2.50.133.55: /* Departure functions for Peng-Robinson equation of state */

2014-01-04T09:35:53Z

Departure functions for Peng-Robinson equation of state

← Older revision		Revision as of 11:35, 4 January 2014
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	~~Claude~~ is ~~her name~~ and ~~she completely digs that title~~. ~~Bookkeeping~~ is ~~how he supports his family~~ and ~~his salary has been truly fulfilling~~. ~~Some time ago I chose to live~~ in ~~Arizona but I require to transfer for my family~~. The ~~favorite hobby for him~~ and ~~his kids~~ is to ~~play badminton~~ but he is ~~struggling to find time for it~~.<br><br>~~my homepage :~~: [http://~~Enjoythisworld~~.com/~~UserProfile~~/~~tabid~~/~~464~~/~~userId~~/~~33651/Default~~.~~aspx Enjoythisworld~~.~~com~~]		The '''Kelvin equation''' describes the change in vapour pressure due to a curved liquid/vapor interface ([[meniscus]]) with radius <math>r</math> (for example, in a [[capillary]] or over a droplet). The vapor pressure of a curved surface is higher than that of a flat and non-curved surface. The Kelvin equation is dependent upon thermodynamic principles and does not allude to special properties of materials. It is also used for determination of pore size distribution of a [[porous medium]] using [[BET theory\|adsorption porosimetry]]. The equation is named in honor of [[William Thomson, 1st Baron Kelvin\|William Thomson]], also known as Lord Kelvin.

			The Kelvin equation may be written in the form

			:<math>\ln {p \over p_0}= {2 \gamma V_{\rm{m}} \over rRT}</math>

			where <math>p</math> is the actual [[vapour pressure]],
			<math>p_0</math> is the [[saturated vapour pressure]],
			<math>\gamma</math> is the [[surface tension]], <math>V_{\rm{m}}</math> is the [[molar volume]] of the liquid, <math>R</math> is the [[universal gas constant]], <math>r</math> is the radius of the droplet, and <math>T</math> is [[temperature]].

			[[Equilibrium vapor pressure]] depends on droplet size.
			* If <math>p>p_0</math>, then liquid evaporates from the droplets
			* If <math>p <p_0</math>, then the gas condenses on to the droplets increasing their volumes

			As <math>r</math> increases, <math>p</math> decreases and the droplets grow into bulk liquid.

			If we now cool the vapour, then <math>T</math> decreases, but so does <math>p_0</math>. This means <math>p/p_0</math> increases as the liquid is cooled. We can treat <math>\gamma</math> and
			<math>V_{\rm{m}}</math> as approximately fixed, which means that the critical radius <math>r</math> must also decrease.
			The further a vapour is supercooled, the smaller the critical radius becomes. Ultimately it gets as small as a few molecules and the liquid undergoes homogeneous [[nucleation]] and growth.

			The change in vapor pressure can be attributed to changes in the [[Laplace pressure]]. When the Laplace pressure rises in a droplet, the droplet tends to evaporate more easily.

			When applying the Kelvin equation, two cases must be distinguished: A drop of liquid in its own vapor will result in a positively curved liquid surface or a bubble of vapor in a liquid, will result in a negatively curved liquid surface.

			The form of the Kelvin equation here is not the form in which it appeared in Lord Kelvin's article of 1871. [[Ostwald–Freundlich equation#Derivation from Kelvin's equation\|The derivation]] of the form that appears in this article from Kelvin's original equation was presented by Robert von Helmholtz (son of German physicist [[Hermann von Helmholtz]]) in his dissertation of 1885.<ref>Robert von Helmholtz (1886) [http://books.google.com/books?id=9xVbAAAAYAAJ&pg=PA508#v=onepage&q&f=false "Untersuchungen über Dämpfe und Nebel, besonders über solche von Lösungen"] (Investigations of vapors and mists, especially of such things from solutions), ''Annalen der Physik'', '''263''' (4) : 508-543. On pages 523-525, Robert von Helmholtz converts Kelvin's equation to the form that appears here (which is actually the Ostwald-Freundlich equation).</ref>

			==See also==
			* [[Condensation]]
			* [[Laplace pressure]]

			==References==

			{{Reflist}}

			==Further reading==

			* Sir William Thomson (1871) [http://books.google.com/books?id=ZeYXAAAAYAAJ&pg=PA448#v=onepage&q&f=false "On the equilibrium of vapour at a curved surface of liquid,"] ''Philosophical Magazine'', series 4, '''42''' (282) : 448-452.
			* S. J. Gregg and K. S. W. Sing, ''Adsorption, Surface Area and Porosity'', 2nd edition, Academic Press, New York, (1982) p.121
			* Arthur W. Adamson and Alice P. Gast, ''Physical Chemistry of Surfaces'', 6th edition, Wiley-Blackwell (1997) p.54
			* Butt, Hans-Jürgen, Kh Graf, and MichaelThe Kappl. "The Kelvin Equation." Physics and Chemistry of Interfaces. Weinheim: Wiley-VCH, 2006. 16-19. Print.
			<br />
			[[Category:Surface chemistry]]
			[[Category:Physical chemistry]]

			[[de:Kelvin-Gleichung]]

en>ChrisGualtieri: Typo fixing, typos fixed: i.e → i.e. using AWB

2012-07-18T04:10:40Z

Typo fixing, typos fixed: i.e → i.e. using AWB

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Claude is her name and she completely digs that title. Bookkeeping is how he supports his family and his salary has been truly fulfilling. Some time ago I chose to live in Arizona but I require to transfer for my family. The favorite hobby for him and his kids is to play badminton but he is struggling to find time for it.<br><br>my homepage :: [http://Enjoythisworld.com/UserProfile/tabid/464/userId/33651/Default.aspx Enjoythisworld.com]

Departure function - Revision history

2.50.133.55: /* Departure functions for Peng-Robinson equation of state */

en>ChrisGualtieri: Typo fixing, typos fixed: i.e → i.e. using AWB