sethoflagos

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.

Looks very much like the parts are cut from a fair sized slab of 6mm thick elemental silicon. Thank you for bringing this to our notice. And sharing an imaginative application that certainly sparked my interest!

Metalloid rather than a metal per se. It's got a very high melting point so it won't object too much to having a hot pan placed on it. Pretty tough too.

Several reasons, but we can begin with entropy since you've overlooked a major consideration. The copper ions (actually Cu(H2O)6 2+) and sulphate ions have many more degrees of freedom floating around in the liquid phase than they do locked up in a solid crystalline phase - enough for that route to be thermodynamically favoured. Dissolving copper sulphate in water is an exothermic process anyway, due to the additional ligand bonds formed in the hydrated complex ion, so the Gibbs Free Energy arrow is only ever going to point in one direction (at normal ambient conditions at least). The extra bonding energy formed in such complex ions helps low reactivity elements (including platinum group metals) to leap up the reactivity index, so the latter is only a very approximate indicator, and often misleading if taken at face value.

It depends on your sign convention. For myself, work performed on the system by the environment is -ve, because that's how I was taught. And that's the convention adopted by your book. But if energy is added to a system, the energy of that system must increase, and that's the mental picture that it's important to hold on to.

The exercise is misleadingly worded. If a +ve amount of work is 'done on the system' then this must be understood as energy being added to the system whatever sign convention you are following, and therefore the internal energy change arising from that work must increase. This is where your method gave the wrong answer. The term 'expansion work' is commonly used as a synonym for any PdV process even when, as in your example, the system is being compressed. We know that the book intends compression because their PdV term is negative, and therefore dV is negative.

Raw coal-fired power station flue gas is hot. So to use it, you have to cool it down to a level that will not kill your vegetation. When you cool it to that degree much of the water content condenses out, dissolves the SOx and NOx combustion products, and produces a very acidic 'rain', which will likewise kill your vegetation. At least partial removal of the NOx and SOx is possible (I was involved in commissioning a few stages of the Flue-gas Desulphurisation Project at Drax Power Station in the 1990s) but it is a seriously expensive process.

If you're specifically interested in thermal storage where space is at a premium, then the quantity of interest may be the volumetric heat capacity (typically MJ/m^3/K) There's a table you can play around with at https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities Fond memories of playing in front on my grandmother's Rayburn oven predispose me toward cast iron. However, water or high density masonry are probably more cost effective.