tag:blogger.com,1999:blog-16612221.post5509874752648153258..comments2024-03-19T03:14:04.172-04:00Comments on Rabett Run: Pressure BroadeningEliRabetthttp://www.blogger.com/profile/07957002964638398767noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-16612221.post-43451575910455581352007-07-11T21:22:00.000-04:002007-07-11T21:22:00.000-04:00Could we see some experimental evidence? Measured ...Could we see some experimental evidence? Measured from real 10 cm length gas boxes? And see how well those results match up with the spectralcalc.com stuff...<BR/><BR/>That'd close up the argument pretty well.<BR/><BR/>-flavius colliumAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-11903712904761793772007-07-09T00:00:00.000-04:002007-07-09T00:00:00.000-04:00There may be some limit on the number of accesses....There may be some limit on the number of accesses. I have not hit that yet.EliRabetthttps://www.blogger.com/profile/07957002964638398767noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-74001956521859077232007-07-08T23:50:00.000-04:002007-07-08T23:50:00.000-04:00Hey, you got something against Lorentzians and Gau...Hey, you got something against Lorentzians and Gaussians? <BR/><BR/>I count them among my best friends (right up there with the Lilliputians) and all this talk of "squashing them" has some of us mice a bit miffed.<BR/><BR/>Speaking of miffed, my spectral Calculator stopped working. It appears that they are now requiring me to subscribe.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-38292784677541350252007-07-08T23:01:00.000-04:002007-07-08T23:01:00.000-04:00A rather longer exposition on squashed Lorentzian...A <A HREF="http://rabett.blogspot.com/2007/07/high-pressure-limit.html" REL="nofollow"> rather longer exposition</A> on squashed Lorentzians and GaussiansEliRabetthttps://www.blogger.com/profile/07957002964638398767noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-70655975218997707252007-07-07T13:15:00.000-04:002007-07-07T13:15:00.000-04:00Horatio,Nice explanation! Thanks!Horatio,<BR/><BR/>Nice explanation! Thanks!CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-63835637540616185472007-07-07T11:41:00.000-04:002007-07-07T11:41:00.000-04:00Here's my attempt at an explanation.In the case wh...Here's my attempt at an explanation.<BR/><BR/>In the case where the pressure is increased but the amount of CO2 is kept constant (VMR reduced), the pressure broadening does not affect the total (integrated) absorption because:<BR/><BR/>1) the total number of molecules of CO2 available to absorb remains constant<BR/>2) The probability per unit time that any one of them will absorb a photon does not change <BR/>3) the number of photons available to <I>be</I> absorbed per unit time remains the same*<BR/>4) only the distribution of final energy states changes (which determines the wavelength of the photon that each molecule can absorb.) <BR/> <BR/><BR/>Essentially, what has happened is that some of the molecules that, at low pressure, would have absorbed a photon with wavelength on line center now absorb a photon with wavelength off line center (either longer or shorter wavelength).<BR/><BR/>So, at higher pressure, fewer photons will now be absorbed that have wavelength on line center and the decrease is balanced with an increase in the total number of "off center" (higher and lower energy) photons absorbed.<BR/><BR/>*This assumes the number of photons available (per unit time) for absorption off line center is essentially the same as on line center, which will be (almost) true near the peak of the black body emission curve, where the emission intensity varies very slowly with wavelength. <BR/><BR/>Of course, this would not be true if the emission were concentrated within a narrow line (laser emission, for example). In that case, pressure broadening might have a significant effect on total absorption if the absorption line center is essentially coincident with the emission line. <BR/><BR/>--Horatio AlgeranonAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-26006775527709187552007-07-06T22:17:00.000-04:002007-07-06T22:17:00.000-04:00decrease the total transmission, I meant to say.decrease the total transmission, I meant to say.CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-91563390953172416582007-07-06T22:16:00.000-04:002007-07-06T22:16:00.000-04:00Eli - Think of if as stomping on a Lorentzian (nat...Eli - <I>Think of if as stomping on a Lorentzian (natural line shape till it forms a flat Gaussian.</I><BR/><BR/>Some of technical terms are hard for me to understand. Let me see if I can translate that into everyday language: the transition amplitude for each molecule is proportional to the square of the matrix element. The volume absorption coefficient comes from summing these over the number of final states, essentially one per molecule-line. When some of these states are collisionally or otherwise shifted from the ground state (squashed) the number of atoms with shifted states has to be subtracted from those at line center (stomping). If this is so, I understand why the integrated absorption coefficient stays constant.<BR/><BR/>For sufficiently long paths, though, transmission could be nearly zero for line center and for the 1/e point, while still letting a lot through in between. In that case, pressure broadening could decrease the total absorption by expanding the (near) zero transmission region despite no change in the integrated absorption coefficent.CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-68257854187099246732007-07-06T16:22:00.000-04:002007-07-06T16:22:00.000-04:00A truly persipicacious question anon. The quick a...A truly persipicacious question anon. The quick and dirty answer is that both the number density and the half width of the broadening are proportional to the total pressure. <BR/><BR/>This means that the added absorption from more CO2 gets spread out in the same proportion by the broadening.<BR/><BR/>Only when second order effects become important will this change. I want to fool about a bit tonite and see if I can write a meaningful update on this pointEliRabetthttps://www.blogger.com/profile/07957002964638398767noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-79327304888489010252007-07-06T11:32:00.000-04:002007-07-06T11:32:00.000-04:00It's very surprising to to me that the %transmitta...It's very surprising to to me that the %transmittance at the line center would be the same (93%) on your first and second graph, even though the amount of CO2 differs by a factor of ten.<BR/><BR/>I understand that it's the total area under the line that determines total absorption, but it just seems surprising to me that <I>all</I> the additional absorption is being done off center.<BR/><BR/>I would have expected the absorption on center to change a little bit, at least. Perhaps it did, but if so, not by much (not that I can make out on that graph, at any rate).<BR/><BR/>This has to be more than coincidence. What is the physical reason why the absorption on center does not change?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-37855350303818131542007-07-06T09:57:00.000-04:002007-07-06T09:57:00.000-04:00Anon 4:29, we are horribly embarrassed and contrit...Anon 4:29, we are horribly embarrassed and contrite.<BR/><BR/>CIP the broadening (to first order) simply spreads the absorption cross-section. Think of if as stomping on a Lorentzian (natural line shape till it forms a flat Gaussian. A similar question (which we can look at later, is does Doppler broadening increase total absorption.EliRabetthttps://www.blogger.com/profile/07957002964638398767noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-8577151860983644322007-07-06T08:26:00.000-04:002007-07-06T08:26:00.000-04:00Eli - At low pressures only a relatively few molec...Eli - <I>At low pressures only a relatively few molecules will collide at any instant, and pressure broadening occurs in the so called binary collision limit.</I><BR/><BR/>On average, zero, according to my math. But it's not the number colliding at an instant that's important, its the number colliding during the emission time.<BR/><BR/>You say that total absorbtion cross section is not affected by pressure broadening. Why is that the case? I would (probably naively) expect that pressure broadening would increase total absorbtion.CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-86134950231477591502007-07-06T07:29:00.000-04:002007-07-06T07:29:00.000-04:00Minor quibble, about an error that one sees perpet...Minor quibble, about an error that one sees perpetuated more often than it should be: <I>g</I> is not the gravitational constant (which is <I>G</I> ~ 6.674 × 10^-11 m^3 kg^-1 s^-2 and is substantially constant) ... <I>g</I> is the acceleration due to gravity (which is ~9.81 m s^-2 and not particularly constant).<BR/><BR/>Keep up the good work guys (and dolls and bunnies).Anonymousnoreply@blogger.com