Pressure

Pressure
Common symbols	p, P
SI unit	Pascal (Pa)
In SI base units	1 N/m2 or 1 kg/(m·s2)
Derivations from other quantities	p = F / A

Pressure as exerted by particle collisions inside a closed container.

Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled gage pressure)^[a] is the pressure relative to the local atmospheric or ambient pressure.

Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre; similarly, the pound-force per square inch (psi) is the traditional unit of pressure in the imperial and US customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure and the torr is defined as ¹⁄₇₆₀ of this. Manometric units such as the centimetre of water, millimetre of mercury and inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer.

Definition

Pressure is the amount of force acting per unit area. The symbol for pressure is p or P.^[1] The IUPAC recommendation for pressure is a lower-case p.^[2] However, upper-case P is widely used. The usage of P vs p depends on the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, and on writing style.

Formula

Mathematically:

where:

is the pressure,

is the normal force,

is the area of the surface on contact.

Pressure is a scalar quantity. It relates the vector surface element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:

The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation.

It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.

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.

Units

Mercury column

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m² or kg·m⁻¹·s⁻²). This name for the unit was added in 1971;^[3] before that, pressure in SI was expressed simply in newtons per square metre.

Other units of pressure, such as pounds per square inch and bar, are also in common use. The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm⁻² or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm² or kg/cm²) and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm² (98.0665 kPa or 14.223 psi).

Since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to energy density and may be measured in units such as joules per cubic metre.

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 most other fields, where the hecto- prefix is rarely used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth.

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 7005101325000000000♠101325 Pa.

Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., centimetres of water, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury's high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When millimetres of mercury or inches of mercury are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units.^{[citation needed]} One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimetres of mercury in most of the world, and lung pressures in centimetres of water are still common.
Underwater divers use the metre sea water (msw or MSW) and foot sea water (fsw or FSW) units of pressure, and these are the standard units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers. A msw is defined as 0.1 bar, and is not the same as a linear metre of depth, and 33.066 fsw = 1 atm.^[4] Note that the pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft
Gauge pressure is often given in units with 'g' appended, e.g. 'kPag', 'barg' or 'psig', and units for measurements of absolute pressure are sometimes given a suffix of 'a', to avoid confusion, for example 'kPaa', 'psia'. However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure^[5] For example, "p_g = 100 psi" rather than "p = 100 psig".

Differential pressure is expressed in units with 'd' appended; this type of measurement is useful when considering sealing performance or whether a valve will open or close.

Presently or formerly popular pressure units include the following:

• atmosphere (atm)
• manometric units:
  • centimetre, inch, and millimetre of mercury (torr)
  • Height of equivalent column of water, including millimetre (mm H
    2O), centimetre (cm H
    2O), metre, inch, and foot of water
• imperial and customary units:
  • kip, short ton-force, long ton-force, pound-force, ounce-force, and poundal per square inch
  • short ton-force and long ton-force per square inch
  • fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and decompression
• non-SI metric units:
  • bar, decibar, millibar
    • msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and decompression
  • 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)

Pressure units

	Pascal	Bar	Technical atmosphere	Standard atmosphere	Torr	Pounds per square inch
	(Pa)	(bar)	(at)	(atm)	(Torr)	(psi)
1 Pa	≡ 1 N/m2	10−5	6995101970000000000♠1.0197×10−5	6994986919999999999♠9.8692×10−6	6997750060000000000♠7.5006×10−3	6996145037700000000♠1.450377×10−4
1 bar	105	≡ 100 kPa ≡ 106 dyn/cm2	7000101970000000000♠1.0197	6999986920000000000♠0.98692	7002750060000000000♠750.06	7001145037700000000♠14.50377
1 at	7004980665000000000♠0.980665×105	6999980665000000000♠0.980665	≡ 1 kp/cm2	6999967841100000000♠0.9678411	7002735559200000000♠735.5592	7001142233400000000♠14.22334
1 atm	7005101325000000000♠1.01325×105	7000101325000000000♠1.01325	7000103319999999999♠1.0332	1	≡ 7002760000000000000♠760	7001146959500000000♠14.69595
1 Torr	7002133322399999999♠133.3224	6997133322400000000♠1.333224×10−3	6997135955100000000♠1.359551×10−3	6997131578900000000♠1.315789×10−3	≡ 1/760 atm ≈ 1 mmHg	6998193367800000000♠1.933678×10−2
1 psi	7003689480000000000♠6.8948×103	6998689480000000000♠6.8948×10−2	6998703069000000000♠7.03069×10−2	6998680460000000000♠6.8046×10−2	7001517149300000000♠51.71493	≡ 1 lbF /in2

Examples

The effects of an external pressure of 700bar on an aluminum cylinder with 5mm wall thickness

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 negative gradient of pressure is called the force density.
Another example is of a common knife. If we try to cut a fruit with the flat side it obviously will not cut. But if we take the thin side, it will cut smoothly. The reason is that the flat side has a greater surface area (less pressure) and so it does not cut the fruit. When we take the thin side, the surface area is reduced and so it cuts the fruit easily and quickly. This is one example of a practical application of pressure.

For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure. An example of this is the air pressure in an automobile tire, which might be said to be "220 kPa (32 psi)", but is actually 220 kPa (32 psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa (14.7 psi), the absolute pressure in the tire is therefore about 320 kPa (46.7 psi). In technical work, this is written "a gauge pressure of 220 kPa (32 psi)". Where space is limited, such as on pressure 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 of 32 psi is sometimes written as "32 psig" and an absolute pressure as "32 psia", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.^[6]

Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is 100 kPa, a gas (such as helium) at 200 kPa (gauge) (300 kPa [absolute]) is 50% denser than the same gas at 100 kPa (gauge) (200 kPa [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.

Scalar nature

In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, 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 a very small point (becoming less true as we approach the atomic scale), and the pressure will still have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense 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 (at right angle) to the surface.

A closely related quantity is the stress tensor σ, which relates the vector force to the vector area via

This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure.

According to the theory of general relativity, pressure increases the strength of a gravitational field (see stress–energy tensor) and so adds to the mass-energy cause of gravity. This effect is unnoticeable at everyday pressures but is significant in neutron stars, although it has not been experimentally tested.^[7]

Types

Fluid pressure

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

Fluid pressure occurs in one of two situations:

1. an open condition, called "open channel flow", e.g. the ocean, a swimming pool, or the atmosphere.
2. a closed condition, called "closed conduit", e.g. a water line or gas line.

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

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

The concepts of fluid pressure are predominantly attributed to the discoveries of Blaise Pascal and Daniel Bernoulli. Bernoulli's equation can be used in almost any situation to determine the pressure at any point in a fluid. The equation makes some assumptions about the fluid, such as the fluid being ideal^[8] and incompressible.^[8] An ideal fluid is a fluid in which there is no friction, it is inviscid,^[8] zero viscosity.^[8] The equation for all points of a system filled with a constant-density fluid is

^[9]

where:

p = pressure of the fluid

γ = ρg = density·acceleration of gravity = specific weight of the fluid.^[8]

v = velocity of the fluid

g = acceleration of gravity

z = elevation

= pressure head

= velocity head

Applications

• Hydraulic brakes
• Artesian well
• Blood pressure
• Hydraulic head
• Plant cell turgidity
• Pythagorean cup

Explosion or deflagration pressures

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

Negative pressures

low pressure chamber in Bundesleistungszentrum Kienbaum, Germany

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

• When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of −21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa).
• When attractive intermolecular forces (e.g., van der Waals forces or hydrogen bonds) between the particles of a fluid exceed repulsive forces due to thermal motion. These forces explain ascent of sap in tall plants. An apparent negative pressure must act on water molecules at the top of any tree taller than 10 m, which is the pressure head of water that balances the atmospheric pressure. Intermolecular forces maintain cohesion of columns of sap that run continuously in xylem from the roots to the top leaves.^[10]
• The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed "vacuum pressure" (not to be confused with the negative gauge pressure of a vacuum).
• For non-isotropic stresses in rigid bodies, depending on how the orientation of a surface is chosen, the same distribution of forces may have a component of positive pressure along one surface normal, with a component of negative pressure acting along the another surface normal.
  • The stresses in an electromagnetic field are generally non-isotropic, with the pressure normal to one surface element (the normal stress) being negative, and positive for surface elements perpendicular to this.
• In the cosmological constant.

Stagnation pressure

Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by:

where

is the stagnation pressure

is the flow velocity

is the static pressure.

The pressure of a moving fluid can be measured using a Pitot tube, 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 pressures or stagnation pressures.

Surface pressure and surface tension

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

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

Surface tension is another example of surface pressure, but with a reversed sign, because "tension" is the opposite to "pressure".

Pressure of an ideal gas

In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume.

where:

p is the absolute pressure of the gas

n is the amount of substance

T is the absolute temperature

V is the volume

R is the ideal gas constant.

Real gases exhibit a more complex dependence on the variables of state.^[11]

Vapor pressure

Vapor pressure is the pressure of a vapor in thermodynamic equilibrium with its condensed phases in a closed system. All liquids and solids have a tendency to evaporate into a gaseous form, and all gases have a tendency to condense back to their liquid or solid form.
The atmospheric pressure boiling point of a liquid (also known as the normal boiling point) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure and lift the liquid to form vapor bubbles inside the bulk of the substance. Bubble formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial vapor pressure.

Liquid pressure

When a person swims under the water, water pressure is felt acting on the person's eardrums. The deeper that person swims, the greater the pressure. The pressure felt is due to the weight of the water above the person. As someone swims deeper, there is more water above the person and therefore greater pressure. The pressure a liquid exerts depends on its depth.
Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. The pressure due to a liquid in liquid columns of constant density or at a depth within a substance is represented by the following formula:

where:

p is liquid pressure

g is gravity at the surface of overlaying material

ρ is density of liquid

h is height of liquid column or depth within a substance

Another way of saying this same formula is the following:

Derivation of this equation

This is derived from the definitions of pressure and weight density. Consider an area at the bottom of a vessel of liquid. The weight of the column of liquid directly above this area produces pressure. From the definition: we can express this weight of liquid as where the volume of the column is simply the area multiplied by the depth. Then we have With the "area" in the numerator and the "area" in the denominator canceling each other out, we are left with: Written with symbols, this is our original equation:

The pressure a liquid exerts against the sides and bottom of a container depends on the density and the depth of the liquid. If atmospheric pressure is neglected, liquid pressure against the bottom is twice as great at twice the depth; at three times the depth, the liquid pressure is threefold; etc. Or, if the liquid is two or three times as dense, the liquid pressure is correspondingly two or three times as great for any given depth. Liquids are practically incompressible – that is, their volume can hardly be changed by pressure (water volume decreases by only 50 millionths of its original volume for each atmospheric increase in pressure). Thus, except for small changes produced by temperature, the density of a particular liquid is practically the same at all depths.

Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the total pressure acting on a liquid. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere. When this distinction is important, the term total pressure is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure.

It is important to recognize that the pressure does not depend on the amount of liquid present. Volume is not the important factor – depth is. The average water pressure acting against a dam depends on the average depth of the water and not on the volume of water held back. For example, a wide but shallow lake with a depth of 3 m (10 ft) exerts only half the average pressure that a small 6 m (20 ft) deep pond does (note that the total force applied to the longer dam will be greater, due to the greater total surface area for the pressure to act upon, but for a given 5 foot section of each dam, the 10ft deep water will apply half the force of 20ft deep water). A person will feel the same pressure whether his/her head is dunked a metre beneath the surface of the water in a small pool or to the same depth in the middle of a large lake. If four vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimetres deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference what vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the narrower vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.

Restating this as energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, gravitational potential energy is large but liquid pressure energy is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure energy. The sum of pressure energy and gravitational potential energy per unit volume is constant throughout the volume of the fluid and the two energy components change linearly with the depth.^[12] Mathematically, it is described by Bernoulli's equation where velocity head is zero and comparisons per unit volume in the vessel are:

Terms have the same meaning as in section Fluid pressure.

Direction of liquid pressure

An experimentally determined fact about liquid pressure is that it is exerted equally in all directions.^[13] If someone is submerged in water, no matter which way that person tilts his/her head, the person will feel the same amount of water pressure on his/her ears. Because a liquid can flow, this pressure isn't only downward. Pressure is seen acting sideways when water spurts sideways from a leak in the side of an upright can. Pressure also acts upward, as demonstrated when someone tries to push a beach ball beneath the surface of the water. The bottom of a boat is pushed upward by water pressure (buoyancy).

When a liquid presses against a surface, there is a net force that is perpendicular to the surface. Although pressure doesn't have a specific direction, force does. A submerged triangular block has water forced against each point from many directions, but components of the force that are not perpendicular to the surface cancel each other out, leaving only a net perpendicular point.^[13] This is why water spurting from a hole in a bucket initially exits the bucket in a direction at right angles to the surface of the bucket in which the hole is located. Then it curves downward due to gravity. If there are three holes in a bucket (top, bottom, and middle), then the force vectors perpendicular to the inner container surface will increase with increasing depth – that is, a greater pressure at the bottom makes it so that the bottom hole will shoot water out the farthest. The force exerted by a fluid on a smooth surface is always at right angles to the surface. The speed of liquid out of the hole is , where h is the depth below the free surface.^[13] Interestingly, this is the same speed the water (or anything else) would have if freely falling the same vertical distance h.

Kinematic pressure

is the kinematic pressure, where is the pressure and constant mass density. The SI unit of P is m²/s². Kinematic pressure is used in the same manner as kinematic viscosity in order to compute Navier–Stokes equation without explicitly showing the density .

Navier–Stokes equation with kinematic quantities

Gas laws

From Wikipedia, the free encyclopedia

The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would hold to a good approximation for all gases. Gases behave in a similar way over a wide variety of conditions because they all have molecules which are widely spaced, and the equation of state for an ideal gas is derived from kinetic theory. The earlier gas laws are now considered as special cases of the ideal gas equation, with one or more of the variables held constant.

Boyle's Law

Boyle's Law, published in 1662, states that, at constant temperature, the product of the pressure and volume of a given mass of an ideal gas in a closed system is always constant. It can be verified experimentally using a pressure gauge and a variable volume container. It can also be derived from the kinetic theory of gases: if a container, with a fixed number of molecules inside, is reduced in volume, more molecules will strike a given area of the sides of the container per unit time, causing a greater pressure.

As a mathematical equation, Boyle's Law is written as either:

, or

, or

where P is the pressure, and V is the volume of a gas, and k₁ is the constant in this equation (and is not the same as the proportionality constants in the other equations below). The statement of Boyle 's law is as follows:

The volume of a given mass of a gas is inversely related to the pressure exerted on it at a given temperature and given number of moles.

Charles' Law

Charles' Law, or the law of volumes, was found in 1787 by Jacques Charles. It states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature, assuming in a closed system.
As a mathematical equation, Charles' Law is written as either:

, or

, or

where V is the volume of a gas, T is the absolute temperature and k₂ is a proportionality constant (which is not the same as the proportionality constants in the other equations in this article).

Gay-Lussac's Law

Gay-Lussac's Law, or the Pressure Law, was found by Joseph Louis Gay-Lussac in 1809. It states that, for a given mass and constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature.
As a mathematical equation, Gay-Lussac's Law is written as either:

, or

, or

where P is the pressure, T is the absolute temperature, and k₃ is another proportionality constant.

Avogadro's Law

Avogadro's Law states that the volume occupied by an ideal gas is directly proportional to the number of molecules of the gas present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm³ (or litres). The relation is given by

where n is equal to the number of molecules of gas (or the number of moles of gas).

Combined and Ideal Gas Laws

The Combined Gas Law or General Gas Equation is obtained by combining Boyle's Law, Charles' Law, and Gay-Lussac's Law. It shows the relationship between the pressure, volume, and temperature for a fixed mass (quantity) of gas:

This can also be written as:

With the addition of Avogadro's Law, the combined gas law develops into the Ideal Gas Law:

where

p is pressure

V is volume

n is the number of moles

R is the universal gas constant

T is temperature (K)

where the proportionality constant, now named R, is the universal gas constant with a value of 0.08206 (atm∙L)/(mol∙K). An equivalent formulation of this Law is:

where

p is the pressure

V is the volume

N is the number of gas molecules

k is the Boltzmann constant (1.381×10⁻²³ J·K⁻¹ in SI units)

T is the absolute temperature

These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature.

This law has the following important consequences:

1. If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.
2. If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.
3. If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.
4. If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.

Other gas laws

• Graham's law states that the rate at which gas molecules diffuse is inversely proportional to the square root of its density. Combined with Avogadro's law (i.e. since equal volumes have equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight.

• Dalton's law of partial pressures states that the pressure of a mixture of gases simply is the sum of the partial pressures of the individual components. Dalton's Law is as follows:

,

OR

where P_Total is the total pressure of the atmosphere, P_Gas is the pressure of the gas mixture in the atmosphere, and P_H2O is the water pressure at that temperature.

• Henry's law states that:

At constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

Albedo

From Wikipedia, the free encyclopedia

Percentage of diffusely reflected sunlight in relation to various surface conditions

Albedo (/ælˈbiːdoʊ/), or reflection coefficient, derived from Latin albedo "whiteness" (or reflected sunlight) in turn from albus "white", is the diffuse reflectivity or reflecting power of a surface.
It is the ratio of reflected radiation from the surface to incident radiation upon it. Its dimensionless nature lets it be expressed as a percentage and is measured on a scale from zero for no reflection of a perfectly black surface to 1 for perfect reflection of a white surface. NOTE: Since it is the ratio of all reflected radiation to incident radiation it will include the diffuse AND the specular radiation reflected. It is, however, common to assume a surface reflects in either a totally specular manner or a totally diffuse manner, as this can simplify calculations.

Albedo depends on the frequency of the radiation. When quoted unqualified, it usually refers to some appropriate average across the spectrum of visible light. In general, the albedo depends on the directional distribution of incident radiation, except for Lambertian surfaces, which scatter radiation in all directions according to a cosine function and therefore have an albedo that is independent of the incident distribution. In practice, a bidirectional reflectance distribution function (BRDF) may be required to accurately characterize the scattering properties of a surface, but albedo is very useful as a first approximation.

The albedo is an important concept in climatology, astronomy, and calculating reflectivity of surfaces in LEED sustainable-rating systems for buildings. The average overall albedo of Earth, its planetary albedo, is 30 to 35% because of cloud cover, but widely varies locally across the surface because of different geological and environmental features.^[1]

The term was introduced into optics by Johann Heinrich Lambert in his 1760 work Photometria.

Terrestrial albedo

Sample albedos

Surface	Typical albedo
Fresh asphalt	0.04[2]
Worn asphalt	0.12[2]
Conifer forest (Summer)	0.08,[3] 0.09 to 0.15[4]
Deciduous trees	0.15 to 0.18[4]
Bare soil	0.17[5]
Green grass	0.25[5]
Desert sand	0.40[6]
New concrete	0.55[5]
Ocean ice	0.5–0.7[5]
Fresh snow	0.80–0.90[5]

Albedos of typical materials in visible light range from up to 0.9 for fresh snow to about 0.04 for charcoal, one of the darkest substances. Deeply shadowed cavities can achieve an effective albedo approaching the zero of a black body. When seen from a distance, the ocean surface has a low albedo, as do most forests, whereas desert areas have some of the highest albedos among landforms. Most land areas are in an albedo range of 0.1 to 0.4.^[7] The average albedo of Earth is about 0.3.^[8] This is far higher than for the ocean primarily because of the contribution of clouds.

2003–2004 mean annual clear-sky and total-sky albedo

Earth's surface albedo is regularly estimated via Earth observation satellite sensors such as NASA's MODIS instruments on board the Terra and Aqua satellites. As the total amount of reflected radiation cannot be directly measured by satellite, a mathematical model of the BRDF is used to translate a sample set of satellite reflectance measurements into estimates of directional-hemispherical reflectance and bi-hemispherical reflectance (e.g.^[9]).

Earth's average surface temperature due to its albedo and the greenhouse effect is currently about 15 °C. If Earth were frozen entirely (and hence be more reflective) the average temperature of the planet would drop below −40 °C.^[10] If only the continental land masses became covered by glaciers, the mean temperature of the planet would drop to about 0 °C.^[11] In contrast, if the entire Earth is covered by water—a so-called aquaplanet—the average temperature on the planet would rise to just under 27 °C.^[12]

White-sky and black-sky albedo

It has been shown that for many applications involving terrestrial albedo, the albedo at a particular solar zenith angle θ_i can reasonably be approximated by the proportionate sum of two terms: the directional-hemispherical reflectance at that solar zenith angle, , and the bi-hemispherical reflectance, the proportion concerned being defined as the proportion of diffuse illumination .
Albedo can then be given as:

Directional-hemispherical reflectance is sometimes referred to as black-sky albedo and bi-hemispherical reflectance as white-sky albedo. These terms are important because they allow the albedo to be calculated for any given illumination conditions from a knowledge of the intrinsic properties of the surface.^[13]

Astronomical albedo

The albedos of planets, satellites and asteroids can be used to infer much about their properties. The study of albedos, their dependence on wavelength, lighting angle ("phase angle"), and variation in time comprises a major part of the astronomical field of photometry. For small and far objects that cannot be resolved by telescopes, much of what we know comes from the study of their albedos. For example, the absolute albedo can indicate the surface ice content of outer Solar System objects, the variation of albedo with phase angle gives information about regolith properties, whereas unusually high radar albedo is indicative of high metal content in asteroids.

Enceladus, a moon of Saturn, has one of the highest known albedos of any body in the Solar System, with 99% of EM radiation reflected. Another notable high-albedo body is Eris, with an albedo of 0.96.^[14] Many small objects in the outer Solar System^[15] and asteroid belt have low albedos down to about 0.05.^[16] A typical comet nucleus has an albedo of 0.04.^[17] Such a dark surface is thought to be indicative of a primitive and heavily space weathered surface containing some organic compounds.

The overall albedo of the Moon is around 0.12, but it is strongly directional and non-Lambertian, displaying also a strong opposition effect.^[18] Although such reflectance properties are different from those of any terrestrial terrains, they are typical of the regolith surfaces of airless Solar System bodies.

Two common albedos that are used in astronomy are the (V-band) geometric albedo (measuring brightness when illumination comes from directly behind the observer) and the Bond albedo (measuring total proportion of electromagnetic energy reflected). Their values can differ significantly, which is a common source of confusion.

In detailed studies, the directional reflectance properties of astronomical bodies are often expressed in terms of the five Hapke parameters which semi-empirically describe the variation of albedo with phase angle, including a characterization of the opposition effect of regolith surfaces.
The correlation between astronomical (geometric) albedo, absolute magnitude and diameter is:^[19] ,
where is the astronomical albedo, is the diameter in kilometers, and is the absolute magnitude.

Examples of terrestrial albedo effects

Illumination

Although the albedo–temperature effect is best known in colder, whiter regions on Earth, the maximum albedo is actually found in the tropics where year-round illumination is greater. The maximum is additionally in the northern hemisphere, varying between three and twelve degrees north.^[20] The minima are found in the subtropical regions of the northern and southern hemispheres, beyond which albedo increases without respect to illumination.^[20]

Insolation effects

The intensity of albedo temperature effects depend on the amount of albedo and the level of local insolation (solar irradiance); high albedo areas in the arctic and antarctic regions are cold due to low insolation, where areas such as the Sahara Desert, which also have a relatively high albedo, will be hotter due to high insolation. Tropical and sub-tropical rain forest areas have low albedo, and are much hotter than their temperate forest counterparts, which have lower insolation. Because insolation plays such a big role in the heating and cooling effects of albedo, high insolation areas like the tropics will tend to show a more pronounced fluctuation in local temperature when local albedo changes.^{[citation needed]}

Climate and weather

Albedo affects climate and drives weather. All weather is a result of the uneven heating of Earth caused by different areas of the planet having different albedos. Essentially, for the driving of weather, there are two types of albedo regions on Earth: Land and ocean. Land and ocean regions produce the four basic different types of air masses, depending on latitude and therefore insolation: Warm and dry, which form over tropical and sub-tropical land masses; warm and wet, which form over tropical and sub-tropical oceans; cold and dry which form over temperate, polar and sub-polar land masses; and cold and wet, which form over temperate, polar and sub-polar oceans. Different temperatures between the air masses result in different air pressures, and the masses develop into pressure systems. High pressure systems flow toward lower pressure, driving weather from north to south in the northern hemisphere, and south to north in the lower; however due to the spinning of Earth, the Coriolis effect further complicates flow and creates several weather/climate bands and the jet streams.

Albedo–temperature feedback

When an area's albedo changes due to snowfall, a snow–temperature feedback results. A layer of snowfall increases local albedo, reflecting away sunlight, leading to local cooling. In principle, if no outside temperature change affects this area (e.g. a warm air mass), the raised albedo and lower temperature would maintain the current snow and invite further snowfall, deepening the snow–temperature feedback. However, because local weather is dynamic due to the change of seasons, eventually warm air masses and a more direct angle of sunlight (higher insolation) cause melting. When the melted area reveals surfaces with lower albedo, such as grass or soil, the effect is reversed: the darkening surface lowers albedo, increasing local temperatures, which induces more melting and thus reducing the albedo further, resulting in still more heating.

Snow

Snow albedo is highly variable, ranging from as high as 0.9 for freshly fallen snow, to about 0.4 for melting snow, and as low as 0.2 for dirty snow.^[21] Over Antarctica they average a little more than 0.8. If a marginally snow-covered area warms, snow tends to melt, lowering the albedo, and hence leading to more snowmelt because more radiation is being absorbed by the snowpack (the ice–albedo positive feedback). Cryoconite, powdery windblown dust containing soot, sometimes reduces albedo on glaciers and ice sheets.^[22] Hence, small errors in albedo can lead to large errors in energy estimates, which is why it is important to measure the albedo of snow-covered areas through remote sensing techniques rather than applying a single value over broad regions.

Small-scale effects

Albedo works on a smaller scale, too. In sunlight, dark clothes absorb more heat and light-coloured clothes reflect it better, thus allowing some control over body temperature by exploiting the albedo effect of the colour of external clothing.^[23]

Solar photovoltaic effects

Albedo can affect the electrical energy output of solar photovoltaic devices. For example, the effects of a spectrally responsive albedo are illustrated by the differences between the spectrally weighted albedo of solar photovoltaic technology based on hydrogenated amorphous silicon (a-Si:H) and crystalline silicon (c-Si)-based compared to traditional spectral-integrated albedo predictions. Research showed impacts of over 10%.^[24] More recently, the analysis was extended to the effects of spectral bias due to the specular reflectivity of 22 commonly occurring surface materials (both human-made and natural) and analyzes the albedo effects on the performance of seven photovoltaic materials covering three common photovoltaic system topologies: industrial (solar farms), commercial flat rooftops and residential pitched-roof applications.^[25]

Trees

Because forests generally have a low albedo, (the majority of the ultraviolet and visible spectrum is absorbed through photosynthesis), some scientists have suggested that greater heat absorption by trees could offset some of the carbon benefits of afforestation (or offset the negative climate impacts of deforestation). In the case of evergreen forests with seasonal snow cover albedo reduction may be great enough for deforestation to cause a net cooling effect.^[26] Trees also impact climate in extremely complicated ways through evapotranspiration. The water vapor causes cooling on the land surface, causes heating where it condenses, acts a strong greenhouse gas, and can increase albedo when it condenses into clouds^[27] Scientists generally treat evapotranspiration as a net cooling impact, and the net climate impact of albedo and evapotranspiration changes from deforestation depends greatly on local climate ^[28]

In seasonally snow-covered zones, winter albedos of treeless areas are 10% to 50% higher than nearby forested areas because snow does not cover the trees as readily. Deciduous trees have an albedo value of about 0.15 to 0.18 whereas coniferous trees have a value of about 0.09 to 0.15.^[4]
Studies by the Hadley Centre have investigated the relative (generally warming) effect of albedo change and (cooling) effect of carbon sequestration on planting forests. They found that new forests in tropical and midlatitude areas tended to cool; new forests in high latitudes (e.g. Siberia) were neutral or perhaps warming.^[29]

Water

Water reflects light very differently from typical terrestrial materials. The reflectivity of a water surface is calculated using the Fresnel equations (see graph).

Reflectivity of smooth water at 20 °C (refractive index=1.333)

At the scale of the wavelength of light even wavy water is always smooth so the light is reflected in a locally specular manner (not diffusely). The glint of light off water is a commonplace effect of this. At small angles of incident light, waviness results in reduced reflectivity because of the steepness of the reflectivity-vs.-incident-angle curve and a locally increased average incident angle.^[30]

Although the reflectivity of water is very low at low and medium angles of incident light, it becomes very high at high angles of incident light such as those that occur on the illuminated side of Earth near the terminator (early morning, late afternoon, and near the poles). However, as mentioned above, waviness causes an appreciable reduction. Because light specularly reflected from water does not usually reach the viewer, water is usually considered to have a very low albedo in spite of its high reflectivity at high angles of incident light.

Note that white caps on waves look white (and have high albedo) because the water is foamed up, so there are many superimposed bubble surfaces which reflect, adding up their reflectivities. Fresh 'black' ice exhibits Fresnel reflection.

Clouds

Cloud albedo has substantial influence over atmospheric temperatures. Different types of clouds exhibit different reflectivity, theoretically ranging in albedo from a minimum of near 0 to a maximum approaching 0.8. "On any given day, about half of Earth is covered by clouds, which reflect more sunlight than land and water. Clouds keep Earth cool by reflecting sunlight, but they can also serve as blankets to trap warmth."^[31]

Albedo and climate in some areas are affected by artificial clouds, such as those created by the contrails of heavy commercial airliner traffic.^[32] A study following the burning of the Kuwaiti oil fields during Iraqi occupation showed that temperatures under the burning oil fires were as much as 10 °C colder than temperatures several miles away under clear skies.^[33]

Aerosol effects

Aerosols (very fine particles/droplets in the atmosphere) have both direct and indirect effects on Earth's radiative balance. The direct (albedo) effect is generally to cool the planet; the indirect effect (the particles act as cloud condensation nuclei and thereby change cloud properties) is less certain.^[34] As per ^[35] the effects are:

• Aerosol direct effect. Aerosols directly scatter and absorb radiation. The scattering of radiation causes atmospheric cooling, whereas absorption can cause atmospheric warming.
• Aerosol indirect effect. Aerosols modify the properties of clouds through a subset of the aerosol population called cloud condensation nuclei. Increased nuclei concentrations lead to increased cloud droplet number concentrations, which in turn leads to increased cloud albedo, increased light scattering and radiative cooling (first indirect effect), but also leads to reduced precipitation efficiency and increased lifetime of the cloud (second indirect effect).

Black carbon

Another albedo-related effect on the climate is from black carbon particles. The size of this effect is difficult to quantify: the Intergovernmental Panel on Climate Change estimates that the global mean radiative forcing for black carbon aerosols from fossil fuels is +0.2 W m⁻², with a range +0.1 to +0.4 W m⁻².^[36] Black carbon is a bigger cause of the melting of the polar ice cap in the Arctic than carbon dioxide due to its effect on the albedo.^[37]

Human activities

Human activities (e.g. deforestation, farming, and urbanization) change the albedo of various areas around the globe. However, quantification of this effect on the global scale is difficult.^{[citation needed]}

Other types of albedo

Single-scattering albedo is used to define scattering of electromagnetic waves on small particles. It depends on properties of the material (refractive index); the size of the particle or particles; and the wavelength of the incoming radiation.