Trace monoid - Revision history

en>BD2412: /* Normal forms */clean up - no longer dab needed, replaced: {{Disambiguation needed| → AWB

2014-09-12T14:40:05Z

Normal forms: clean up - no longer dab needed, replaced: {{Disambiguation needed| → [[, removed: [[date=January 2012}} using AWB

← Older revision		Revision as of 16:40, 12 September 2014
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	~~[[Image:SFT-benzene.png\|thumb\|Temperature dependence of the surface tension of [[benzene]]]]~~		Hello, my name is Andrew and my wife doesn't like it at all. I am an invoicing officer and I'll be promoted quickly. Alaska is exactly where he's usually been living. The favorite pastime for him and his kids is to play lacross and he would by no means give it up.<br><br>Take a look at my website ... free psychic ([http://Publicpledge.com/blogs/post/7034 publicpledge.com])

	~~The '''Eötvös rule''~~'~~, named after the Hungarian physicist [[Loránd Eötvös\|Loránd (Roland) Eötvös]] (1848–1919) enables the prediction of the [[surface tension]] of an arbitrary [[liquid]] pure substance~~ at all ~~[[temperature]]s~~. ~~The [[density]], [[molar mass]]~~ and ~~the [[critical temperature]] of the liquid have to~~ be ~~known~~. ~~At the [[critical point (thermodynamics)\|critical point]] the surface tension~~ is ~~zero~~.

	The ~~first assumption of the Eötvös rule is:~~

	~~1. The surface tension is a linear function of the temperature.~~
	~~:This assumption~~ is approximately fulfilled for most known liquids. When plotting the surface tension versus the temperature a fairly straight line can be seen which has a surface tension of zero at the critical temperature.

	~~The Eötvös rule also gives a relation of the surface tension behaviour of different liquids in respect to each other:~~

	~~2. The temperature dependence of the surface tension can be plotted for all liquids in a way that the data collapses~~ to ~~a single master curve. To do so either the molar mass, the density, or the molar volume of the corresponding liquid has to be known.~~

	~~== The Eötvös rule ==~~

	~~If ''V'' is the molar volume~~ and ~~''T''<sub>c</sub> the critical temperature of a liquid the [[surface tension]] γ is given~~ by~~<ref name="phywe">{{cite web\|url=http://www.nikhef.nl/~h73/kn1c/praktikum/phywe/LEP/Experim/1_4_05~~.~~pdf\|title=Surface Tension by the Ring Method (Du Nouy Method)\|accessdate=2007-09-08\|publisher=PHYWE\|format=pdf}}</ref>~~
	:<~~math~~>~~\gamma V^{2/3} = k(T_c - T)\,~~<~~/math~~>
	~~where ''k'' is~~ a ~~constant valid for all liquids~~. ~~The Eötvös constant has a value of 2~~.~~1×10<sup>−7</sup> [[Joule\|J]]/(K·[[mole (unit)\|mol]]<sup>2/3</sup>)~~.

	~~More precise values can be gained when considering that the line normally passes the temperature axis 6 [[Kelvin\|K]] before the critical point:~~

	~~:<math>\gamma V^{2/3} = k~~(~~T_c - 6 \ \mathrm{K} - T)\,</math>~~

	~~The molar volume ''V'' is given by the molar mass ''M'' and the density ρ~~

	~~:<math>V = M / \rho\,</math>~~

	~~The term <math>\gamma V^{2/3}</math> is also referred to as the "molar surface tension" γ<sub>mol</sub> :~~
	~~:<math>\gamma_{mol} = \gamma V^{2/3}\,</math>~~

	~~A useful representation that prevents the use of the unit mol<sup>−2/3</sup> is given by the~~ [~~[Avogadro constant]] N<sub>A</sub>~~ :
	~~:<math>\gamma = k' \left( \frac{M}{\rho N_A} \right)^{-2/3}(T_c - 6 \ \mathrm{K} - T) = k' \left( \frac{N_A}{V} \right)^{2/3}(T_c - 6 \ \mathrm{K} - T)<~~/~~math>~~

	~~As [[John Lennard-Jones]] and Corner showed in 1940 by means of the [[statistical mechanics]] the constant ''k''′ is nearly equal to the [[Boltzmann constant]].~~

	~~=== Water ===~~
	~~For water, the following equation is valid between 0 and 100 °C.~~
	~~:<math>\gamma = 0.07275 \ \mathrm{ N~~/~~m} \cdot (1-0~~.~~002 \cdot (T - 291 \ \mathrm{K}))<~~/~~math>~~

	~~== Historical ==~~

	As a student, Eötvös started to research surface tension and developed a new method for its determination. The Eötvös rule was first found phenomenologically and published in 1886.<ref>{{cite journal\|first=L. \|last=Eötvös \|journal=[[Annalen der Physik]] \|year=1886 \|volume=27 \|page=448}} Cited in: {{cite journal\|last=Palit\|first=Santi R.\|title=Thermodynamic Interpretation of the Eötvös Constant\|journal=Nature\|year=1956\|volume=177\|issue=4521\|pages=1180–1180\|doi=10.1038/~~1771180a0\|bibcode = 1956Natur.177.1180P }}<~~/~~ref> In 1893 [[William Ramsay]] and Shields showed an improved version considering that the line normally passes the temperature axis 6 [[Kelvin\|K]] before the critical point~~. ~~[[John Lennard-Jones]~~] ~~and Corner published (1940~~) ~~a derivation of the equation by means of [[statistical mechanics]]. In 1945 [[E. A. Guggenheim]] gave a further improved variant of the equation.~~

	~~==References==~~
	~~<references/>~~

	~~{{DEFAULTSORT:Eotvos rule}}~~
	~~[[Category:Physical chemistry]]~~
	~~[[Category:Thermodynamic equations]]~~

2.97.25.150: /* Trace monoid */ Remove spurious link to logical consequence

2013-11-04T10:46:01Z

Trace monoid: Remove spurious link to logical consequence

← Older revision		Revision as of 12:46, 4 November 2013
Line 1:		Line 1:
	~~Hi there~~. ~~Allow me start by introducing~~ the ~~writer~~, ~~her name~~ is ~~Sophia Boon but she by no means really liked that title~~. ~~Distributing production~~ is ~~how he makes~~ a ~~living~~. ~~I am truly fond~~ of to go to ~~karaoke but I~~'~~ve been using on new issues lately~~. ~~My wife~~ and ~~I live~~ in ~~Mississippi~~ and ~~I adore each day residing here~~.<br><br>~~my web blog: psychic phone~~ [[~~http~~://~~kard~~.dk/~~?p=24252 kard.dk~~]]		[[Image:SFT-benzene.png\|thumb\|Temperature dependence of the surface tension of [[benzene]]]]

			The '''Eötvös rule''', named after the Hungarian physicist [[Loránd Eötvös\|Loránd (Roland) Eötvös]] (1848–1919) enables the prediction of the [[surface tension]] of an arbitrary [[liquid]] pure substance at all [[temperature]]s. The [[density]], [[molar mass]] and the [[critical temperature]] of the liquid have to be known. At the [[critical point (thermodynamics)\|critical point]] the surface tension is zero.

			The first assumption of the Eötvös rule is:

			1. The surface tension is a linear function of the temperature.
			:This assumption is approximately fulfilled for most known liquids. When plotting the surface tension versus the temperature a fairly straight line can be seen which has a surface tension of zero at the critical temperature.

			The Eötvös rule also gives a relation of the surface tension behaviour of different liquids in respect to each other:

			2. The temperature dependence of the surface tension can be plotted for all liquids in a way that the data collapses to a single master curve. To do so either the molar mass, the density, or the molar volume of the corresponding liquid has to be known.

			== The Eötvös rule ==

			If ''V'' is the molar volume and ''T''<sub>c</sub> the critical temperature of a liquid the [[surface tension]] γ is given by<ref name="phywe">{{cite web\|url=http://www.nikhef.nl/~h73/kn1c/praktikum/phywe/LEP/Experim/1_4_05.pdf\|title=Surface Tension by the Ring Method (Du Nouy Method)\|accessdate=2007-09-08\|publisher=PHYWE\|format=pdf}}</ref>
			:<math>\gamma V^{2/3} = k(T_c - T)\,</math>
			where ''k'' is a constant valid for all liquids. The Eötvös constant has a value of 2.1×10<sup>−7</sup> [[Joule\|J]]/(K·[[mole (unit)\|mol]]<sup>2/3</sup>).

			More precise values can be gained when considering that the line normally passes the temperature axis 6 [[Kelvin\|K]] before the critical point:

			:<math>\gamma V^{2/3} = k(T_c - 6 \ \mathrm{K} - T)\,</math>

			The molar volume ''V'' is given by the molar mass ''M'' and the density ρ

			:<math>V = M / \rho\,</math>

			The term <math>\gamma V^{2/3}</math> is also referred to as the "molar surface tension" γ<sub>mol</sub> :
			:<math>\gamma_{mol} = \gamma V^{2/3}\,</math>

			A useful representation that prevents the use of the unit mol<sup>−2/3</sup> is given by the [[Avogadro constant]] N<sub>A</sub> :
			:<math>\gamma = k' \left( \frac{M}{\rho N_A} \right)^{-2/3}(T_c - 6 \ \mathrm{K} - T) = k' \left( \frac{N_A}{V} \right)^{2/3}(T_c - 6 \ \mathrm{K} - T)</math>

			As [[John Lennard-Jones]] and Corner showed in 1940 by means of the [[statistical mechanics]] the constant ''k''′ is nearly equal to the [[Boltzmann constant]].

			=== Water ===
			For water, the following equation is valid between 0 and 100 °C.
			:<math>\gamma = 0.07275 \ \mathrm{ N/m} \cdot (1-0.002 \cdot (T - 291 \ \mathrm{K}))</math>

			== Historical ==

			As a student, Eötvös started to research surface tension and developed a new method for its determination. The Eötvös rule was first found phenomenologically and published in 1886.<ref>{{cite journal\|first=L. \|last=Eötvös \|journal=[[Annalen der Physik]] \|year=1886 \|volume=27 \|page=448}} Cited in: {{cite journal\|last=Palit\|first=Santi R.\|title=Thermodynamic Interpretation of the Eötvös Constant\|journal=Nature\|year=1956\|volume=177\|issue=4521\|pages=1180–1180\|doi=10.1038/1771180a0\|bibcode = 1956Natur.177.1180P }}</ref> In 1893 [[William Ramsay]] and Shields showed an improved version considering that the line normally passes the temperature axis 6 [[Kelvin\|K]] before the critical point. [[John Lennard-Jones]] and Corner published (1940) a derivation of the equation by means of [[statistical mechanics]]. In 1945 [[E. A. Guggenheim]] gave a further improved variant of the equation.

			==References==
			<references/>

			{{DEFAULTSORT:Eotvos rule}}
			[[Category:Physical chemistry]]
			[[Category:Thermodynamic equations]]

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-05T22:48:32Z

ISBNs (Build KC)

New page

Hi there. Allow me start by introducing the writer, her name is Sophia Boon but she by no means really liked that title. Distributing production is how he makes a living. I am truly fond of to go to karaoke but I've been using on new issues lately. My wife and I live in Mississippi and I adore each day residing here.<br><br>my web blog: psychic phone [[http://kard.dk/?p=24252 kard.dk]]