The subroutine optical_2 of SoD’s radiative transfer model calculates the optical thickness of a layer of air. Emission line strength involves also the Planck emission spectrum calculated by the subroutine planckmv. (In my version of the model the optical_2 is replaced by optical_3p, but the additional features of my version are not of interest in your application.) My zip-file (link in a comment above) contains also files 01_hit08.par, 02_hit08.par, and 05_hit08.par which contain part of the lines H2O, CO2, and CO -lines of the full HITRANo8 database. Very weak lines have been excluded and so have high wavenumbers (over 4000 1/cm), which might be important in combustion environment.

I have coded also a small application that can be used to filter out from the full HITRAN08 database those lines that are of interest. That’s available from

http://pirila.fi/energy/kuvat/HitranFilter.msi

but using that requires that the full HITRAN-database has been downloaded.

You might find the information that you search for also from SpetralCalc web pages.

]]>Take a thermally isolated gas column and a negligible-thermal-mass thermometer that initially is thermally isolated from everything. Then bring the thermometer into thermal communication with the column at a high altitude so that the mean translational kinetic energy of the thermometer’s molecules equals that of the gas’s at that altitude.

Return the thermometer to isolation and, in that isolated state, bring it to a lower altitude, where, as Velasco et al. say, the mean molecular translational kinetic energy in the gas column is higher—but in accordance with the thermodynamic definition the temperature is the same. What happens to the thermometer’s mean molecular kinetic energy when the thermometer is brought into thermal communication with the column at the lower, higher-mean-kinetic-energy altitude?

Although I’ll leave you to draw your own conclusions, I’ll confess that the question is more complicated than it may seem to at first. True, Velasco et al. do say there’s a mean-kinetic-energy difference between altitudes. But that difference is an over-time mean that for any significant number of molecules is no doubt only a minuscule fraction of the that difference’s variance. At any time instant, that is, the mean molecular kinetic energy in one altitude range is only slightly more likely to be less than in a lower altitude range than it is to be higher.

And that doesn’t even take into account quantum mechanics, which for all I know so smears the “time instant” as to make that all meaningless; in this I’m venturing beyond what I understand.

But I do understand logic, and I remain convinced that Dr. Brown’s proof is invalid.

]]>“Two different columns of gas with different lapse rates. Place them in good thermal contact at the bottom, so that the bottoms remain at the same temperature. They must therefore be at different temperatures at the top. Run a heat engine between the two reservoirs at the top and it will run forever, because as fast as heat is transferred from one column to another, (warming the top) it warms the bottom of that column by an identical amount, causing heat to be transferred at the bottom to both cool the column back to its original temperature profile and re-warm the bottom of the other column. The heat simply circulates indefinitely, doing work as it does, until the gas in both columns approaches absolute zero in temperature, converting all of their mutual heat content into work.”

]]>To the extent that’s true, it’s irrelevant to Dr. Brown’s proof. And, to the extent that it’s relevant to Dr. Brown’s proof, it isn’t true.

It is true that an ideal-gas column whose possible microstates constitute a microcanonical ensemble when the column is thermally isolated will, upon thermal communication with another, erstwhile-isolated column, have a vastly expanded ensemble of microstates which is different from that microcanonical ensemble. But how does that fact validate Dr. Brown’s proof or establish the B-E Law, on which his proof is based?

On the other hand, the resultant composite system’s microstates themselves constitute a microcanonical ensemble—with its own non-zero kinetic-energy gradient in the presence of gravity and thus its own non-zero kinetic-theory lapse rate.

It is only if we use the kinetic-theory definition of temperature that Dr. Brown’s initial assumption—a non-zero lapse rate at equilibrium in an isolated gas column—makes any sense. And, under that definition, Velasco et al. show that coupling two different-lapse-rate columns (say, columns having different amounts of the same-molecular-weight ideal gas) would simply result in a new, (also isolated) composite system having a lower but still non-zero kinetic-theory-temperature-definition lapse rate.

Nothing requires the perpetual motion in which the B-E Law says such a coupling would result.

]]>The B-E Law contemplates two thermally isolated systems that are initially at equilibrium and for the sake of argument exhibit different lapse rates in the presence of gravity. Consequently, at least one of them has a non-zero thermal-equilibrium lapse rate. If those erstwhile-isolated systems are then thermally coupled at two different altitudes, the B E Law says that net heat flow between them would last forever (or, apparently, at least until their temperatures decay to absolute zero if they are coupled through heat engines) as the two systems attempt to maintain their pre-coupling lapse rates.

But I know of no law of physics that says this would be the result. What law of physics says the net heat flow would not be zero instead or at least decay to zero as the now-coupled systems approach a common, composite-system equilibrium lapse rate? Unless there is one, Dr. Brown’s “proof” is invalid. This was the point of my initial comment: one would be better advised to rely on Velasco et al. for proof of (near) isothermality than to adopt Dr. Brown’s reasoning.

]]>Here Dr. Payne implicitly employs the statistical-mechanical definition of temperature, which equals mean molecular kinetic energy exactly only for the canonical ensemble, not the microcanonical ensemble. (I might note in passing that no real-world system is characterized by the canonical ensemble any more than by the microcanonical ensemble.)

But if Dr. Brown had been using that definition, his proof would have been the following. Take a thermally isolated gas column in a gravitational field. Its microstates constitute a microcanonical ensemble. But, according to the statistical-mechanical definition of temperature, such a system has no defined temperature. Therefore, that column has no lapse rate—zero or non-zero—if you use the statistical-mechanical definition of temperature. Q.E.D: it has no non-zero lapse rate.

That would have been a valid proof of no non-zero statistical-mechanical-temperature-definition lapse rate.

But that’s not what Dr. Brown did. What he did was rely on the B-E Law, of which I am aware of no proof.

]]>But I know of no law of physics that says this would be the result. What law of physics says the net heat flow would not be zero instead or at least decay to zero as the now-coupled systems approach a common, composite-system equilibrium lapse rate? Unless there is one, Dr. Brown’s “proof” is invalid. This was the point of my initial comment: one would be better advised to rely on Velasco et al. for proof of (near) isothermality than to adopt Dr. Brown’s reasoning.

]]>True, that is one of the definitions of temperature, namely, the thermodynamic one. If Dr. Brown had been using that definition, though, his proof would have been as follows. The isolated gas column is at equilibrium. By definition, that means no net heat flows. The temperature definition I choose to use is the thermodynamic one, in accordance with which temperature is equal if no net heat flows. Equal temperature means zero temperature gradient, i.e., zero lapse rate. Q.E.D.

That would have been a valid proof (of no thermodynamic-definition lapse rate at equilibrium). But his proof instead relied on what I’ve dubbed the “Brown-Eschenbach Law of Lapse-Rate Conservation” (the “B-E Law”). So his proof necessarily used the gas-law, or kinetic-theory, definition.

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