are subtracted, the result may be very far from what should be expected. There are many other ways that assumptions about the "negligible" errors involved in these digital representations may cause problems at run time or later including analogue to digital conversion where resolution and bit-rates are necessarily limited, financial calculations where floating points or other imprecise number systems do not 'take care of the pennies' etc. All of these have something in common with the electronic engineering issues discussed above, although they are different in nature.

Interaction with the outside world

Digital systems that interact with the outside world, whether though a keyboard and mouse, a network or even via a disk drive gain a element of risk that also must be considered. There is a chance that the user may click another button before this calculation is complete, the network may be flooded with requests for this service quicker than the software can provide it or the disk may be full when we try to write to it, or the file we need to read may have been deleted or moved. Modern computer programming languages provide the mechanism of throwing and catching exceptions so that the developer can handle these and many other possibilities without making the structure and logic of their code impenetrably complex to readers and future developers. Some languages, for example java, are designed to remind the developer about the exceptions that may be thrown — and so that should be caught, handled or declared of negligible interest — at each point. Others, like C#, provide the mechanism but do not enforce the practice in this way. These examples are related to probabilities introduced by the IO systems of the computer.

Negligible

Examples in electronic engineering

Examples in probability

Examples in software engineering

One might expect that a deterministic thing like a piece of software does not suffer from the vagaries of the negligible but this is not the case in at least two areas.

Digital representation of real-world variables

Interaction with the outside world

Real gas

An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. Additionally, the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container. The real gases that actually exist do not exhibit these exact properties, although the approximation is often good enough to treat real gases as ideal gases. There are basically three types of ideal gas:
- the classical or Maxwell-Boltzmann ideal gas,
- the ideal quantum Bose gas, composed of bosons, and
- the ideal quantum Fermi gas, composed of fermions.

Classical ideal gas

The thermodynamic properties of an ideal gas can be described by two equations: The equation of state of a classical ideal gas is given by the ideal gas law. :

PV = nRT = NkT\,

The internal energy of an ideal gas is given by: :

U = \hat_V nRT = \hat_V NkT

where

\hat_V

is a constant (e.g. equal to 3/2 for a monatomic gas) and: (with SI units appended) :
- U is internal energy (joule) :
- P is the pressure (pascal) :
- V is the volume (cubic meter) :
- n is the amount of gas (mole) :
- R is the ideal gas constant (joule per kelvin per mole) :
- T is the absolute temperature (kelvin) :
- N is the number of particles :
- k is the Boltzmann constant (joule per kelvin per particle), :
- nR=Nk is the amount of gas (joule per kelvin). The probability distribution of particles by velocity or energy is given by the Boltzmann distribution. The ideal gas law is an extension of experimentally discovered gas laws. Real fluids at low density and high temperature, approximate the behavior of a classical ideal gas. However, at lower temperature or higher density, a real fluid deviates strongly from the behavior of an ideal gas, particularly as it condenses from a gas into a liquid or solid.

Heat capacities of an ideal gas

The heat capacity at constant volume of an ideal gas is: :

C_V = \left(\frac\right)_V =  \hat_V Nk

It is seen that the constant

\hat_V

is just the dimensionless specific heat capacity at constant volume. It is equal to half the number of degrees of freedom per particle. For a monatomic gas this is just

\hat_V=3/2

while for a diatomic gas it is

\hat_V=5/2

. It is seen that macroscopic measurements on heat capacity provide information on the microscopic structure of the molecules. The heat capacity at constant pressure of an ideal gas is: :

C_P = \left(\frac\right)_P = (\hat_V+1) Nk

where

H=U+PV

is the enthalpy of the gas. It is seen that

\hat_P

is also a constant and that the dimensionless heat capacities are related by: :

\hat_P-\hat_V=1

The entropy of an ideal gas

Using the results of thermodynamics only, we can go a long way in determining the expression for the entropy of an ideal gas. This is an important step since, according to the theory of thermodynamic potentials, of which the internal energy U is one, if we can express the entropy as a function of U and the volume V, then we will have a complete statement of the thermodynamic behavior of the ideal gas. We will be able to derive both the ideal gas law and the expression for internal energy from it. Since the entropy is an exact differential, using the chain rule, the change in entropy when going from a reference state 0 to some other state with entropy S may be written as

\Delta S

where: :

\Delta S = \int_^dS
=\int_^ \left(\frac\right)_V\!dT
+\int_^ \left(\frac\right)_T\!dV

Using the definition of the heat capacity at constant volume for the first differential and the appropriate Maxwell relation for the second we have: :

\Delta S
=\int_^ \frac\,dT+\int_^\left(\frac\right)_VdV

Using the expressions for an ideal gas and integrating yields: :

\Delta S
= Nk\ln\left(\frac\right)

where all constants have been incorporated into the logarithm as f(N) which is some function of the particle number N having the same dimensions as

VT^

in order that the argument of the logarithm be dimensionless. We now impose the constraint that the entropy be extensive. This will mean that when the extensive parameters (V and N) are multiplied by a constant, the entropy will be multiplied by the same constant. Mathematically: :

\Delta S(T,aV,aN)=a\Delta S(T,V,N)\,

From this we find an equation for the function f(N) :

af(N)=f(aN)\,

Differentiating this with respect to a, setting a equal to unity, and then solving the differential equation yields f(N): :

f(N)=\phi N\,

where φ is some constant with the dimensions of

VT^/N

. Substituting into the equation for the change in entropy: :

\frac = \ln\left(\frac\right)\,

This is about as far as we can go using thermodynamics alone. Note that the above equation is flawed - as the temperature approaches zero, the entropy approaches negative infinity, in contradiction to the third law of thermodynamics. In the above "ideal" development, there is a critical point, not at absolute zero, at which the argument of the logarithm becomes unity, and the entropy becomes zero. This is unphysical. The above equation is a good approximation only when the argument of the logarithm is much larger than unity - the concept of an ideal gas breaks down at low values of V/N. Nevertheless, there will be a "best" value of the constant in the sense that the predicted entropy is as close as possible to the actual entropy, given the flawed assumption of ideality. It remained for quantum mechanics to introduce a reasonable value for the value of φ which yields the Sackur-Tetrode equation for the entropy of an ideal gas. It too suffers from a divergent entropy at absolute zero, but is a good approximation to an ideal gas over a large range of densities.

Thermodynamic potentials of an ideal gas

Since the dimensionless heat capacity at constant pressure

\hat_P

is a constant we can express the entropy in what will prove to be a more convenient form: :

\frac=\ln\left( \frac\right)+\hat_P

where Φ is now the undetermined constant. The chemical potential of the ideal gas is calculated from the corresponding equation of state (see thermodynamic potential): :

\mu=\left(\frac\right)_

where G is the Gibbs free energy and is equal to U+PV-TS so that: :

\mu(T,V,N)=-kT\ln\left(\frac\right)

The thermodynamic potentials for an ideal gas can now be written as functions of T, V, and N as: : The most informative way of writing the potentials is in terms of their natural variables, since each of these equations can be used to derive all of the other thermodynamic variables of the system. In terms of their natural variables, the thermodynamic potentials of a single-specie ideal gas are: :

U(S,V,N)=\hat_V Nk\left(\frac\right)^

A(T,V,N)=-NkT\left(1+\ln\left(\frac\right)\right)

H(S,P,N)=\hat_P Nk\left(\frac\right)^

G(T,P,N)=-NkT\ln\left(\frac\right)

Ideal quantum gases

In the above mentioned Sackur-Tetrode equation, the best choice of the entropy constant was found to be proportional to the quantum thermal wavelength of a particle, and the point at which the argument of the logarithm becomes zero is roughly equal to the point at which the average distance between particles becomes equal to the thermal wavelength. In fact, quantum theory itself predicts the same thing. Any gas behaves as an ideal gas at high enough temperature and low enough density, but at the point where the Sackur-Tetrode equation begins to break down, the gas will begin to behave as a quantum gas, composed of either bosons or fermions. Just as there is a classical ideal gas, there are ideal quantum gases. An ideal gas of bosons will be governed by Bose-Einstein statistics and the distribution of energy will be in the form of a Bose-Einstein distribution. An ideal gas of fermions will be governed by Fermi-Dirac statistics and the distribution of energy will be in the form of a Fermi-Dirac distribution. Category:Gases ko:이상기체 ja:理想気体

Temperature

Temperature is the physical property of a system which underlies the common notions of "hot" and "cold"; the material with the higher temperature is said to be hotter. Physically, temperature is a measure of the random agitation of matter and ambiant photons, under the effect of thermal fluctuations. It is a fundamental parameter in thermodynamics and it is conjugate to entropy. More quantitatively, the order of magnitude of the fluctuations of the energy associated with an atom, molecule or another elementary constituant of a physical system is

k_B T

, where

k_B

is Boltzmann's constant, and T is temperature, expressed in Kelvins.

Overview

The formal properties of temperature are studied in thermodynamics and statistical mechanics. The temperature of a system at thermodynamic equilibrium is defined by a relation between the amount of heat

\delta Q

incident on the system during an infinitesimal quasistatic transformation, and the variation

\delta S

of its entropy during this transformation. :

\delta S = \frac

Contrarly to entropy and heat, whose microscopic definitions are valid even far away from thermodynamic equilibrium temperature can only be defined at thermodynamic equilibrium, or local thermodynamic equilibrium (see below). As a system receives heat its temperature rises, similarly a loss of heat from the system tends to decrease its temperature (at the - uncommon - exception of negative temperature, see below). When two systems are at the same temperature, no heat transfer occurs between them. When a temperature difference does exist, heat will tend to move from the higher-temperature system to the lower-temperature system, until they are at thermal equilibrium. This heat transfer may occur via conduction, convection or radiation (see heat for additional discussion of the various mechanisms of heat transfer). Temperature is also related to the amount of internal energy and enthalpy of a system. The higher the temperature of a system, the higher its internal energy and enthalpy are. Temperature is an intensive property of a system, meaning that it does not depend on the system size or the amount of material in the system. Other intensive properties include pressure and density. By contrast, mass and volume are extensive properties, and depend on the amount of material in the system.

Role of temperature in nature

Temperature plays an important role in almost all fields of science, including physics, chemistry, and biology. Many physical properties of materials including the phase (solid, liquid, gaseous or plasma), density, solubility, vapor pressure, and electrical conductivity depend on the temperature. Temperature also plays an important role in determining the rate and extent to which chemical reactions occur. This is one reason why the human body has several elaborate mechanisms for maintaining the temperature at 37 °C, since temperatures only a few degrees higher can result in harmful reactions with serious consequences. Temperature also controls the type and quantity of thermal radiation emitted from a surface. One application of this effect is the incandescent light bulb, in which a tungsten filament is electrically heated to a temperature at which significant quantities of visible light are emitted. Temperature-dependence of the speed of sound in air c, density of air ρ and acoustic impedance Z vs. temperature °C

Temperature measurement

Main article: Temperature measurement Temperature measurement using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Rømer. Fahrenheit's scale is still in use, alongside the Celsius scale and the Kelvin scale.

Units of temperature

The basic unit of temperature (symbol: T) in the International System of Units (SI) is the kelvin (K). One kelvin is formally defined as 1/273.16 of the temperature of the triple point of water (the point at which water, ice and water vapor exist in equilibrium). The temperature 0 K is called absolute zero and corresponds to the point at which the molecules and atoms have the least possible thermal energy. An important unit of temperature in theoretical physics is the Planck temperature (1.4 × 10³² K). In the field of plasma physics, because of the high temperatures encountered and the electromagnetic nature of the phenomena involved, it is customary to express temperature in electronvolts (eV) or kiloelectronvolts (keV), where 1 eV = 11,605 K. In the study of QCD matter one routinely meets temperatures of the order of a few hundred MeV, equivalent to about 10¹² K. For everyday applications, it is often convenient to use the Celsius scale, in which 0 °C corresponds to the temperature at which water freezes and 100 °C corresponds to the boiling point of water at sea level. In this scale a temperature difference of 1 degree is the same as a 1 K temperature difference, so the scale is essentially the same as the kelvin scale, but offset by the temperature at which water freezes (273.15 K). Thus the following equation can be used to convert from degrees Celsius to kelvins. :

\mathrm

In the United States, the Fahrenheit scale is widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F. The following formula can be used to convert from Fahrenheit to Celsius: :

\mathrm

See temperature conversion formulas for conversions between most temperature scales. ¹ Only the kelvin, Celsius, Fahrenheit, and Rankine scales are in use today.
² Some numbers in this table have been rounded off.
³ Normal human body temperature is 36.8 °C ±0.7 °C, or 98.2 °F ±1.3 °F.

Negative temperatures

:See main article: Negative temperature. For some systems and specific definitions of temperature, it is possible to obtain a negative temperature. A system with a negative temperature is not colder than absolute zero, but rather it is, in a sense, hotter than infinite temperature (sic).

Articles about temperature ranges:

- 10⁻¹² K = 1 picokelvin (pK)
- 10⁻⁹ K = 1 nanokelvin (nK)
- 10⁻⁶ K = 1 microkelvin (µK)
- 10⁻³ K = 1 millikelvin (mK)
- 10⁰ K = 1 kelvin
- 10¹ K = 10 kelvins
- 10² K = 100 kelvins
- 10³ K = 1,000 kelvin = 1 kilokelvin (kK)
- 10⁴ K = 10,000 kelvins = 10 kK
- 10⁵ K = 100,000 kelvins = 100 kK
- 10⁶ K = 1 megakelvin (MK)
- 10⁹ K = 1 gigakelvin (GK)
- 10¹² K = 1 terakelvin (TK) See Orders of magnitude (temperature).

Theoretical foundation of temperature

Zeroth-law definition of temperature

While most people have a basic understanding of the concept of temperature, its formal definition is rather complicated. Before jumping to a formal definition, let us consider the concept of thermal equilibrium. If two closed systems with fixed volumes are brought together, so that they are in thermal contact, changes may take place in the properties of both systems. These changes are due to the transfer of heat between the systems. When a state is reached in which no further changes occur, the systems are in thermal equilibrium. Now a basis for the definition of temperature can be obtained from the so-called zeroth law of thermodynamics which states that if two systems, A and B, are in thermal equilibrium and a third system C is in thermal equilibrium with system A then systems B and C will also be in thermal equilibrium (being in thermal equilibrium is a transitive relation; moreover, it is an equivalence relation). This is an empirical fact, based on observation rather than theory. Since A, B, and C are all in thermal equilibrium, it is reasonable to say each of these systems shares a common value of some property. We call this property temperature. Generally, it is not convenient to place any two arbitrary systems in thermal contact to see if they are in thermal equilibrium and thus have the same temperature. Also, it would only provide an ordinal scale. Therefore, it is useful to establish a temperature scale based on the properties of some reference system. Then, a measuring device can be calibrated based on the properties of the reference system and used to measure the temperature of other systems. One such reference system is a fixed quantity of gas. The ideal gas law indicates that the product of the pressure and volume (P · V) of a gas is directly proportional to the temperature: :

P \cdot V = n \cdot R \cdot T

(1) where 'T is temperature, n is the number of moles of gas and R is the gas constant. Thus, one can define a scale for temperature based on the corresponding pressure and volume of the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by 8.31... In practice, such a gas thermometer is not very convenient, but other measuring instruments can be calibrated to this scale. Equation 1 indicates that for a fixed volume of gas, the pressure increases with increasing temperature. Pressure is just a measure of the force applied by the gas on the walls of the container and is related to the energy of the system. Thus, we can see that an increase in temperature corresponds to an increase in the thermal energy of the system. When two systems of differing temperature are placed in thermal contact, the temperature of the hotter system decreases, indicating that heat is leaving that system, while the cooler system is gaining heat and increasing in temperature. Thus heat always moves from a region of high temperature to a region of lower temperature and it is the temperature difference that drives the heat transfer between the two systems.

Temperature in gases

As mentioned previously for a monatomic ideal gas the temperature is related to the translational motion or average speed of the atoms. The kinetic theory of gases uses statistical mechanics to relate this motion to the average kinetic energy of atoms and molecules in the system. For this case 7736 K = 7463 degrees Celsius corresponds to an average kinetic energy of one electronvolt; to take room temperature (300 K) as an example, the average energy of air molecules is 300/7736 eV, or 0.0388 electronvolt. This average energy is independent of particle mass, which seems counterintuitive to many people. Although the temperature is related to the average kinetic energy of the particles in a gas, each particle has its own energy which may or may not correspond to the average. However, after an examination of some basic physics equations it makes perfect sense. The second law of thermodynamics states that any two given systems when interacting with each other will later reach the same average energy. Temperature is a measure of the average kinetic energy of a system. The formula for the kinetic energy of an atom is:
:

K_t = \begin \frac \end mv^2

(Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. Additional degrees of freedom are available, so molecular rotation or vibration must be included.)

Thus, particles of greater mass (say a neon atom relative to a hydrogen molecule) will move slower than lighter counterparts, but will have the same average energy. This average energy is independent of the mass because of the nature of a gas, all particles are in random motion with collisions with other gas molecules, solid objects that may be in the area and the container itself (if there is one). A visual illustration of this [http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm from Oklahoma State University] makes the point more clear. Not all the particles in the container have different velocities, regardless of whether there are particles of more than one mass in the container, but the average kinetic energy is the same because of the ideal gas law. In a gas the distribution of energy (and thus speeds) of the particles corresponds to the Boltzmann distribution. An electronvolt is a very small unit of energy, approximately 1.602×10^-19 joule.

Temperature of the vacuum

When a satellite in empty space is heated by sunshine and cooled by radiating energy away it is not in thermodynamic equilibrium and has no well-defined temperature. A system in a vacuum will radiate its thermal energy, i.e. convert heat into electromagnetic waves. If vacuum is filled with electromagnetic waves (say, radiation from walls of vacuum chamber, or relic microwave radiation in space) then the system will exchange by energy with these waves and thermally equilibrates at some finite (non zero) temperature. Cosmic microwave background radiation being remnant of radiation of hot early universe when radiation was in thermal equilibrium with matter has Planck spectrum (black body spectrum) with the temperature (at present) of about 2.7 K.

Second-law definition of temperature

In the previous section temperature was defined in terms of 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 a measure of the disorder in a system. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability. Consider a series of coin tosses. A perfectly ordered system would be one in which every coin toss would come up either heads or tails. For any number of coin tosses, there is only one combination of outcomes corresponding to this situation. On the other hand, there are multiple combinations that can result in disordered or mixed systems, where some fraction are heads and the rest tails. As the number of coin tosses increases, the number of combinations corresponding to imperfectly ordered systems increases. For a very large number of coin tosses, the number of combinations corresponding to ~50% heads and ~50% tails dominates and obtaining an outcome significantly different from 50/50 becomes extremely unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy. Now, we have stated previously that temperature controls the flow of heat between two systems and we have just shown that the universe, and we would expect any natural system, tends to progress so as to maximize entropy. Thus, we would expect there to be some relationship between temperature and entropy. In order to find this relationship let's first consider the relationship between heat, work and temperature. A heat engine is a device for converting heat into mechanical work and analysis of the Carnot heat engine provides the necessary relationships we seek. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, q_H and the heat ejected at the low temperature, q_C. The efficiency is the work divided by the heat put into the system or: :

\textrm = \frac  = \frac = 1 - \frac

(2) where w_cy is the work done per cycle. We see that the efficiency depends only on q_C/q_H. Because q_C and q_H correspond to heat transfer at the temperatures T_C and T_H, respectively, q_C/q_H should be some function of these temperatures: :

\frac = f(T_H,T_C)

(3) Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between T₁ and T₃ must have the same efficiency as one consisting of two cycles, one between T₁ and T₂, and the second between T₂ and T₃. This can only be the case if: :

q_ = \frac

which implies: :

q_13 = f(T_1,T_3) = f(T_1,T_2)f(T_2,T_3)

Since the first function is independent of T₂, this temperature must cancel on the right side, meaning f(T₁,T₃) is of the form g(T₁)/g(T₃) (i.e. f(T₁,T₃) = f(T₁,T₂)f(T₂,T₃) = g(T₁)/g(T₂)· g(T₂)/g(T₃) = g(T₁)/g(T₃)), where g is a function of a single temperature. We can now choose a temperature scale with the property that: :

\frac = \frac

(4) Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature: :

\textrm = 1 - \frac = 1 - \frac

(5) Notice that for T_C = 0 K the efficiency is 100% and that efficiency becomes greater than 100% 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 the lowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion and rearranging gives: :

\frac  - \frac = 0

where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by: :

dS = \frac

(6) where the subscript indicates a reversible process. The change of this state function around any cycle is zero, as is necessary for any state function. This function corresponds to the entropy of the system, which we described previously. We can rearranging Equation 6 to get a new definition for temperature in terms of entropy and heat: :

T = \frac

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

\frac = \frac

(8) The reciprocal of the temperature is the rate of increase of entropy with energy.

References

External links

- [http://www.unitconversion.org/unit_converter/temperature.html Online Temperature Converter] - convert between various units of temperature, such as kelvin, Celsius, Fahrenheit, Rankine, Reaumur, and even Triple point of water
- [http://www.unitconversion.org/unit_converter/temperature-v.html Interactive Temperature Conversion Table] - convert selected unit to all other units of temperature
- [http://www.indiana.edu/~animal/fun/conversions/temperature.html Temperature Conversions: Celsius, Fahrenheit, Kelvin, Réaumur and Rankine]
- [http://www.unidata.ucar.edu/staff/blynds/tmp.html An elementary introduction to temperature aimed at a middle school audience]
- [http://www.straightdope.com/mailbag/mtempscales.html Why do we have so many temperature scales?]
- [http://thermodynamics-information.net A Brief History of Temperature Measurement] Category:Meteorology Category:Physical quantity Category:Thermodynamics Category:Heat ko:온도 ja:温度 th:อุณหภูมิ

Pressure

:For the psychological or political context, see Peer pressure. Pressure (symbol: p) is the force per unit area acting on a surface in a direction perpendicular to that surface. Mathematically: :

p = F/A\,

where p is the pressure, F is the normal force, and A is the area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics and it is conjugate to volume. A closely related quantity is the stress tensor σ which relates the vector force F to the vector area A via :

\mathbf=\mathbf

This tensor may be divided up into a scalar part (pressure) and a traceless tensor part shear. The shear tensor gives the force in directions parallel to the surface, usually due to viscous or frictional forces. The stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure. shear

Example

As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The gradient of pressure is force density. In the human body, baroreceptors monitor blood pressure.

Relative or gauge pressure

For gases, pressure is sometimes measured, not as an absolute pressure, but relative to atmospheric pressure; such measurements are sometimes called gauge pressure. An example of this is the air pressure in a car tire, which might be said to be "220 kPa," but is actually 220 kPa above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa, the absolute pressure in the tire is therefore about 320 kPa. In technical work, this is written "a gauge pressure of 220 kPa." Where space is limited, such as on gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)," is permitted. In non-SI technical work, a gauge pressure is sometimes written as "32 psig," though the other methods explained above that avoid attaching characters to the unit of pressure are preferred [http://physics.nist.gov/Pubs/SP811/sec07.html#7.4 ¹].

Scalar nature of pressure

In static gas, the gas as a whole does not appear to move, the individual molecules of the gas, which we cannot see, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.

Hydrostatic pressure

Hydrostatic pressure is the pressure due to the weight of a fluid. :p = ρgh where ρ (rho) is density of the fluid, g is acceleration due to gravity, and h is height of the fluid above the point being measured. See also Pascal's law.

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, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by the Mach number of the fluid. In addition, there can be differences in pressure due to differences in the elevation (height) of the fluid. See Bernoulli's equation. The pressure of a moving fluid can be measured using a Pitot probe, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressure or stagnation pressure.

Units

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N·m^-2 or kg·m^-1·s^-2). This special name for the unit was added in 1971; before that, pressure in SI was expressed in units such as N/m². Non-SI measures (still in use in some parts of the world) include the pound-force per square inch (psi) and the bar. The cgs unit of pressure is the barye (ba). It is equal to 1 dyn·cm^-2. Pressure is still sometimes expressed in kgf/cm² or grams-force/cm² (sometimes as kg/cm² and g/cm² without properly identifying the force units). But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as a unit of force is expressly forbidden in SI; the unit of force in SI is the newton (N). The technical atmosphere (symbol: at) is 1 kgf/cm². Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in practically all other fields, where the hecto prefix is hardly ever used. In Canadian weather reports, the normal unit is kPa. The obsolete unit inch of mercury (inHg) is still sometimes used in the United States. Blood pressure is still measured in millimetres of mercury in most of the world, and lung pressures in centimeters of water are still common. These obsolete manometric units of pressure are based on the pressure exerted by the weight of some "standard" fluid under some "standard" gravity. They are effectively attempts to define a unit for expressing the readings of a manometer. When millimetres or inches of mercury are used today, they have precise definitions that can be expressed in terms of SI units. The water-based units depend on the density of water, a measured, rather than defined, quantity. The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at earth mean sea level and is defined as follows. :standard atmosphere = 101325 Pa = 101.325 kPa = 1013.25 hPa. A rule of thumb commonly used by scuba divers is that one atmosphere is approximately equal to the pressure exerted by ten metres of water. Non-SI units presently or formerly in use include the following.
- atmosphere.
- manometric units:
- centimetre, inch, and millimetre of mercury (Torr).
- millimetre, centimetre, metre, inch, and foot of water.
- imperial units:
- kip, ton-force (short), ton-force (long), pound-force, ounce-force, and poundal per square inch.
- pound-force, ton-force (short), and ton-force (long) per square foot.
- non-SI metric units:
- bar, millibar.
- kilogram-force, or kilopond, per square centimetre (technical atmosphere).
- gram-force and tonne-force (metric ton-force) per square centimetre.
- barye (dyne per square centimetre).
- kilogram-force and tonne-force per square metre.
- sthene per square metre (pieze).

External links

- [http://calc.skyrocket.de/en/ Online unit converter] - conversion of many different units.
- [http://avc.comm.nsdlib.org/cgi-bin/wiki_grade_interface.pl?An_Exercise_In_Air_Pressure An exercise in air pressure]
- [http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html Pressure being a scalar quantity] Category:Diving Category:Meteorology Category:Physical quantity Category:Thermodynamics ko:압력 ms:Tekanan ja:圧力

Elastic collision

An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision. Elastic collisions occur only if there is no conversion of kinetic energy into other forms, as in the collision of atoms (Rutherford backscattering is one example). In the case of macroscopic bodies this will not be the case as some of the energy will become heat. In a collision between polyatomic molecules, some kinetic energy may be converted into vibrational and rotational energy of the molecules, but otherwise molecular collisions appear to be elastic. Collisions that are not elastic are known as inelastic collisions.

Equations and calculation in the one-dimensional case

Total kinetic energy remains constant throughout, hence:

m_v_^2+m_v_^2=m_v_'^2+m_v_'^2

Total momentum remains constant as well:

\,\! m_v_+m_v_=m_v_'+m_v_'

Solving for

v_'

and

v_'

results in the following: :

v_' = \frac

and :

v_' = \frac

Property: :

v_'-v_' = v_-v_

i.e.:
- the relative velocity of one particle with respect to the other is reversed by the collision
- the average of the momenta before and after the collision is the same for both particles As can be expected, the solution is invariant under adding a constant to all velocities, which is like using a frame of reference with constant translational velocity. The velocity of the center of mass does not change by the collision. With respect to the center of mass both velocities are reversed by the collision: in the case of particles of different mass, a heavy particle moves slowly toward the center of mass, and bounces back with the same low speed, and a light particle moves fast toward the center of mass, and bounces back with the same high speed. From the solution above we see that in the case of a large

v_

, the value of

v_'

is small if the masses are approximately the same: hitting a much lighter particle does not change the velocity much, hitting a much heavier particle causes the fast particle to bounce back with high speed. Therefore a neutron moderator (a medium which slows down fast neutrons, thereby turning them into thermal neutrons capable of sustaining a chain reaction) is a material full of atoms with light nuclei (with the additional property that they do not easily absorb neutrons): the lightest nuclei have about the same mass as a neutron. Category:Classical mechanics Category:Introductory physics

Force

:For other senses of this word, see force (disambiguation). In physics, a force is an external cause responsible for any change of a physical system. For instance, a person holding a dog by a rope is experiencing the force applied by the rope on their hand, and the cause for its pulling forward is the force exercised by the rope. The kinetic expression of this change is, according to Newton's second law, acceleration, non kinetic expressions such as deformation can also occur. The SI unit for force is the newton.

Elementary concepts

Force in its most primitive definition can be thought of as that which when acting alone causes an object to accelerate. In a practical sense forces can be divided into two groups: contact forces and field forces. Contact forces require the physical contact of one object with other such as a hammer striking a nail or the force exerted by a gas under pressure - gas produced by exploding gunpowder forces a heavy ball out of a cannon. Field forces on the other hand need no physical medium of contact. Gravity and magnetism are examples of such forces. It should be noted however, that fundamentally all forces are in fact field forces. The force of hammer striking the nail in the previous example turns out to be a clash of the electric forces in both hammer and nail. Nevertheless it is appropriate in some cases to maintain these two classifications for ease of understanding.

Quantitative definition

In physics models, the point-like system is used, where objects are represented as one-dimensional points at their centre of mass. The only change the system can experience is a change of its momentum (its speed). Since the rise of the atomic theory, any physical system has been considered in classical physics as composed of point-like systems called atoms or molecules. Therefore, all forces can be defined by their effect; that is, by the change of movement they induce on point-like systems. This change of movement can be quantified by the acceleration (the derivative of velocity). The discovery by Isaac Newton that a given force will induce an acceleration in inverse proportion to a quantity called the mass of inertia or inertial mass which is independent of the speed of the system is Newton's second law. This law allows us to predict the effect of a force on any point-like system whose mass is known. It is usually written as: :F = dp/dt = d(m·v)/dt = m·a (in the case where m does not depend on t) where :F is the force (a vector quantity), :p is the momentum, :t is the time, :v is the velocity, :m is the mass, and :a=d²x/dt² is the acceleration, the second derivative with respect to t of the position vector x. If the mass m is measured in kilograms and the acceleration a is measured in metres per second squared, then the unit of force is kilogram × metre/second squared. This unit is called the newton: 1 N = 1 kg x 1 m/s². This equation is a system of three second-order differential equations with respect to the three-dimensional position vector which is an unknown function of time. This equation can be solved if F is a known function of x and some of its derivatives and if the mass m is known. Morevover the boundary conditions are required; for example, the values of the position vector and x and the velocity v at the starting time, say t=0. Of course, this formula is only useful if one knows the numerical values of F and m. The definition above is an implicit definition, arrived at as follows. One defines a reference system (one litre of water) and a reference force (the gravitational force applied by the Earth on it at the altitude of Paris). One takes Newton's second law for granted (one postulates that it is true) and measures the acceleration induced by the reference force on the reference system. This gives us a mass unit (1 kg) and a force unit (the older unit of 1 kilogram-force = 9.81 N). Once this is done, one can measure any force by the acceleration it induces on the reference system and measure the inertial mass of any system by measuring the acceleration induced on this system by the reference force. Force is often considered a f

Kinetic theory of gases

Postulates

Pressure

Temperature

RMS speeds of molecules

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External links

Macroscopic

Examples

Macroscopy in physics

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Molecule

Chemical bond

Size

Empirical formula

Chemical formula

Molecular geometry

Molecular spectroscopy

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Related lists

Collision

Physical collision

Dynamics

Billiards

Traffic

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Attacks by means of a deliberate collision

Others

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Telecommunications

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Volume

Volume formula

Volume measures: other metric units

Volume measures: USA

Volume measures: UK

Volume measures: cooking

Relationship to density

Volume comparisons

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Negligible

Examples in electronic engineering

Examples in probability

Examples in software engineering

Digital representation of real-world variables

Interaction with the outside world

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Negligible

Examples in electronic engineering

Examples in probability

Examples in software engineering

Digital representation of real-world variables

Interaction with the outside world

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Real gas

Classical ideal gas

Heat capacities of an ideal gas

The entropy of an ideal gas

Thermodynamic potentials of an ideal gas

Ideal quantum gases

Temperature

Overview

Role of temperature in nature

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Units of temperature

Negative temperatures

Articles about temperature ranges:

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Zeroth-law definition of temperature

Temperature in gases

Temperature of the vacuum

Second-law definition of temperature

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References

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Pressure

Example

Relative or gauge pressure

Scalar nature of pressure