The stress–energy tensor involves the use of superscripted variables (not exponents; see tensor index notation and Einstein summation notation). If Cartesian coordinates in SI units are used, then the components of the position four-vector are given by: x0 = t, x1 = x, x2 = y, and x3 = z, where t is time in seconds, and x, y, and z are distances in meters.
The stress–energy tensor is defined as the tensorTαβ of order two that gives the flux of the αth component of the momentumvector across a surface with constant xβcoordinate. In the theory of relativity, this momentum vector is taken as the four-momentum. In general relativity, the stress–energy tensor is symmetric,
In some alternative theories like Einstein–Cartan theory, the stress–energy tensor may not be perfectly symmetric because of a nonzero spin tensor, which geometrically corresponds to a nonzero torsion tensor.
The components of the stress-energy tensor
Because the stress–energy tensor is of order 2, its components can be displayed in 4 × 4 matrix form:
In the following, k and ℓ range from 1 through 3:
The time–time component is the density of relativistic mass, i.e., the energy density divided by the speed of light squared, while being in the co-moving frame of reference. It has a direct physical interpretation. In the case of a perfect fluid this component is
where is the relativistic mass per unit volume, and for an electromagnetic field in otherwise empty space this component is
where E and B are the electric and magnetic fields, respectively.
The flux of relativistic mass across the xk surface is equivalent to the density of the kth component of linear momentum,
The components
represent flux of kth component of linear momentum across the xℓ surface. In particular,
(not summed) represents normal stress in the kth co-ordinate direction (k = 1, 2, 3), which is called "pressure" when it is the same in every direction, k. The remaining components
In solid state physics and fluid mechanics, the stress tensor is defined to be the spatial components of the stress–energy tensor in the proper frame of reference. In other words, the stress energy tensor in engineeringdiffers from the relativistic stress–energy tensor by a momentum-convective term.
Covariant and mixed forms
Most of this article works with the contravariant form, Tμν of the stress–energy tensor. However, it is often necessary to work with the covariant form,
The divergence of the non-gravitational stress–energy is zero. In
other words, non-gravitational energy and momentum are conserved,
When gravity is negligible and using a Cartesian coordinate system for spacetime, this may be expressed in terms of partial derivatives as
The integral form of this is
where N is any compact four-dimensional region of spacetime; is its boundary, a three-dimensional hypersurface; and is an element of the boundary regarded as the outward pointing normal.
In flat spacetime and using Cartesian coordinates, if one
combines this with the symmetry of the stress–energy tensor, one can
show that angular momentum is also conserved:
Consequently, if is any Killing vector field, then the conservation law associated with the symmetry generated by the Killing vector field may be expressed as
The integral form of this is
In special relativity
In special relativity,
the stress–energy tensor contains information about the energy and
momentum densities of a given system, in addition to the momentum and
energy flux densities.
Given a Lagrangian Density that is a function of a set of fields
and their derivatives, but explicitly not of any of the spacetime
coordinates, we can construct the tensor by looking at the total
derivative with respect to one of the generalized coordinates of the
system. So, with our condition
By using the chain rule, we then have
Written in useful shorthand,
Then, we can use the Euler–Lagrange Equation:
And then use the fact that partial derivatives commute so that we now have
We can recognize the right hand side as a product rule. Writing it as the derivative of a product of functions tells us that
Now, in flat space, one can write . Doing this and moving it to the other side of the equation tells us that
And upon regrouping terms,
This is to say that the divergence of the tensor in the brackets is 0. Indeed, with this, we define the stress–energy tensor:
By construction it has the property that
Note that this divergenceless property of this tensor is equivalent to four continuity equations. That is, fields have at least four sets of quantities that obey the continuity equation. As an example, it can be seen that
is the energy density of the system and that it is thus possible to
obtain the Hamiltonian density from the stress–energy tensor.
Indeed, since this is the case, observing that , we then have
We can then conclude that the terms of represent the energy flux density of the system.
Trace
Note that the trace of the stress–energy tensor is defined to be , where
When we use the formula for the stress–energy tensor found above,
Using the raising and lowering properties of the metric and that ,
In general relativity, the partial derivatives used in special relativity are replaced by covariant derivatives.
What this means is that the continuity equation no longer implies that
the non-gravitational energy and momentum expressed by the tensor are
absolutely conserved, i.e. the gravitational field can do work on matter
and vice versa. In the classical limit of Newtonian gravity, this has a simple interpretation: kinetic energy is being exchanged with gravitational potential energy,
which is not included in the tensor, and momentum is being transferred
through the field to other bodies. In general relativity the Landau–Lifshitz pseudotensor is a unique way to define the gravitational field energy and momentum densities. Any such stress–energy pseudotensor can be made to vanish locally by a coordinate transformation.
In curved spacetime, the spacelike integral
now depends on the spacelike slice, in general. There is in fact no way
to define a global energy–momentum vector in a general curved
spacetime.
where is the mass–energy density (kilograms per cubic meter), is the hydrostatic pressure (pascals), is the fluid's four velocity, and is the reciprocal of the metric tensor. Therefore, the trace is given by
Noether's theorem
implies that there is a conserved current associated with translations
through space and time. This is called the canonical stress–energy
tensor. Generally, this is not symmetric and if we have some gauge
theory, it may not be gauge invariant because space-dependent gauge transformations do not commute with spatial translations.
In general relativity,
the translations are with respect to the coordinate system and as such,
do not transform covariantly. See the section below on the
gravitational stress–energy pseudo-tensor.
In the presence of spin or other intrinsic angular momentum, the
canonical Noether stress energy tensor fails to be symmetric. The
Belinfante–Rosenfeld stress energy tensor is constructed from the
canonical stress–energy tensor and the spin current in such a way as to
be symmetric and still conserved. In general relativity, this modified
tensor agrees with the Hilbert stress–energy tensor.
By the equivalence principle
gravitational stress–energy will always vanish locally at any chosen
point in some chosen frame, therefore gravitational stress–energy cannot
be expressed as a non-zero tensor; instead we have to use a pseudotensor.
In general relativity, there are many possible distinct
definitions of the gravitational stress–energy–momentum pseudotensor.
These include the Einstein pseudotensor and the Landau–Lifshitz pseudotensor.
The Landau–Lifshitz pseudotensor can be reduced to zero at any event in
spacetime by choosing an appropriate coordinate system.
A vacuum is a space devoid of matter. The word is derived from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space.
In engineering and applied physics on the other hand, vacuum refers to
any space in which the pressure is considerably lower than atmospheric
pressure. The Latin term in vacuo is used to describe an object that is surrounded by a vacuum.
The quality of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%. But higher-quality vacuums are possible. Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth (10−12) of atmospheric pressure (100 nPa), and can reach around 100 particles/cm3. Outer space
is an even higher-quality vacuum, with the equivalent of just a few
hydrogen atoms per cubic meter on average in intergalactic space.
Vacuum has been a frequent topic of philosophical debate since ancient Greek times, but was not studied empirically until the 17th century. Evangelista Torricelli produced the first laboratory vacuum in 1643, and other experimental techniques were developed as a result of his theories of atmospheric pressure. A Torricellian vacuum
is created by filling a tall glass container closed at one end with
mercury, and then inverting it in a bowl to contain the mercury (see
below).
Vacuum became a valuable industrial tool in the 20th century with the introduction of incandescent light bulbs and vacuum tubes, and a wide array of vacuum technologies has since become available. The development of human spaceflight has raised interest in the impact of vacuum on human health, and on life forms in general.
The word vacuum comes from Latin 'an empty space, void', noun use of neuter of vacuus, meaning "empty", related to vacare, meaning "to be empty".
Vacuum is one of the few words in the English language that contains two consecutive letters u.
Historical understanding
Historically, there has been much dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers debated the existence of a vacuum, or void, in the context of atomism, which posited void and atom as the fundamental explanatory elements of physics. Following Plato,
even the abstract concept of a featureless void faced considerable
skepticism: it could not be apprehended by the senses, it could not,
itself, provide additional explanatory power beyond the physical volume
with which it was commensurate and, by definition, it was quite
literally nothing at all, which cannot rightly be said to exist. Aristotle
believed that no void could occur naturally, because the denser
surrounding material continuum would immediately fill any incipient
rarity that might give rise to a void.
In his Physics,
book IV, Aristotle offered numerous arguments against the void: for
example, that motion through a medium which offered no impediment could
continue ad infinitum, there being no reason that something would come to rest anywhere in particular. Although Lucretius argued for the existence of vacuum in the first century BC and Hero of Alexandria tried unsuccessfully to create an artificial vacuum in the first century AD.
In the medieval Muslim world, the physicist and Islamic scholar, Al-Farabi (Alpharabius, 872–950), conducted a small experiment concerning the existence of vacuum, in which he investigated handheld plungers in water.
He concluded that air's volume can expand to fill available space, and
he suggested that the concept of perfect vacuum was incoherent. According to Nader El-Bizri, the physicist Ibn al-Haytham (Alhazen, 965–1039) and the Mu'tazilitheologians disagreed with Aristotle and Al-Farabi, and they supported the existence of a void. Using geometry, Ibn al-Haytham mathematically demonstrated that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body. According to Ahmad Dallal, Abū Rayhān al-Bīrūnī also states that "there is no observable evidence that rules out the possibility of vacuum". The suctionpump was described by Arab engineer Al-Jazari in the 13th century, and later appeared in Europe from the 15th century.
European scholars such as Roger Bacon, Blasius of Parma and Walter Burley in the 13th and 14th century focused considerable attention on issues concerning the concept of a vacuum. Eventually following Stoic physics in this instance, scholars from the 14th century onward increasingly departed from the Aristotelian perspective in favor of a supernatural
void beyond the confines of the cosmos itself, a conclusion widely
acknowledged by the 17th century, which helped to segregate natural and
theological concerns.
Almost two thousand years after Plato, René Descartes also proposed a geometrically based alternative theory of atomism, without the problematic nothing–everything dichotomy
of void and atom. Although Descartes agreed with the contemporary
position, that a vacuum does not occur in nature, the success of his namesake coordinate system
and more implicitly, the spatial–corporeal component of his metaphysics
would come to define the philosophically modern notion of empty space
as a quantified extension of volume. By the ancient definition however,
directional information and magnitude were conceptually distinct.
Medieval thought experiments
into the idea of a vacuum considered whether a vacuum was present, if
only for an instant, between two flat plates when they were rapidly
separated. There was much discussion of whether the air moved in quickly enough as the plates were separated, or, as Walter Burley
postulated, whether a 'celestial agent' prevented the vacuum arising.
The commonly held view that nature abhorred a vacuum was called horror vacui. There was even speculation that even God could not create a vacuum if he wanted and the 1277 Paris condemnations of BishopEtienne Tempier,
which required there to be no restrictions on the powers of God, led to
the conclusion that God could create a vacuum if he so wished.
Jean Buridan reported in the 14th century that teams of ten horses could not pull open bellows when the port was sealed.
In 1654, Otto von Guericke invented the first vacuum pump and conducted his famous Magdeburg hemispheres
experiment, showing that, owing to atmospheric pressure outside the
hemispheres, teams of horses could not separate two hemispheres from
which the air had been partially evacuated. Robert Boyle improved Guericke's design and with the help of Robert Hooke further developed vacuum pump technology. Thereafter, research into the partial vacuum lapsed until 1850 when August Toepler invented the Toepler Pump and in 1855 when Heinrich Geissler invented the mercury displacement pump, achieving a partial vacuum of about 10 Pa (0.1 Torr). A number of electrical properties become observable at this vacuum level, which renewed interest in further research.
While outer space provides the most rarefied example of a
naturally occurring partial vacuum, the heavens were originally thought
to be seamlessly filled by a rigid indestructible material called aether. Borrowing somewhat from the pneuma of Stoic physics, aether came to be regarded as the rarefied air from which it took its name.
Early theories of light posited a ubiquitous terrestrial and celestial
medium through which light propagated. Additionally, the concept
informed Isaac Newton's explanations of both refraction and of radiant heat. 19th century experiments into this luminiferous aether
attempted to detect a minute drag on the Earth's orbit. While the Earth
does, in fact, move through a relatively dense medium in comparison to
that of interstellar space, the drag is so minuscule that it could not
be detected. In 1912, astronomerHenry Pickering
commented: "While the interstellar absorbing medium may be simply the
ether, [it] is characteristic of a gas, and free gaseous molecules are
certainly there".
Later, in 1930, Paul Dirac proposed a model of the vacuum as an infinite sea of particles possessing negative energy, called the Dirac sea. This theory helped refine the predictions of his earlier formulated Dirac equation, and successfully predicted the existence of the positron, confirmed two years later. Werner Heisenberg's uncertainty principle, formulated in 1927, predicted a fundamental limit within which instantaneous position and momentum,
or energy and time can be measured. This has far reaching consequences
on the "emptiness" of space between particles. In the late 20th century,
so-called virtual particles that arise spontaneously from empty space were confirmed.
Classical field theories
The strictest criterion to define a vacuum is a region of space and time where all the components of the stress–energy tensor
are zero. This means that this region is devoid of energy and momentum,
and by consequence, it must be empty of particles and other physical
fields (such as electromagnetism) that contain energy and momentum.
Gravity
In general relativity, a vanishing stress–energy tensor implies, through Einstein field equations, the vanishing of all the components of the Ricci tensor. Vacuum does not mean that the curvature of space-time is necessarily flat: the gravitational field can still produce curvature in a vacuum in the form of tidal forces and gravitational waves (technically, these phenomena are the components of the Weyl tensor). The black hole
(with zero electric charge) is an elegant example of a region
completely "filled" with vacuum, but still showing a strong curvature.
In the theory of classical electromagnetism, free space has the following properties:
Electromagnetic radiation travels, when unobstructed, at the speed of light, the defined value 299,792,458 m/s in SI units.
The superposition principle is always exactly true.
For example, the electric potential generated by two charges is the
simple addition of the potentials generated by each charge in isolation.
The value of the electric field at any point around these two charges is found by calculating the vector sum of the two electric fields from each of the charges acting alone.
In quantum mechanics and quantum field theory,
the vacuum is defined as the state (that is, the solution to the
equations of the theory) with the lowest possible energy (the ground state of the Hilbert space). In quantum electrodynamics this vacuum is referred to as 'QED vacuum' to distinguish it from the vacuum of quantum chromodynamics, denoted as QCD vacuum. QED vacuum is a state with no matter particles (hence the name), and no photons.
As described above, this state is impossible to achieve experimentally.
(Even if every matter particle could somehow be removed from a volume,
it would be impossible to eliminate all the blackbody photons.)
Nonetheless, it provides a good model for realizable vacuum, and agrees
with a number of experimental observations as described next.
QED vacuum has interesting and complex properties. In QED vacuum,
the electric and magnetic fields have zero average values, but their
variances are not zero. As a result, QED vacuum contains vacuum fluctuations (virtual particles that hop into and out of existence), and a finite energy called vacuum energy.
Vacuum fluctuations are an essential and ubiquitous part of quantum
field theory. Some experimentally verified effects of vacuum
fluctuations include spontaneous emission and the Lamb shift. Coulomb's law and the electric potential in vacuum near an electric charge are modified.
Theoretically, in QCD multiple vacuum states can coexist. The starting and ending of cosmological inflation
is thought to have arisen from transitions between different vacuum
states. For theories obtained by quantization of a classical theory,
each stationary point of the energy in the configuration space gives rise to a single vacuum. String theory is believed to have a huge number of vacua – the so-called string theory landscape.
Outer space
has very low density and pressure, and is the closest physical
approximation of a perfect vacuum. But no vacuum is truly perfect, not
even in interstellar space, where there are still a few hydrogen atoms
per cubic meter.
Stars, planets, and moons keep their atmospheres
by gravitational attraction, and as such, atmospheres have no clearly
delineated boundary: the density of atmospheric gas simply decreases
with distance from the object. The Earth's atmospheric pressure drops to
about 32 millipascals (4.6×10−6 psi) at 100 kilometres (62 mi) of altitude, the Kármán line,
which is a common definition of the boundary with outer space. Beyond
this line, isotropic gas pressure rapidly becomes insignificant when
compared to radiation pressure from the Sun and the dynamic pressure of the solar winds, so the definition of pressure becomes difficult to interpret. The thermosphere in this range has large gradients of pressure, temperature and composition, and varies greatly due to space weather. Astrophysicists prefer to use number density to describe these environments, in units of particles per cubic centimetre.
But although it meets the definition of outer space, the
atmospheric density within the first few hundred kilometers above the
Kármán line is still sufficient to produce significant drag on satellites. Most artificial satellites operate in this region called low Earth orbit and must fire their engines every couple of weeks or a few times a year (depending on solar activity). The drag here is low enough that it could theoretically be overcome by radiation pressure on solar sails, a proposed propulsion system for interplanetary travel.
Planets are too massive for their trajectories to be significantly
affected by these forces, although their atmospheres are eroded by the
solar winds.
The quality of a vacuum is indicated by the amount of matter
remaining in the system, so that a high quality vacuum is one with very
little matter left in it. Vacuum is primarily measured by its absolute pressure, but a complete characterization requires further parameters, such as temperature and chemical composition. One of the most important parameters is the mean free path
(MFP) of residual gases, which indicates the average distance that
molecules will travel between collisions with each other. As the gas
density decreases, the MFP increases, and when the MFP is longer than
the chamber, pump, spacecraft, or other objects present, the continuum
assumptions of fluid mechanics do not apply. This vacuum state is called high vacuum,
and the study of fluid flows in this regime is called particle gas
dynamics. The MFP of air at atmospheric pressure is very short, 70 nm, but at 100 mPa (~1×10−3Torr) the MFP of room temperature air is roughly 100 mm, which is on the order of everyday objects such as vacuum tubes. The Crookes radiometer turns when the MFP is larger than the size of the vanes.
Vacuum quality is subdivided into ranges according to the
technology required to achieve it or measure it. These ranges do not
have universally agreed definitions, but a typical distribution is shown
in the following table. As we travel into orbit, outer space and ultimately intergalactic space, the pressure varies by several orders of magnitude.
Pressure ranges of each quality of vacuum in different units
Atmospheric pressure is variable but standardized at 101.325 kPa (760 Torr).
Low vacuum, also called rough vacuum or coarse vacuum, is vacuum that can be achieved or measured with rudimentary equipment such as a vacuum cleaner and a liquid column manometer.
Medium vacuum is vacuum that can be achieved with a single
pump, but the pressure is too low to measure with a liquid or mechanical
manometer. It can be measured with a McLeod gauge, thermal gauge or a capacitive gauge.
High vacuum is vacuum where the MFP
of residual gases is longer than the size of the chamber or of the
object under test. High vacuum usually requires multi-stage pumping and
ion gauge measurement. Some texts differentiate between high vacuum and very high vacuum.
Ultra high vacuum requires baking the chamber to remove trace
gases, and other special procedures. British and German standards
define ultra high vacuum as pressures below 10−6 Pa (10−8 Torr).
Deep space is generally much more empty than any artificial
vacuum. It may or may not meet the definition of high vacuum above,
depending on what region of space and astronomical bodies are being
considered. For example, the MFP of interplanetary space is smaller than
the size of the Solar System, but larger than small planets and moons.
As a result, solar winds exhibit continuum flow on the scale of the
Solar System, but must be considered a bombardment of particles with
respect to the Earth and Moon.
Perfect vacuum is an ideal state of no particles at all. It cannot be achieved in a laboratory,
although there may be small volumes which, for a brief moment, happen
to have no particles of matter in them. Even if all particles of matter
were removed, there would still be photons and gravitons, as well as dark energy, virtual particles, and other aspects of the quantum vacuum.
Hard vacuum and soft vacuum are terms that are defined with a dividing line defined differently by different sources, such as 1 Torr, or 0.1 Torr, the common denominator being that a hard vacuum is a higher vacuum than a soft one.
Relative versus absolute measurement
Vacuum is measured in units of pressure,
typically as a subtraction relative to ambient atmospheric pressure on
Earth. But the amount of relative measurable vacuum varies with local
conditions. On the surface of Venus,
where ground level atmospheric pressure is much higher than on Earth,
much higher relative vacuum readings would be possible. On the surface
of the moon with almost no atmosphere, it would be extremely difficult
to create a measurable vacuum relative to the local environment.
Similarly, much higher than normal relative vacuum readings are possible deep in the Earth's ocean. A submarine
maintaining an internal pressure of 1 atmosphere submerged to a depth
of 10 atmospheres (98 metres; a 9.8 metre column of seawater has the
equivalent weight of 1 atm) is effectively a vacuum chamber keeping out
the crushing exterior water pressures, though the 1 atm inside the
submarine would not normally be considered a vacuum.
Therefore, to properly understand the following discussions of
vacuum measurement, it is important that the reader assumes the relative
measurements are being done on Earth at sea level, at exactly 1
atmosphere of ambient atmospheric pressure.
Measurements relative to 1 atm
A glass McLeod gauge, drained of mercury
The SI unit of pressure is the pascal (symbol Pa), but vacuum is often measured in torrs, named for an Italian physicist Torricelli (1608–1647). A torr is equal to the displacement of a millimeter of mercury (mmHg) in a manometer with 1 torr equaling 133.3223684 pascals above absolute zero pressure. Vacuum is often also measured on the barometric scale or as a percentage of atmospheric pressure in bars or atmospheres. Low vacuum is often measured in millimeters of mercury
(mmHg) or pascals (Pa) below standard atmospheric pressure. "Below
atmospheric" means that the absolute pressure is equal to the current
atmospheric pressure.
In other words, most low vacuum gauges that read, for example
50.79 Torr. Many inexpensive low vacuum gauges have a margin of error
and may report a vacuum of 0 Torr but in practice this generally
requires a two-stage rotary vane or other medium type of vacuum pump to
go much beyond (lower than) 1 torr.
Measuring instruments
Many devices are used to measure the pressure in a vacuum, depending on what range of vacuum is needed.
Hydrostatic gauges (such as the mercury column manometer)
consist of a vertical column of liquid in a tube whose ends are exposed
to different pressures. The column will rise or fall until its weight
is in equilibrium with the pressure differential between the two ends of
the tube. The simplest design is a closed-end U-shaped tube, one side
of which is connected to the region of interest. Any fluid can be used,
but mercury
is preferred for its high density and low vapour pressure. Simple
hydrostatic gauges can measure pressures ranging from 1 torr (100 Pa) to
above atmospheric. An important variation is the McLeod gauge
which isolates a known volume of vacuum and compresses it to multiply
the height variation of the liquid column. The McLeod gauge can measure
vacuums as high as 10−6 torr (0.1 mPa), which is the lowest
direct measurement of pressure that is possible with current technology.
Other vacuum gauges can measure lower pressures, but only indirectly by
measurement of other pressure-controlled properties. These indirect
measurements must be calibrated via a direct measurement, most commonly a
McLeod gauge.
The kenotometer is a particular type of hydrostatic gauge,
typically used in power plants using steam turbines. The kenotometer
measures the vacuum in the steam space of the condenser, that is, the
exhaust of the last stage of the turbine.
Mechanical or elastic gauges depend on a Bourdon
tube, diaphragm, or capsule, usually made of metal, which will change
shape in response to the pressure of the region in question. A variation
on this idea is the capacitance manometer, in which the
diaphragm makes up a part of a capacitor. A change in pressure leads to
the flexure of the diaphragm, which results in a change in capacitance.
These gauges are effective from 103 torr to 10−4 torr, and beyond.
Thermal conductivity gauges rely on the fact that the
ability of a gas to conduct heat decreases with pressure. In this type
of gauge, a wire filament is heated by running current through it. A thermocouple or Resistance Temperature Detector
(RTD) can then be used to measure the temperature of the filament. This
temperature is dependent on the rate at which the filament loses heat
to the surrounding gas, and therefore on the thermal conductivity. A
common variant is the Pirani gauge which uses a single platinum filament as both the heated element and RTD. These gauges are accurate from 10 torr to 10−3 torr, but they are sensitive to the chemical composition of the gases being measured.
Ionization gauges are used in ultrahigh vacuum. They come in two types: hot cathode and cold cathode. In the hot cathode
version an electrically heated filament produces an electron beam. The
electrons travel through the gauge and ionize gas molecules around them.
The resulting ions are collected at a negative electrode. The current
depends on the number of ions, which depends on the pressure in the
gauge. Hot cathode gauges are accurate from 10−3 torr to 10−10 torr. The principle behind cold cathode
version is the same, except that electrons are produced in a discharge
created by a high voltage electrical discharge. Cold cathode gauges are
accurate from 10−2 torr to 10−9 torr. Ionization
gauge calibration is very sensitive to construction geometry, chemical
composition of gases being measured, corrosion and surface deposits.
Their calibration can be invalidated by activation at atmospheric
pressure or low vacuum. The composition of gases at high vacuums will
usually be unpredictable, so a mass spectrometer must be used in
conjunction with the ionization gauge for accurate measurement.
Uses
Light bulbs contain a partial vacuum, usually backfilled with argon, which protects the tungsten filament
This
shallow water well pump reduces atmospheric air pressure inside the
pump chamber. Atmospheric pressure extends down into the well, and
forces water up the pipe into the pump to balance the reduced pressure.
Above-ground pump chambers are only effective to a depth of
approximately 9 meters due to the water column weight balancing the
atmospheric pressure.
Manifold vacuum can be used to drive accessories on automobiles. The best known application is the vacuum servo, used to provide power assistance for the brakes. Obsolete applications include vacuum-driven windscreen wipers and Autovac
fuel pumps. Some aircraft instruments (Attitude Indicator (AI) and the
Heading Indicator (HI)) are typically vacuum-powered, as protection
against loss of all (electrically powered) instruments, since early
aircraft often did not have electrical systems, and since there are two
readily available sources of vacuum on a moving aircraft, the engine and
an external venturi.
Vacuum induction melting uses electromagnetic induction within a vacuum.
Maintaining a vacuum in the condenser is an important aspect of the efficient operation of steam turbines. A steam jet ejector or liquid ring vacuum pump
is used for this purpose. The typical vacuum maintained in the
condenser steam space at the exhaust of the turbine (also called
condenser backpressure) is in the range 5 to 15 kPa (absolute),
depending on the type of condenser and the ambient conditions.
Evaporation and sublimation into a vacuum is called outgassing. All materials, solid or liquid, have a small vapour pressure,
and their outgassing becomes important when the vacuum pressure falls
below this vapour pressure. Outgassing has the same effect as a leak
and will limit the achievable vacuum. Outgassing products may condense
on nearby colder surfaces, which can be troublesome if they obscure
optical instruments or react with other materials. This is of great
concern to space missions, where an obscured telescope or solar cell can
ruin an expensive mission.
The most prevalent outgassing product in vacuum systems is water
absorbed by chamber materials. It can be reduced by desiccating or
baking the chamber, and removing absorbent materials. Outgassed water
can condense in the oil of rotary vane pumps
and reduce their net speed drastically if gas ballasting is not used.
High vacuum systems must be clean and free of organic matter to minimize
outgassing.
Ultra-high vacuum systems are usually baked, preferably under
vacuum, to temporarily raise the vapour pressure of all outgassing
materials and boil them off. Once the bulk of the outgassing materials
are boiled off and evacuated, the system may be cooled to lower vapour
pressures and minimize residual outgassing during actual operation. Some
systems are cooled well below room temperature by liquid nitrogen to shut down residual outgassing and simultaneously cryopump the system.
Pumping and ambient air pressure
Deep
wells have the pump chamber down in the well close to the water
surface, or in the water. A "sucker rod" extends from the handle down
the center of the pipe deep into the well to operate the plunger. The
pump handle acts as a heavy counterweight against both the sucker rod
weight and the weight of the water column standing on the upper plunger
up to ground level.
Fluids cannot generally be pulled, so a vacuum cannot be created by suction.
Suction can spread and dilute a vacuum by letting a higher pressure
push fluids into it, but the vacuum has to be created first before
suction can occur. The easiest way to create an artificial vacuum is to
expand the volume of a container. For example, the diaphragm muscle
expands the chest cavity, which causes the volume of the lungs to
increase. This expansion reduces the pressure and creates a partial
vacuum, which is soon filled by air pushed in by atmospheric pressure.
To continue evacuating a chamber indefinitely without requiring
infinite growth, a compartment of the vacuum can be repeatedly closed
off, exhausted, and expanded again. This is the principle behind positive displacement pumps,
like the manual water pump for example. Inside the pump, a mechanism
expands a small sealed cavity to create a vacuum. Because of the
pressure differential, some fluid from the chamber (or the well, in our
example) is pushed into the pump's small cavity. The pump's cavity is
then sealed from the chamber, opened to the atmosphere, and squeezed
back to a minute size.
A cutaway view of a turbomolecular pump, a momentum transfer pump used to achieve high vacuum
The above explanation is merely a simple introduction to vacuum
pumping, and is not representative of the entire range of pumps in use.
Many variations of the positive displacement pump have been developed,
and many other pump designs rely on fundamentally different principles. Momentum transfer pumps,
which bear some similarities to dynamic pumps used at higher pressures,
can achieve much higher quality vacuums than positive displacement
pumps. Entrapment pumps
can capture gases in a solid or absorbed state, often with no moving
parts, no seals and no vibration. None of these pumps are universal;
each type has important performance limitations. They all share a
difficulty in pumping low molecular weight gases, especially hydrogen, helium, and neon.
The lowest pressure that can be attained in a system is also
dependent on many things other than the nature of the pumps. Multiple
pumps may be connected in series, called stages, to achieve higher
vacuums. The choice of seals, chamber geometry, materials, and pump-down
procedures will all have an impact. Collectively, these are called vacuum technique.
And sometimes, the final pressure is not the only relevant
characteristic. Pumping systems differ in oil contamination, vibration,
preferential pumping of certain gases, pump-down speeds, intermittent
duty cycle, reliability, or tolerance to high leakage rates.
In ultra high vacuum systems, some very "odd" leakage paths and outgassing sources must be considered. The water absorption of aluminium and palladium becomes an unacceptable source of outgassing, and even the adsorptivity of hard metals such as stainless steel or titanium
must be considered. Some oils and greases will boil off in extreme
vacuums. The permeability of the metallic chamber walls may have to be
considered, and the grain direction of the metallic flanges should be
parallel to the flange face.
The lowest pressures currently achievable in laboratory are about 1×10−13 torrs (13 pPa). However, pressures as low as 5×10−17 torrs (6.7 fPa) have been indirectly measured in a 4 K (−269.15 °C; −452.47 °F) cryogenic vacuum system. This corresponds to ≈100 particles/cm3.
Humans and animals exposed to vacuum will lose consciousness after a few seconds and die of hypoxia
within minutes, but the symptoms are not nearly as graphic as commonly
depicted in media and popular culture. The reduction in pressure lowers
the temperature at which blood and other body fluids boil, but the
elastic pressure of blood vessels ensures that this boiling point
remains above the internal body temperature of 37 °C. Although the blood will not boil, the formation of gas bubbles in bodily fluids at reduced pressures, known as ebullism,
is still a concern. The gas may bloat the body to twice its normal size
and slow circulation, but tissues are elastic and porous enough to
prevent rupture. Swelling and ebullism can be restrained by containment in a flight suit. Shuttle
astronauts wore a fitted elastic garment called the Crew Altitude
Protection Suit (CAPS) which prevents ebullism at pressures as low as
2 kPa (15 Torr). Rapid boiling will cool the skin and create frost, particularly in the mouth, but this is not a significant hazard.
Animal experiments show that rapid and complete recovery is
normal for exposures shorter than 90 seconds, while longer full-body
exposures are fatal and resuscitation has never been successful. A study by NASA on eight chimpanzees found all of them survived two and a half minute exposures to vacuum.
There is only a limited amount of data available from human accidents,
but it is consistent with animal data. Limbs may be exposed for much
longer if breathing is not impaired. Robert Boyle was the first to show in 1660 that vacuum is lethal to small animals.
An experiment indicates that plants are able to survive in a low pressure environment (1.5 kPa) for about 30 minutes.
Cold or oxygen-rich atmospheres can sustain life at pressures
much lower than atmospheric, as long as the density of oxygen is similar
to that of standard sea-level atmosphere. The colder air temperatures
found at altitudes of up to 3 km generally compensate for the lower
pressures there. Above this altitude, oxygen enrichment is necessary to prevent altitude sickness in humans that did not undergo prior acclimatization, and spacesuits are necessary to prevent ebullism above 19 km. Most spacesuits use only 20 kPa (150 Torr) of pure oxygen. This pressure is high enough to prevent ebullism, but decompression sickness and gas embolisms can still occur if decompression rates are not managed.
Rapid decompression can be much more dangerous than vacuum
exposure itself. Even if the victim does not hold his or her breath,
venting through the windpipe may be too slow to prevent the fatal
rupture of the delicate alveoli of the lungs. Eardrums
and sinuses may be ruptured by rapid decompression, soft tissues may
bruise and seep blood, and the stress of shock will accelerate oxygen
consumption leading to hypoxia. Injuries caused by rapid decompression are called barotrauma. A pressure drop of 13 kPa (100 Torr), which produces no symptoms if it is gradual, may be fatal if it occurs suddenly.