sethoflagos

If the analogy holds into the 2nd Law I get the result: (a/aref)^[3(k-1)] >= Tref/T where k is the isentropic constant, T is the bulk temperature of the universe and the ref subscript indicates values at some arbitrary reference time. This is the sort of thing I was thinking about as the 2nd Law setting constraints on the rate of expansion. I've uploaded my working as an attachment if anyone's interested. Univ. Expansion.docx

IFF omega = 1 exactly. Not sure if this will display correctly, but did we lose a minus sign somewhere? If so it, appears that any divergence from 1 would increase with time making it a metastable solution at best. This was how I saw the problem presented somewhere, but it's now clear from your explanation that one can view it from the other direction - zero curvature on the largest scales imposes omega =1. It still looks as if something is being driven towards an asymptote. Your post is going to take me a while to absorb. You've mentioned this analogy between FLRW and gas expansion before. Many thanks for taking the time to present it so clearly.

I think what started me thinking along these lines is the density parameter of the universe being so very close to 1. Not only is it a curious value for a random number, but I see no clear reason why omega shouldn't vary with time. Unless of course the balance of its various components is being continuously and dynamically adjusted in order to drive it toward unity. I've not a clue regarding a possible mechanism, but it just has a sort of 2nd Law feel to it.

It's a very old metaphor for a quick, natural exit.

Are you talking about disease of the young or the old? There's a difference. During my lifetime there have been significant global reductions in mortality of the young and one would hope that this positive trend will continue. However, as one who has seen most of his former friends and work colleagues pass on, I would suggest that there are positives in not exiting this world to a fanfare of dementia and double incontinence. We are mortal and sooner or later something will get us. There are a whole raft of fatal conditions that evolution has not eradicated because there is no advantage to the survival of our genes in doing so. This is part of the human condition whether we choose to accept it or not. There does come a time when the survival of our offspring is best served by the removal of our burden on them. It would seem selfish not to accept this. Better to make peace with oneself, and when the time comes, accept pneumonia as the old person's friend. There are many much worse ways to go.

How many of these statements can be paraphrased as: 'Significant variation in property X would reduce the ability of the universe to meet the spatial volume and particle diversity requirements of the 2nd Law of Thermodynamics.' All of them I think. I have a nagging suspicion that the cart may be being put before the horse. Perhaps the universe simply does what it is obliged to do to meet the 2nd Law. The settings of the various coupling constants etc then become less of a 'lucky lottery ticket' and more of a forced asymptotic approach to optimum values.

With the possible exception of whatever beast lies lurking in the heart of a black hole, there is no such property as 'incompressible'. The term simply betrays a lack of ambition in mustering the scale of forces necessary to facilitate the compression. Neutron stars would make pretty effective car presses. Even for Saabs and Volvos.

How does the OP manage to cope with that most unsafe of environments, real life with its utterly unbearable lack of any retrospective editing facility?

I think I owe @Ken Fabianand @exchemistan apology here. I took a closer look at the overall changes in gravitational potential energy due to isothermal nett downward diffusion of CO2 in the atmospheric column and obtained a result I didn't expect. For sure, descent of CO2, and the corresponding ascent of an equimolar flow of the lighter gases does result in a small local reduction in GPE, However, It also results in a small local reduction in pressure due to the reduced mass of the air above, and this results in expansion. The figure is tiny, but it is not local - it raises the entire air column above it with a corresponding increase in GPE. As far as I can tell, the two effects cancel out exactly at least when subject to a uniform gravitational field. So wiith zero contribution from GPE and enthalpy, the only drivers for Total Free Energy are the entropy terms which favour a constant mole ratio. I'm sure variation of gravity with height must have some small second order effect. Because centrifuges again, where such gradients are many orders of magnitude greater.

A while ago I highlighted this paper https://www.liebertpub.com/doi/10.1089/ast.2022.0027 ... which - well just glance through it at least. It describes a catalytic conveyor belt for churning out a steady stream of modestly sized RNA sequences. Which when coupled with a mechanism to produce its raw material input nucleoside phosphate monomers (see https://www.cambridge.org/core/journals/quarterly-reviews-of-biophysics/article/nucleic-acids-function-and-potential-for-abiogenesis/842529B9BDAD6E86F7919827725C1931) ... appears to have the potential to fast-track evolution of the apparently highly improbable by a factor of many orders of magnitude. Obviously, there is still a long way to go with this, but the bottom line is that we know with certainty that the first stirrings of life were present on earth very early in its history. And recent progress as described above are a credible basis for suspecting that the mechanisms may have been non-magickal.

Fleetwood Mac's Rumours album. Not really my kind of music, but they were a part of my 'growing up' and the passing of Christine Perfect/McVie has knocked me a bit off kilter. A tear in the eye when I listen to 'Songbird'.

I presume the near simultaneous disappearance of 2 reputation points from my posts on this topic, and your reappearance on this site are not unconnected events. Just to be clear. None of negative reps you received for the quoted post came from me. They are the result of how others perceived your behaviour.

Everything we have ever observed regarding the 2nd Law of Thermodynamics flatly refutes the idea of reincarnation as a global destiny. It is entirely the wrong picture to have in your head as to the nature of entropy. Our destiny is to boldly go where no one has been before. The future cannot ever revisit the past. Having said that, of the many 'pop science' definitions of entropy that have been kicking around for the last century and a half, I've found the greatest assistance from picturing an increasing entropy as a measure of increasing global diversity. It has at least the virtue of a more positive vibe than 'chaos'. Or 'gunk'.

When you refer to 'an old keurig machine' are we talking about a coffee machine? In which case it will probably be the air purge pump. Google tells me that these typically have a maximum rated air output pressure of 350 mmHg.

An interesting point that got me puzzling over the differences in Stokes drag between the macroscopic and molecular. We know from school chemistry that one mole of say, hydrogen at stp can occupy a sphere of radius 0.175 metres and present a surface area of 0.096 m2. Not much to resist the quarter of a Newton or so of buoyancy forces propelling it upwards. But what happens when the hydrogen is diluted? It's still the same 2 grammes of hydrogen experiencing the same 0.26 N force, but now each molecule is an isolated 'sphere' of radius 4.46 nm in an ocean of heavier particles. And the total area presented for drag to act upon is a little over 150 km2. I'm sure I've probably taken a few liberties in extrapolating viscous behaviour below the sub-micron scale. However, nine orders of magnitude is a pretty comfortable safety margin to conclude that buoyancy probably has considerably less impact at the molecular level than our everyday macroscopic experience might lead us to expect.

Rather than extract heat from the engine block, you could in principle raise superheated steam from the far greater heat output in the exhaust. This is the principle employed in Combined Cycle Gas Turbine (CCGT) power stations where each gas turbine exhausts into a Heat Recovery Steam Generator (HRSG) for driving a supplementary steam turbine. This increases station electrical output by about 50% for a given fuel consumption. Not a very practical proposition for a car though.

Now you've sparked my interest! The Reynolds and Chilton-Colburn analogies describe strong correlations between the flows of heat, mass and momentum which apply irrespective of whether the transport mechanism is via molecular diffusion or eddy diffusion. Essentially, the direction of transport of each is so as to flatten the gradient driving it. For instance, one thing I am well aware of is that the further your hydrogen plume moves away from the source, the more dilute the hydrogen becomes due to convective admixture of air, and correspondingly, the higher the concentration of hydrogen in the surrounding atmosphere. The trend is uniformly toward equalisation of concentration. The gradient tends toward zero. I don't see the thermodynamic exception you're referring to, and am curious since it suggests a significant and unappreciated asymmetry in what I understood to be a very consistent picture.

@Ken Fabian seems to be effectively stating that the maximum random-direction particle velocity due to thermal agitation exceeds the local bulk velocity of the ascending/expanding plume. Therefore at any point in the plume, some of the hydrogen content must be travelling downwards. Is there a flaw in this logic? It does appear consistent with the Briggs equations and Gaussian dispersion equation used in dispersion studies of flue and flare stacks that I've had some (albeit limited) exposure to.

'Weather' tends to keep the troposphere very well mixed as you suggest. Ozone is a rather strange fish on several counts. The long and short of it is that it has a short half life at normal sea level temperatures so it's natural distribution is generally limited to the frigid upper atmosphere where it's created.

While posting, I had uranium enrichment by centrifuging UF6 in mind. While I have the opportunity, I need to clarify that I've quoted Gibbs' Free Energy rather too freely in my post. In context I'm referencing more of a total free energy so dH should be understood to include gravitational potential energy which is indeed the the active quantity. It's the -ve change in this that enables a +ve entropy change. Analogous to an exothermic reaction without actually being one!

Consider dG = dH - TdS For a column of atmosphere at uniform density & pressure under a gravitational field, a downwards vertical flow is favoured (supporting the argument of @studiot) since the release of gravitational energy increases total enthalpy sufficiently to counter the reduction in entropy due to reduced occupancy of the higher levels of the column. So we have established an equilibrium condition with a vertical density/pressure and entropy gradients much as the atmosphere we see around us. But for further gravitational settling of, say, CO2 to take place, the gravitational potential energy released is now countered not only by the entropy gradient, but also the necessary displacement of an equal volume of lower density gases previously below it generating an adverse temperature gradient and expansion of the lower levels due to both the temperature gradient and the reduced mass of the upper part of the column. In short, while dH is likely not zero for a perfectly uniform gas mixture (constant mole fractions) it becomes so small that it can support only a tiny mole fraction gradient. I therefore suspect that while @exchemist and @Ken Fabian are not quite 100% accurate in their assertions, in practical terms they are very close to measurable reality. It's certainly an approximation I used throughout my working career without a qualm. The 'phosgene' counter argument simply reflects the very low rate of diffusion of high molecular weight gases. The thermodynamic equilibrium remains an (approximately) evenly dispersed mixture. It's just that these cases take their time about reaching equilibrium.

Bear in mind that Antarctica has been sat in splendid isolation under some degree of permanent ice sheets since at least the Eocene-Oligocene boundary some 35 million years ago. Simply a less dramatically eventful story than the relatively recent ebbs and flows of the Northern ice sheets. The major differences seem to stem mainly from one pole being covered by a continental land mass (very stable) and the other by an ocean.

To do justice to your question, @Externet I should add that strictly speaking my response corresponds to the 'design load' on the nozzle when there is either no flow (due to eg a closed valve), or when the fluid is sufficiently viscous that its shearing force on the pipe wall far exceeds its gain in momentum. At the other end of the spectrum, we could in theory propose the unrestricted flow of a zero viscosity fluid where none of the fluid inertial acceleration is lost to shear at the pipe wall. In this case, the only axial force acting on the pipe in opposition to the restraining force of the interference fit, would be the vessel pressure acting on the pipe thickness (your 'torus' case). Real flowing cases should be expected to fall somewhere between these limits. In short, good question. Deserved a more considered answer.

I think you probably intended 'proton, electron and antineutrino' here?

The force acting to propel the pipe back out of the hole in the vessel is equal to absolute fluid pressure times the area of the hole in the vessel.