tag:blogger.com,1999:blog-8890671936020885112.post8025531796803981231..comments2015-07-27T18:52:30.942-07:00Comments on The Oil ConunDRUM: The homework problem to end all homework problems@whuthttp://www.blogger.com/profile/18297101284358849575noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-8890671936020885112.post-5038869707378075222013-06-07T15:20:47.863-07:002013-06-07T15:20:47.863-07:00I will have to pick up Pierre's book, thanks f...I will have to pick up Pierre's book, thanks for the tip.WHThttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-8890671936020885112.post-26137197787569421802013-06-04T18:24:27.342-07:002013-06-04T18:24:27.342-07:00Did you see the derivation in Ray Pierrehumbert...Did you see the derivation in Ray Pierrehumbert's "Principles of Planetary Climate"?<br /><br />As best as I recall it, yours is both more thorough and clearer to me. Congratulations.David B. Bensonhttps://www.blogger.com/profile/02917182411282836875noreply@blogger.comtag:blogger.com,1999:blog-8890671936020885112.post-40125593148584905132013-05-26T17:53:18.769-07:002013-05-26T17:53:18.769-07:00Good comments here:
http://rankexploits.com/musing...Good comments here:<br />http://rankexploits.com/musings/2013/doug-cotton-is-banned-admin/#comment-113695<br /><br />In particular, DeWitt Payne points out (like Vaughan Pratt) that Venus has higher degrees of freedom for CO2, than appears for its vibrational model energies.<br /><br />WHThttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-8890671936020885112.post-60287139601436329292013-05-22T18:29:11.232-07:002013-05-22T18:29:11.232-07:00This was another comment from Pekka
"Math is...This was another comment from Pekka<br /><br />"Math is a tool that transforms input to output. As I’m sure that your output is wrong, I assume that your input is also wrong. You have probably done the math in between correctly.<br /><br />In the previous case of lapse rate you were talking on “virial” something, don’t remember the exact phrase.. My impression was that you didn’t know what you were talking about, but didn’t consider that interesting enough to dig deeper."<br /><br />WHThttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-8890671936020885112.post-84912728383021380572013-05-22T18:24:20.164-07:002013-05-22T18:24:20.164-07:00In regards to this comment I made elsewhere
"...In regards to this comment I made elsewhere<br /><br />"Interesting that the Venus CO2 atmosphere is forever phase-changing. CO2 has a supercritical phase that blurs the distinction between gas and liquid phases.<br /><br />The theory works reasonably well for Mars where because of its cold temperatures the CO2 can easily condense out. The lapse rate varies quite a bit there, but I predict the average is 3.24 K/km while the adiabatic theory says 4.9 K/km. Judge for yourself:<br />http://3.bp.blogspot.com/-YwFRLJ1NK7Y/UX_eG1jNlKI/AAAAAAAADcA/KkJq7cz2fGs/s640/mariner-hunten-mars-lapse-rate.gif<br /><br />The climatologist Peter Stone had a theory for lapse rates based on rotating atmospheres [1]. For Mars, he said the curves shown above have a mean lapse rate of 2.5 K/km. His own theory predicted 2 k/km, but that one is really complex.<br /><br />[1]P. H. Stone, “A simplified radiative-dynamical model for the static stability of rotating atmospheres,” J. Atmos. Sci, vol. 29, no. 3, pp. 405–418, 1972.<br /><br />The radiative equilibrium and dusty thin atmosphere of Mars are of course also important."<br /><br />The following is an extended response by Vaughan<br /><br />If you derive the dry adiabatic lapse rate as done in the Wikipedia article on lapse rate you get more than that it is constant, you get the constant itself, namely g/c_p K/km. For Earth’s troposphere this is 9.8/1.00 = 9.8 K/km. For Venus it is 8.9/1.13 = 7.82 K/km; Figure 5.2 on p.192 of Marov and Grinspoon’s The planet Venus plots measurements by Venera-9 through 15 and the Pioneer-Venus Large probe, showing around 8 K/km, in good agreement with theory.<br /><br />Vaughan Pratt | May 20, 2013 at 12:42 pm |<br /><br />Looking more carefully at that figure, which I put up here, I’d say it was closer to 7.3 K/km. At 55 km altitude the temperature has declined about 400 K from that at the surface; 400/55 = 7.3.<br /><br /><br /><br />---<br /><br />I agree with the formula in the Wikipedia article on lapse rate, namely g/c_p. g*MW/c_p isn’t remotely near correct.<br /><br />Are you suggesting that there are 3 or 4 more degrees of freedom unaccounted for in the CO2 molecule?<br /><br />Something like that. Google for the phrase (in quotes)<br />“a triatomic atmosphere generally departs”<br />and note (two lines above that phrase) the temperature-dependent value of 1134 J/kg K for CO2 at 730 K, leading to 7.82 K/km for an ideal gas, bumped up slightly to 8.08 K/km at 90 atmospheres. I have no idea why the empirically observed value is 7.3 K/km, but in any event that’s way less than 8.87/0.839 = 10.57 K/km where 0.839 is c_p for CO2 at STP.<br /><br />CO2 has vibrational modes of energy 0.3, 0.17, and 0.085 eV. These correspond to temperatures of 3400K, 2000K, and 980K. The highest temperature of Venus is +700K so that the lowest energy vibrational mode is only starting to kick in at that temperature.<br /><br />Beats me. Maybe 90 atmospheres is enough to bend an otherwise linear molecule, which would add a low-energy rotational degree of freedom, low enough to be relevant at 730 K. Could the high pressure also smear out the thresholds you cite?<br /><br />All I had to go on was the book’s figure of 1.134 kJ/kg for c_p, which gave a lapse rate not far off the observed value. No idea where 1.134 came from.WHThttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-8890671936020885112.post-69673361679361789022013-05-16T11:12:12.689-07:002013-05-16T11:12:12.689-07:00Another comment from the ether:
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Looks like ...Another comment from the ether:<br />"<br />Looks like you arbitrarily picked n = 5 for the polytropic term. Care ‘splain that, Ricky?<br />"<br /><br />The polytrophic index n=5 derives from f=3/2*(1+N/2) and f=n+1.<br /><br />For Venus, CO2 is the major gas and that is a molecule with 6 degrees of freedom at this range of temperatures. So N=6, f=6, and therefore n=5.<br /><br />For Earth, N=5, f=5.25, and n=4.25.<br /><br />What is perhaps confusing is why I singled out n=5 in the post. That one happens to have an analytical solution for the Lane-Emden equation. But I don't use that particular solution beyond that point. <br />WHThttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-8890671936020885112.post-11281317360837866732013-05-15T21:10:31.661-07:002013-05-15T21:10:31.661-07:00A couple of comments by Pirila
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Pekka Piri...A couple of comments by Pirila<br /><br />"<br /> Pekka Pirilä | May 15, 2013 at 3:12 pm |<br /><br />WHUT,Looking only superficially at your derivation, I’m left wondering, how you can can derive any other polytropic process than adiabatic. I can believe that some other polytrope gives a better agreement with the average lapse rate, but I cannot see any fundamental justification for any particular value. It’s known that the dry adiabatic lapse rate is close to the real one in some limited parts of the atmosphere, while a moist adiabat applies to some other parts and no adiabat in yet other cases.<br /><br />It seems to me extremely unlikely that formal justification can be found for the validity of any other polytrope.<br /><br />Pekka Pirilä | May 15, 2013 at 3:52 pm |<br /><br />WHUT,<br /><br />If you wish to use the latest argument you must state that the standard derivation of the adiabatic lapse rate is wrong.<br /><br />One point you mention is the radial mass conservation, but the Earth radius is very large in comparison with the height of the troposphere and all reasonably dense atmosphere. Therefore the radial effects are negligible.<br /><br />I don’t understand at all what you are saying about the ideal gas law or, how you could get any support from that. Maxent type ideas may give reasonable approximations, but as always they lack rigor, and have more the nature of a rule of thumb.<br />"<br />WHThttps://www.blogger.com/profile/18297101284358849575noreply@blogger.com