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sethoflagos

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Everything posted by sethoflagos

  1. The CMBR map tells us that the early universe was extremely close to thermal equilibrium (and in a relatively low entropy state) at least until recombination. Significant departure from equilibrium began with the ensuing localised gravitational collapses and formation of the first stars. Only then did we have the large thermal and density gradients that are necessary to drive far-from-equilibrium processes.
  2. Ignore any references to thermodynamic work for now - it's irrelevant to what you're trying to get your head around. The stipulation "at a constant temperature" simply implies that transitions between significantly different temperatures require multiple calculations over small temperature changes (ie. integration wrt temperature) Free energy values, especially for water, can easily be obtained from thermodynamic tables or calculated from standard values. But your interest is more in changes in free energy. Consider the process of water freezing. At high temperatures the free energy of liquid water is higher than the free energy of ice. The freezing of water is associated with a negative change in free energy and is therefore disallowed whereas ice will melt spontaneously. At low temperatures the reverse is true. At around 273 K the free energies are equal and so the changes in free energy for both the freezing and melting processes are zero. This defines thermodynamic equilibrium: there is no nett tendency for more water to freeze nor more ice to melt. Having established that principle, we can now look at a slightly more complex process that is (I think!) relevant to your main interest. Let us take our liquid water at (or at least close to) freezing point and expose it to a large departure from equilibrium via a significant source of negentropy: a sealed, insulated vacuum chamber The change in free energy for the transition liquid water to water vapour is positive, and so the liquid starts to boil. But this chills the water, making the transition of water to ice positive also, so we get simultaneous freezing. Eventually the vapour pressure reaches 611 Pa and the free energy of vapourisation falls to zero. As does the free energy of condensation, the free energy of melting, the free energy of freezing and incidentally, the free energies of both sublimation (ice to vapour) and deposition (vapour to ice). Thermodynamic equilibrium is reached at the triple point. But the key point to take home is that by adding a medium entropy material (cold water) to a substantial source of negentropy (the vacuum chamber) we've managed to create a relatively low entropy state (ice) without recourse to external energy input. This simple experiment belies the idea that thermodynamics cannot create ordered systems spontaneously. Given a large enough departure from equilibrium and a good mix of building blocks to play with, structures of arbitrary levels of complexity are not only possible, but inevitable. Even brain matter!
  3. On further consideration, by omitting the pressure terms from the Navier-Stokes, haven't you lost control of the conservation of energy? For a rotating system, I can visualise material falling into an equatorial disk from both sides, but there appears to be no mechanism in your system for it to cross the boundary. The momenta will just cancel (conserving momentum) but then so will the corresponding kinetic energy! Restoring the pressure term (which in context, is an expression of the system internal energy) will keep the 1st Law books straight and avoid some embarrassing infinite densities.
  4. In principle, your equations look okay given your stated constraints, but I would strongly recommend converting to polar coordinates to get as much help as possible from its symmetries. Given that your gravitational field terms are directly analogous to the pressure gradient terms in Navier-Stokes applications that I'm somewhat familiar with, you may find that at least for some simple starting conditions, the method of characteristics may help convert your PDEs into ODEs which would then be amenable to numerical integration. However, you're using Gauss' Law where I would normally be inserting a (simpler) equation of state, and that may complicate matters significantly.
  5. So in this viewpoint, there is no preferred (spatial) direction for any of the forces at play here. I was going to proceed to my follow-up question of what happens (to us) when there's no preferred direction for gravitational forces. But I'm now getting the feeling that you've already answered that. In that it's not about 'us' - it's about how mass acts on spacetime. And we're just little specks riding on that ebb and flow. Humbling thought. Thank you once again, Markus.
  6. Yes, that's the general picture I'm asking about.
  7. All is clear. Many thanks, Markus.
  8. I meant the necessity of the early universe itself being spatially infinite in this case as opposed to a (near) pointlike spatial singularity.
  9. My immediate thought was that cooking may convert some indigestible starch to a more digestible form. But then I started wondering how many calories you would expend in thawing out frozen chips in your stomach.
  10. Yusuf Automotive LPG is an undeveloped market in the US. In Europe it is developed a little more but nothing like as much as in the Middle East, Asia and Australia. Therefore there is little experience on this site regarding your question. Also, the proportion of propane to butane specified for each country varies with climate. In Britain and Ireland, automotive LPG is almost pure propane while some Mediterranean countries specify up to 80% butane. I don't know the standard for Iran (I had to ring a friend to check you had moved onto unleaded gasoline!) but I would expect your LPG to be butane rich and therefore a little more 'gasoline-like' in its combustion characteristics than that used in northern Europe. LPG octane numbers are on the low side (~90) and therefore I personally would be very reluctant to conduct this experiment particularly on an unmodified high compression engine. (Unless I wanted it to be converted to a low compression engine!). I'm sure you must know a good local car mechanic. He is likely to have a much better idea how to proceed given your particular vehicle and the locally available fuels.
  11. Engineering Databook SI Version (aka GPSA Databook), Gas Processors Suppliers Association, 11th Edition 1998 has probably helped resolve more day-to-day issues for me over recent years than any other. But most enjoyable .... probably Pump Handbook, Kurassik & al, 3rd Edition 2001. Comprehensive, very readable, more Aha! moments per chapter than you can shake a stick at. Honourable mention to 'Understanding Atmospheric Dispersion of Accidental Releases', Devaull et al.,AIChE 1995 just for the unfortunate title really.
  12. I've seen a number of references to space flowing across a black hole event horizon at the speed of light. If space can be lost in this way, what happens to the vacuum energy associated with that space? i.e. Does it increase the mass of the black hole?
  13. Many apologies for this OP as I'm sure it has been raised many times before. IFF the universe were truly infinite in spatial extent (and I appreciate the 'unknowability' aspect of this), would this imply perforce that whatever the energy density of the earliest moments of the universe, it too would have been spatially infinite? In such circumstances, would GR predict gravitational effects to be compressive, tensile or ... just undefined.?
  14. By applying an external magnetic field to the system, haven't you introduced new potential energy terms boosting the system total energy? As the magnetic particles descend this new energy gradient to a new equilibrium position how is this energy going to be dissipated other than in the form of heat? As a practical example, you might compare and contrast the removal of particulates from eg coal-fired power station flue gas by electrostatic precipitators. The pretty efficient separation of gas and solids suggests an entropy decrease, but on the other hand, electricity is consumed, and that's going to end up releasing heat somewhere or other.
  15. Wow! A third of a million views! Best come clean since we're under such scrutiny: After much deliberation, I've come to the conclusion that at least one of these statements is correct. A little more thought on my part at the time, and I should have realised this for which I apologise. If the premise of the OP were correct, the kinetic energy necessary for convective flow would be sourced by a reduction in internal energy of the flowing fluid (as is normal in fluid processes). No external shaft work necessary. From this it clearly follows that the OP case is a far-from-equilibrium peturbation for which, I understand, entropy is usually regarded as undefined until equilibrium is reestablished. So even if there was some mechanism by which this process could occur, the 2nd Law would, contrary to the OP, remain intact. Happy new year!
  16. Could one choose to define 'pressure exchange' as an 'exchange of gravitational potential energy'? Not clear on whether pressure is something that can be 'exchanged'. 'Propagated into another medium' for sure, but 'exchanged' usually tends to imply a conserved quantity, doesn't it?
  17. It's effectively a time reversed Coe and Clevenger test - the progressive fluidisation of a packed bed of buoyant particles rather than the more industrially significant progressive compaction of denser particulates from a suspension. I agree with joigus that it's not saying anything significant about pressure here. No measurements seem to be taken so I question whether it's actually saying anything about anything.
  18. Internal energy is primarily associated with fixed volume, closed processes where dU = CvdT holds. Enthalpy is associated with open, fixed pressure processes where dH = CpdT holds. In open processes the product stream is running into space already occupied by something else and that something else needs to be moved somewhere. The additional work required is contained in the PV term in your H = U + PV formula. Hence either in chemistry lab experiments or industrial processes, we generally work with enthalpy changes rather than changes in internal energy. We could use U throughout, but then we'd have to keep track of all the extraneous PV terms and it's easy to miss the odd one or two. There are many 'wrinkles' to the above but I believe you're more interested in the broad overview, and at that level the above works fine for me. Further elaboration can be found in the appropriate textbooks.
  19. Don't worry. I found the answer I was looking for at http://www.astronomy.ohio-state.edu/~dhw/A825/notes2.pdf and http://library.oapen.org/download/?type=document&docid=459733 Le Chatelier's Principle is embedded in Navier-Stokes.
  20. How is Le Chatelier's Principle Accommodated in Statistical Thermodynamics?
  21. It became quite clear after the first dozen or so posts to this thread that the insight I was looking for to answer the OP was not going to emerge. However I am actually quite grateful for this relentless exercise in mudslinging at my methodologies that you and your partner in crime have been engaged in over the last few days. They're not often questioned when employed in my professional activities, but there's always the chance that they might be and it's as well to be forewarned what arguments might be presented, whether these arguments have any significant validity, and what the most effective counter-arguments are. So thanks for that. As things stand, I'm learning more from those who are not posting and could, than from those who are, so as I've made all the points I felt like making and you're just arguing for the sake of it, perhaps it's time to draw this process to a close? Rhetorical question. You're not obliged to respond.
  22. "There are an infinite number of possible paths from an initial point to an end point in a process. In many cases the path matters, however, changes in the thermodynamic properties depend only on the initial and final states and not upon the path." - Philip E. Bloomfield, William A. Steele, "Thermodynamic processes," in AccessScience, ©McGraw-Hill Companies, 2008 Do you understand and accept this principle? If it were so, you would see that the path I choose to take from state A to state B is irrelevant. Obviously, I pick a sequence of paths that are analytic. "Of course, one can especially prepare the system to be in this state; for example compressing the gas into half the space and inserting a partition" - Franz Mandl, "Statistical Physics, 2nd Edition", ISBN: 978-1-118-72343-2, June 2013 What compressed the gas? The partition? You are prevaricating with ad hominem trivia. Seems to be an established habit on this site among some.
  23. On the contrary, it is you who is attempting to extend some unspecified microscopic action to an unspecified macroscopic effect. I know that my formulae work for macroscopic systems. You are the one making the extraordinary claim that they are somehow inappropriate so please demonstrate (with numbers!) why my formulae don't work or withdraw your objections to them. THESIS: ANTITHESIS: SYNTHESIS: Replace the box with a sphere of the same volume, and have the particles converge radially inward to occupy a concentric sphere of half the volume. The principle of the OP is perfectly preserved and the CoM issue goes away. The compression issue remains. Even Mandl invoked a piston to prepare Fig 2.1(b)
  24. So that long walk off a short pier shouldn't exhaust you There is a difference between 'arbitrarily small' and 'zero'. But compression is by far the larger work issue, and this most definitely is NOT arbitrarily small. Even isobaric compression requires 0.5 PV Joules of external work. That's oto 20% of its initial internal energy for heaven's sake. This rises to W = ln(2) PV (=0.7 PV) for isothermal compression; and a minimum of W = ((2^0.4 -1)/ 0.4) PV (= 0.8 PV) for adiabatic compression of a diatomic gas; W = ((2^0.667 -1)/ 0.667) PV (= 0.88 PV) for the monatomic case. This is the source for the 'explosive' energy release when you relax your constraint and allow the gas to undergo free expansion back to its original state. Only it can never find its way back to its original state because it has no mechanism to get rid of its bulk kinetic energy other than by recompression. This puts the lie to Mandl's case that "it would only last a very small fraction of a second". No, we are now engaged in fast, real-time energetic dynamics that are well-understood. Your steady accumulation of 'zero work' over countless eons has led to the paradoxical situation that you cannot now return to the original equilibrium state other than by precise reversal of the process that got you there. A process that you have already stated takes far longer than the age of the universe. Mandl's Fig. 2.1 (a) is a really good starting point for testing wacky ideas, because it is by definition a perpetual motion machine of the third kind. The slightest (and here I do mean arbitrarily small) nudge in the wrong direction turns it into either a perpetual motion machine of the second kind breaking the 2nd Law, or a perpetual motion machine of the first kind breaking the 1st Law. Which kind of wacky are you wishing to defend?
  25. FYI How long is "enormously long compared to the age of the universe"? A trillion years for a 1m cube initially at stp? Well let's rescale. For a 1mm cube this reduces the timeline by a factor of 10^9 ie once in a millenium. So within a km^3 of the earth's atmosphere (a 10^18 scaling factor), the frequency of events is over 30 MHz. Back-of-an-envelope tells me that expansion of 0.5 mm^3 @ 2 bar into 0.5 mm^3 of vacuum releases oto 60 microJoules. 2 kW of acoustic energy is rather a lot. If it came from a point source half a kilometer away, that's still ~0.3 microWatts / m^2 which would interfere with normal conversation. And the same sound intensity level is coming from all directions, no matter where you are. And of course, we're only considering the most extreme events. Lesser events presumably occur far more frequently yet with still comparable energy outputs. We would all be deafened by the noise!
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