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== '''[[Ideal gas law]]''' ==
{{:{{FeaturedArticleTitle}}}}
''by  [[User:Milton Beychok|Milton Beychok]] and [[User:Paul Wormer|Paul Wormer]] (and [[User:Daniel Mietchen|Daniel Mietchen]] and [[User:David E. Volk|David E. Volk]])
<small>
 
==Footnotes==
----
{|  class="wikitable" style="float: right;"
! Values of ''R''
! Units
|-
| 8.314472
|  [[Joule|J]]·[[Kelvin|K]]<sup>-1</sup>·[[Mole (unit)|mol]]<sup>-1</sup>
|-
| 0.082057
| [[Liter|L]]·[[atmosphere (unit)|atm]]·K<sup>-1</sup>·mol<sup>-1</sup>
|-
| 8.205745 × 10<sup>-5</sup>
|  [[metre|m]]<sup>3</sup>·atm·K<sup>-1</sup>·mol<sup>-1</sup>
|-
| 8.314472
| L·k[[Pascal (unit)|Pa]]·K<sup>-1</sup>·mol<sup>-1</sup>
|-
| 8.314472
| m<sup>3</sup>·Pa·K<sup>-1</sup>·mol<sup>-1</sup>
|-
| 62.36367
| L·[[mmHg]]·K<sup>-1</sup>·mol<sup>-1</sup>
|-
| 62.36367
| L·[[torr]]·K<sup>-1</sup>·mol<sup>-1</sup>
|-
| 83.14472
| L·m[[Bar (unit)|bar]]·K<sup>-1</sup>·mol<sup>-1</sup>
|-
| 10.7316
| [[Foot (unit)|ft]]<sup>3</sup>·[[Psi (unit)|psi]]· [[Rankine scale|°R]]<sup>-1</sup>·[[lb-mol]]<sup>-1</sup>
|-
|  0.73024
| ft<sup>3</sup>·atm·°R<sup>-1</sup>·lb-mol<sup>-1</sup>
|}
 
The '''[[ideal gas law]]''' is the [[equation of state]] of an '''ideal gas''' (also known as a '''perfect gas''') that relates its [[Pressure#Absolute pressure versus gauge pressure|absolute pressure]] ''p'' to its [[temperature|absolute temperature]] ''T''. Further parameters that enter the equation are the [[volume]] ''V'' of the container holding the gas and the [[amount of substance|amount]] ''n'' (in [[mole (unit)|moles]]) of gas contained in there. The law reads
:<math> pV = nRT \,</math>
where ''R'' is the [[molar gas constant]], defined as the product of the [[Boltzmann constant]] ''k''<sub>B</sub> and  [[Avogadro's constant]] ''N''<sub>A</sub>
:<math>
R \equiv N_\mathrm{A} k_\mathrm{B}
</math>
Currently, the most accurate value of R is:<ref>[http://physics.nist.gov/cgi-bin/cuu/Value?r Molar gas constant] Obtained from the [[NIST]] website. [http://www.webcitation.org/query?url=http%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fr&date=2009-01-03 (Archived by WebCite® at http://www.webcitation.org/5dZ3JDcYN on Jan 3, 2009)]</ref>  8.314472 ± 0.000015 J·K<sup>-1</sup>·mol<sup>-1</sup>.
 
The law applies to ''ideal gases'' which are hypothetical gases that consist of [[molecules]]<ref>Atoms may be seen as mono-atomic molecules.</ref> that do not interact, i.e., that move through the container independently of each other.  In contrast to what is sometimes stated (see, e.g., Ref.<ref>[http://en.wikipedia.org/w/index.php?oldid=261421829 Wikipedia: Ideal gas law] Version of January 2, 2009</ref>) an ideal gas does not necessarily consist of [[point particle]]s without internal structure, but may be formed by polyatomic molecules with internal rotational, vibrational, and electronic [[degrees of freedom]]. The ideal gas law describes the motion of the [[center of mass|centers of mass]] of the molecules and, indeed, mass centers may be seen as structureless point masses. However, for other properties of ideal gases, such as [[entropy (thermodynamics)|entropy]], the internal structure may play a role.
 
The ideal gas law is a useful approximation for calculating temperatures, volumes, pressures or amount of substance for many gases over a wide range of values, as long as the temperatures and pressures are far from the values where [[condensation]] or [[sublimation]] occur. 
 
Real gases deviate from ideal gas behavior because the intermolecular attractive and repulsive forces cause the motions of the molecules to be correlated.  The deviation is especially significant at low temperatures or high pressures, i.e., close to condensation.  A conventional measure for this deviation is the [[Compressibility factor (gases)|compressibility factor]].
 
There are many equations of state available for use with real gases, the simplest of which is the [[van der Waals equation]].
 
=== Historic background ===
 
The early work on the behavior of gases began in pre-industrialized [[Europe]] in the latter half of the 17th century by [[Robert Boyle]] who formulated ''[[Boyle's law]]'' in 1662 (independently confirmed by [[Edme Mariotte]] at about the same time).<ref name=Savidge>[http://www.ceesi.com/docs_techlib/events/ishm2003/Docs/1040.pdf Compressibility of Natural Gas] Jeffrey L. Savidge, 78th International School for Hydrocarbon Measurement (Class 1040), 2003. From the website of the Colorado Engineering Experiment Station, Inc. (CEESI).</ref>  Their work on air at low pressures established the inverse relationship between pressure and volume, ''V'' = constant / ''p'' at constant temperature and a fixed amount of air. ''Boyle's Law'' is often referred to as the ''Boyles-Mariotte Law''.
 
''[[Ideal gas law|.... (read more)]]''
 
{| class="wikitable collapsible collapsed" style="width: 90%; float: center; margin: 0.5em 1em 0.8em 0px;"
|-
! style="text-align: center;" | &nbsp;[[Volatility (chemistry)#References|notes]]
|-
|
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</small>

Latest revision as of 10:19, 11 September 2020

Nuclear weapons proliferation is one of the four big issues that have held back worldwide deployment of peaceful nuclear power. This article will address the proliferation questions raised in Nuclear power reconsidered.

As of 2022, countries with nuclear weapons have followed one or both of two paths in producing fissile materials for nuclear weapons: enrichment of uranium to very high fractions of U-235, or extraction of fissile plutonium (Pu-239) from irradiated uranium nuclear reactor fuel. The US forged the way on both paths during its World War II Manhattan Project. The fundamental aspects of both paths are well understood, but both are technically challenging. Even relatively poor countries can be successful if they have sufficient motivation, financial investment, and, in some cases, direct or illicit assistance from more technologically advanced countries.

The International Non-proliferation Regime

The International Atomic Energy Agency (IAEA) has a vigorous program to prevent additional countries from acquiring nuclear weapons. The Treaty on the Non-Proliferation of Nuclear Weapons (NPT) is the cornerstone arrangement under which strategic rivals can trust, by independent international verification, that their rivals are not developing a nuclear weapons threat. The large expense of weapons programs makes it very unlikely that a country would start its own nuclear weapons program, if it knows that its rivals are not so engaged. With some notable and worrying exceptions, this program has been largely successful.

Paths to the Bomb

It is frequently claimed that building a civil nuclear power program adds to the weapons proliferation risk. There is an overlap in the two distinct technologies, after all. To build a bomb, one needs Highly Enriched Uranium (HEU) or weapons-grade plutonium (Pu-239). Existing reactors running on Low Enriched Uranium (LEU, under 5% U-235) or advanced reactors running on High Assay LEU (HALEU,up to 20% U-235) use the same technology that can enrich uranium to very high levels, but configured differently. Enrichment levels and centrifuge configurations can be monitored using remote cameras, on-site inspections, and installed instrumentation -- hence the value of international inspections by the IAEA. Using commercial power reactors as a weapons plutonium source is an extremely ineffective, slow, expensive, and easily detectable way to produce Pu. Besides the nuclear physics issues, refueling pressurized water reactors is both time-consuming and obvious to outside observers. That is why the US and other countries developed specialized Pu production reactors and/or uranium enrichment to produce fissile cores for nuclear weapons.

Future Threats and Barriers

Minimizing the risk of future proliferation in states that want to buy nuclear reactors or fuel might require one or more barriers:
1) Insisting on full transparency for all nuclear activities in buyer states, including monitoring and inspections by the International Atomic Energy Agency (IAEA).
2) Limiting fuel processing to just a few supplier states that already have weapons or are approved by the IAEA.
3) Ensuring that fuel at any stage after initial fabrication has an isotopic composition unsuitable for weapons. "Spiking" the initial fuel with non-fissile isotopes, if necessary.
4) Limiting the types of reactors deployed to buyer states. In general, breeders are less secure than burners. Sealed reactor modules are more secure than reactors with on-site fuel processing.
5) Providing incentives and assurances for buyer states to go along with all of the above.
6) Application of diplomatic pressure, sanctions, and other economic measures to non-compliant states.
7) Agreement that any reactor declared rogue by the IAEA will be "fair game" for any state feeling threatened.

Footnotes