GROSS VAPORIZATION. Definitions

Transcription

1 GROSS VAPORIZATION Defntons Vaporzaton: Vaporzaton s the process by whch molecules leave ther prevous lqud or sold phase or attachment to a substrate and become gas molecules. In some papers, the term sublmaton s used to descrbe vaporzaton drectly from the sold phase, whle the term evaporaton s restrcted to vaporzaton from the lqud phase. Snce the process s the same n each case and the resultng gas molecules ndstngushable from one another, ths s a dstncton wthout a measurable dfference. We shall use both the term vaporzaton and on occason the term evaporaton to descrbe ether process. Substrate: Vaporzaton takes place from any surface bearng or contanng water molecules. Most commonly, ths surface s water or ce. Sometmes, however, t s the surface of an atmospherc partculate, a blade of grass, a rock face, or the glass surface of a wndow. When we are not partcularly concerned wth the nature of ths surface, but prmarly wth the process of vaporzaton tself, we wll smply refer to ths undfferentated surface as the substrate. : Gross vaporzaton refers to the process of vaporzaton wthout any consderaton of the reverse process of gross condensaton. Throughout ths paper, use of the terms vaporzaton, evaporaton, and sublmaton wll refer to gross vaporzaton. If net vaporzaton s meant, net vaporzaton wll be specfed. Net Vaporzaton: Net vaporzaton occurs when the rate of gross vaporzaton exceeds the rate of gross condensaton. 1

2 Water Vapor and Steam: It s customary n physcs texts to refer to gaseous water at temperatures greater than the bolng pont as steam. Gaseous water at temperatures less than the bolng pont s referred to as water vapor. Agan, ths s a dstncton wthout a relevant dfference. The processes by whch the gas molecules are formed are dentcal n each case. Moreover, except for dfferences n the mean temperature of the gas as a whole, there are no measurable dfferences n the two populatons. Both populatons wll contan molecules whose ndvdual thermal energes are dentcal to one another. Consequently, we wll use the term vapor to refer to all gaseous water molecules, regardless of both the mean temperature of the populaton and the bolng pont temperature at the ambent pressure. The Zone of Attracton Zone of Attracton: Every aqueous substrate s surrounded by a zone of attracton. Ths s a volume of space where the speeds of vapor molecules leavng the surface of the substrate are dmnshed by the varous attractve forces of that substrate. The zone extends out from the substrate as far as that dmnuton of speed exsts. The zone s not necessarly unform n ts extenson from the surface, but vares topographcally as the ndvdual attractve forces vary from place to place over the substrate. Surface Tenson: Ths zone of attracton s created by three dfferent groups of forces. The frst group s those forces of attracton that exst between water molecule and water molecule. The strongest force of ths group s the hydrogen bond. It s ths bond and the other forces that create what we see as surface tenson n lqud water and surface force and surface energy n ce. Dagrams of surface tenson often show representatons of the surface molecules formng a smooth unbroken skn to keep the sub-surface molecules wthn. Ths s artstc lcense. In realty, ths surface network s contnually beng bent outward by the mpulses transferred to t by the molecules wthn. In addton t s contnually beng bent nward by the bombardment of ar and vapor molecules. It s hardly smooth. 2

3 Ths skn s also contnually beng broken and ruptured as the more energetc molecules wthn break through the bonds of surface tenson to ; and as hgh energy ar and vapor molecules penetrate t from wthout. Sometmes, t s the surface molecule that s or submerges, leavng a rapdly-flled gap n the net. Nevertheless, ths skn effect s very real and the forces that create t are extremely strong ones. As we shall see later, the proporton of water molecules that manage to break these bonds s qute small at most tropospherc temperatures. Hygroscopc Forces: The second group of attractve forces s due to the hygroscopc nature of one or more condensaton nucle or a substrate of some knd. These forces may also nclude the hydrogen bond, but the attracton s between water molecules and some other substance. Common cloud condensaton nucle nclude slca, salt, and varous sulfates. Hygroscopc forces act to ncrease both the strength and the range of the zone of attracton. Ionc Forces: The thrd set of attractve forces s due to onc attracton. Ths ranges all the way from on medated nucleaton (IMN) all the way to the strong attracton between an onzed substrate and onzed vapor molecules. The power of onzed water molecules to attract other water molecules s graphcally llustrated by the condensaton trals n a Wlson cloud chamber. Moreover, n the free atmosphere pure water does not exst. All atmospherc water and ce s a soluton of whatever solutes happen to be avalable at that tme and place. Raoult s Law mandates that solutons wll vaporze at a slower rate than the rate of the pure solvent. Ths means that the more concentrated the soluton, the less the rate of vaporzaton. Cloud droplets formed about solutes such as sea salt may well vaporze at a slower rate than cloud droplets that form about nonsolutes. Other Molecules and the Zone of Attracton: For our purposes, we are concerned only wth the attracton of the aqueous substrate for vapor molecules. It may well be, however, that other gaseous molecules are attracted as well. 3

4 Spatal Varaton of the Attractve Forces: Irregularly-shaped substrates produce rregular zones of attracton. Cloud condensaton nucle are often rregular n shape. The ponts of ce crystals exert weaker attractve forces than do the edges, and the edges exert weaker attractve forces than the flats. In both droplets and ce crystals, onc forces of attracton vary wth the concentraton of solutes and onzed areas from place to place on the substrate. Because of these varatons, the velocty needed by a water or ce molecule to leave the zone of attracton and become a vapor molecule wll lkewse vary from place to place on the substrate. Departure and Outflow Maxwell Dstrbuton of Thermal Energes: There are very good reasons for belevng that gases, lquds, and solds at the same temperature have the same mathematcal dstrbuton of molecular knetc energes. The arguments, however, are not partcularly germane to the present dscusson. We wll smply postulate that the same mathematcal dstrbuton exsts n all three phases. The dstrbuton of knetc energes of those vapor molecules whose next nteracton s wth an object of nterest (here, a substrate) durng some apprecable perod of tme s: df f u = exp k T k T B B du VAP01 Here, f s the mean number of molecular nteractons per square meter per second, u s the ndvdual molecular knetc energy of translaton (measured normal to the surface) of those molecules whose next nteracton s wth that surface. Snce we have postulated that the dstrbuton of energes of translaton s the same for water molecules and vapor molecules, we can rewrte VAP01 to read: 4

5 df f = exp k BT u du k T B VAP02 Here, the subscrpt ndcates that the molecules under observaton have had ther last nteracton wth the object of nterest (the substrate), rather than ther next nteracton. They are leavng the surface, not arrvng at t. Expresson VAP01 measures nflow and arrvals at the substrate, whle expresson VAP02 measures outflow and departures. The dmensons of both equatons are number per unt area per unt tme or, more precsely, the probablty assocated wth that number. Note: In ths expresson and n future expressons, we wll use the tlde (~) under the parameter to ndcate that the parameter apples to water molecules n the expresson. Thermal Dstrbutons: In The Nature of Gas Temperatures, we defned temperature to be a functon of the mean value of the total knetc energes (translaton, rotaton, and vbraton) expressed normal to the thermometrc surface. Ths defnton was expressed n the formula: T = Σ u k B NGT04 If we are dscussng the temperature of the sub-system of water molecules leavng a surface, we can also say: T = u k Σ B VAP03 u Σ Here, s the mean total knetc energy (measured normal to the evaporatng surface) of that sub-set of water molecules leavng the surface durng some apprecable perod of tme, and the other two terms have ther prevous meanngs. 5

6 The concept of ndvdual molecular temperatures : Equaton VAP03 shows that the temperature of a sub-populaton of evaporatng gas molecules s a drect functon of the mean knetc energy of those molecules normal to the surface at the moment of evaporaton. It does not stretch a pont too much to apply ths concept to ndvdual molecules. That s, T = u k Σ B VAP04 Here, energy T u Σ s the temperature of an ndvdual water molecule havng total knetc normal to the surface at the moment of leavng that surface. If we combne equatons VAP02 and VAP04, we get the dstrbuton functon of molecules leavng the surface of the substrate n terms of ther ndvdual molecular temperatures: df f T = exp T T dt VAP05 Note that the most probable molecular temperatures are close to 0 K 1 ; and that the hgher the ndvdual molecular temperature the less lkely some surface molecule s to have that temperature. Ths s entrely apart from the selectve process nherent n the mechansm tself, where the hotter molecules are the only ones allowed to. Selecton and Escape Escape Velocty: For any partcular bondng stuaton, there wll exst some molecular velocty along the proxmty axs that represents the velocty, v. Molecules movng away from the substrate wth less than that crtcal 1 Quantum consderatons mandate aganst a true zero value. 6

7 velocty wll not to become free vapor molecules. Molecules movng away from the substrate that possess that velocty or greater wll 2. Dmnuton of Escape Veloctes: As a prospectve vapor molecule moves away from the surface, the varous attractve forces serve to reduce ts velocty along the proxmty axs and consequently ts knetc energy of translaton along that same axs. Ths means that when the successful molecules jon the vapor phase, they wll have less thermal energy than when they frst left the substrate. Ths process may be expressed as: u = u u vapor substrate VAP06 Note that the loss of energy (heat of vaporzaton) s solely along the proxmty axs. There s no reason to beleve that any of the other knetc energes manfested n any of the other degrees of freedom are affected or dmnshed n any way. Dervaton of Escape Energy: We may readly derve a value for the energy by smply dvdng the expermental heat of vaporzaton per unt mass of a substance by the number of molecules n that unt of mass. Ths wll produce: Here, u u Q = vaporzaton N VAP07 s the knetc energy of (measured normal to and away from vaporzaton the vaporzng surface), Q and N s the number of water molecules per unt of mass. s the heat of vaporzaton per unt of mass Escape Velocty for Lqud Water at NTP: An approxmaton of the energy for a molecule of lqud water at NTP may be calculated by usng the values found n Water: Some Useful Values. 2 Some of the escapng molecules, of course, wll be struck by ncomng ar or vapor molecules and returned to the substrate. Snce these molecules cannot be dstngushed from vapor molecules arrvng from the surroundng atmosphere, we must treat them as smply another part of the nflow. The proporton of such rejects s not very large. 7

8 Let us postulate a water molecule mass of 2.99 x klograms (the mass of the most common sotope of water) as the ndvdual molecular mass ( mɺ ). Then, the velocty becomes: v 2u = m ɺ v 1 2 VAP08 Ths gves us an velocty ( ) of some 884 meters per second from a surface of pure water at NTP under laboratory condtons. The Escape Populaton: To ascertan the proporton of surface molecules lkely to have ths velocty or greater normal to and away from the surface of the substrate, we have to know the standard devaton (σ ) of the speeds along the proxmty axs of the surface populaton. Ths s gven by the expresson: k T σ B = mɺ 1 2 VAP09 Ths gves us a root-mean-square speed (σ) of some 355 meters per second. v That makes the rato of to σ equal The area under a normal curve to the left of the ordnate of 2.49 standard devatons s Ths s the proporton of the surface populaton that possesses veloctes normal to and away from the surface equal to or greater than the velocty. If we assume (ths s the weakest part of the argument) that the subsurface mpulse flux toward the surface s npv p (see Molecular Speeds and Veloctes), ths gves us a mean mpulse flux of some 4.74 x mpulses per unt area and tme. Multplyng that value tmes the proporton gven above gves us an escapng populaton of molecules of some 6.06 x per unt area of surface n unt tme. All of ths s delneated n Table WSV06 n Water: Some Useful Values. 8

9 Therefore, the odds of a water molecule breakng away from a plane surface of water at 0 are a lttle bt better than one n a hundred attempts. Ths success rato goes up as the temperature ncreases. Isotope Selecton: Because s based on velocty and not energy, lghter sotopes are more lkely to than heaver ones. Ths s just the opposte of the condensaton process, where heaver molecules are more lkely to be captured by the zone of attracton than are the lghter ones. The net effect of these two selecton processes s that n the absence of replenshment the mean molecular mass of a water droplet wll ncrease over tme. Vaporzaton from Ice: Weaker bondng at the ponts and edges of ce crystals leads to dfferental rates of vaporzaton. The ponts go frst, becomng rounded. Then, the edges become rounded. Ths same dfferentaton, of course, takes place n the meltng process. The ponts melt frst, then the edges. The general effect of these processes s one of roundng. Water droplets have a very strong tendency to adopt a sphercal shape even when the condensaton nucleus or substrate s rregular. The tendency n ce s not as strong and nowhere near as fast, but t s stll there. Heat of Vaporzaton Transfer of Enthalpy durng Vaporzaton: The net transfer of mass from the lqud and/or sold phase to the vapor phase results n a net gan n enthalpy for the vapor phase and a net loss of enthalpy for the evaporatng phase. Ths s always true. However, ths does not mean that the resultng coolng of the evaporatng surface results n an equvalent warmng of the vapor system. If the evaporatng surface s cooler than the ar, the net result may be a coolng of the ar despte the ncrease n enthalpy. Moreover, the loss of enthalpy by the substrate s not balanced by the gan n enthalpy by the atmosphere. The enthalpy lost by the dmnuton of veloctes and energes due to ntermolecular forces of attracton must be carred on the books as latent heat. 9

10 It should be noted that latent heat s not real heat. It cannot be ether measured or detected although t can be calculated. It s strctly a bookkeepng devce. Because enthalpy and heat are totals, whereas temperature s an average, t s entrely possble to add heat (enthalpy) to a system and effect a reducton n that system s temperature. And, as we shall see n Gross Condensaton, t s also possble to remove heat (enthalpy) from a system and smultaneously effect an ncrease n that system s temperature. * * * * * Summary of Vaporzaton Concepts: 01. Every surface of water or ce n the atmosphere undergoes contnual gross vaporzaton. Every non-water surface that carres one or more transent water molecules undergoes contnual gross vaporzaton. Ths process s spontaneous and ubqutous. It s not necessary to add heat to a substrate to brng about vaporzaton. 02. The amount of gross vaporzaton that takes place from any partcular surface at any partcular tme depends upon the relatve strengths of the ntermolecular bondng forces on the one hand and the ntensty of thermal agtaton (temperature) on the other. 03. Water molecules strongly attract one another. The varous forces of water to water attracton are subsumed under the rubrc of surface tenson. It s a very strong set of forces. 04. The bondng forces also vary wth the hygroscopc nature of the substrate. Some materals are strongly hygroscopc, some less so, some neutral, and some actually repel water. 05. The thrd set of forces nvolves onzaton. Ionzed substrates can be powerful condensaton nucle, and can attract onzed water molecules that mght otherwse be unattracted to the substrate. 10

11 06. The bondng forces vary wth the topology of the surface, especally as ths topology affects the number of other molecules n close enough proxmty to exercse ther attractve forces. 07. The bondng forces vary wth the varous solutes dssolved n the water or ce. As a general rule, these solutes ncrease the strength of the bondng forces. 08. The combnaton of the varous attractve forces n the zone of attracton may attract gas molecules other than smply vapor molecules. 09. The dstrbuton of thermal energes n gases, lquds, and solds s postulated to take the same form n each of the phases. Phases wth the same temperature are assumed to share the same thermal mean and the same dstrbuton of knetc energes of translaton. 10. Thermal agtaton, specfcally knetc energy of translaton drected away from the surface, vares wth surface temperatures. No matter what that surface temperature s, however, some molecules wll have suffcent thermal energes to the bondng forces. 11. Vaporzaton s a strongly selectve process. Only the hotter (hgher knetc energy of translaton) molecules are able to vaporze. Ths dmnshes the mean temperature of those that reman, hence coolng the evaporatng surface. 12. At NTP, for a plane surface of lqud water, a bt over one percent of the molecules movng away from the surface wll have enough velocty to completely and are thus able to vaporze. 13. Because s based on velocty, lghter sotopes are more lkely to vaporze than heaver ones. Ths ncreases the mean molecular mass of those that reman. 14. Vaporzaton from ce vares wth locaton of the molecule on the crystal surface. Ponts vaporze frst, followed by edges. 15. Vaporzaton ncreases the enthalpy of the vapor system and decreases the enthalpy of the evaporatng system. 11

12 16. Overcomng the bondng forces reduces the knetc energy of the escapng molecules and therefore the enthalpy of the system as a whole. Ths loss of energy must be carred on the books as latent heat. 17. The temperature of the resultng vapor system may be ncreased or decreased or reman unchanged by the vaporzaton process. The result depends upon the relatve temperatures and masses of the evaporatng surface and the vapor system and upon the strength of the bondng forces. 18. In consderng heat transfer and temperature changes, t s essental to keep n mnd that heat s a total whle temperature s an average. Ths s partcularly mportant n understandng the nature of latent heat. 12