sethoflagos

The temperature difference between two adjacent regions aotbe typically decays per a lag function (1 - exp(-t / Tn)) where t is elapsed time and Tn is a characteristic time constant. Series of multiple connected regions (like Earth's surface) therefore tend towards the product of multiple lags as they move towards a new equilibrium. A second order lag produces a smooth 'S' shaped function between initial and final states. Higher order lags produce more of an initial delay followed by a more abrupt transition. The principal pattern falls straight out of Fourier's Law. I think you might find it a little more useful than a polynomial fit.

As @swansont infers: This is not true for heat transfer by thermal radiation where dQ is proportional to d(T4). ref (https://en.wikipedia.org/wiki/Thermal_radiation) This point has now been made to you several times and you have failed to address it properly. There is no nett energy transfer at thermal equilibrium. Is that your defence? Under some very special circumstance 0 = 0 whichever way you calculate it?. Not much of a defence is it, really?

Rather than state them, I'll quote them: If you'd stated that this observation was limited to the monatomica gases and low temperature hydrogen, then no one would have batted an eyelid. However, as presented it appeared that you intended this as definitive and universal. When this idea was immediately blown out of the water by @exchemist's query about the temperature of solids, you might have considered retracting. But instead you shifted your ground to the following argument: With the sole exception of the theoretical ideal constant volume process, this isn't even true for the monatomic gases. So far from strengthening your case, it actually weakens it. It certainly comes across as an article of faith. Hence the degree of kickback perhaps. The only instance I can think of where thermodynamics treats translational and internal degrees of freedom differently is in the theoretical analysis of diffusivity coefficients (both thermal and mass). Which sort of makes sense since diffusion is hardly likely to happen without some translational motion. Not particularly relevant to my own areas of study, but if you're interested they get a mention in: https://en.wikipedia.org/wiki/Thermal_conductivity_and_resistivity https://en.wikipedia.org/wiki/Mass_diffusivity

A bit of algebraic rearrangement from what? Case under consideration (for illustrative purposes), constant pressure heating/cooling of a substance for which internal energy is a function of temperature only. PV = RT (per kilomole basis) By Mayer's relation R = CP - CV PV = (CP - CV)T Take partial derivatives and substitute appropriate values for constant pressure process, VdP + PdV = CPdTP - CVdTV 0 + dW = dQ - dU Hence: dU = dQ - dW Obviously, for a constant pressure process, P is anything but proportional to T. That the same ideal gas law applies to argon, nitrogen, carbon dioxide, water, and ethane proves the point I was making. That all these gases have different heat capacities, particularly at higher temperatures, also proves the point I was making. Per the above, your 'proof' seems merely a tedious repetition of the patently false. We are talking about gases... simply place it in a sealed borosilicate glass flask. Last time I checked, even borosilicate glass had a finite Young's modulus and non-zero thermal expansion coefficient. Why are you fixated on particle collisions? Particle collisions are irrelevant to the point I was making. What do temperature and pressure even mean when there are no particle inteeractions to communicate them? In context, it's any defined path between different thermodynamic states. Such as changes in temperature and pressure. Or is your conjecture also confined to conditions of thermodynamic equilibrium only?

The internal energy of thermal radiation within a space occupied by a gas is accounted for by the internal energy of the photon gas that co-occupies that same space, Look at the wikipedia page on 'photon gas' for an explanation. At everyday temperatures, black body photons capable of inducing electron orbital jumps are to all intents and purposes non-existent. The dominant process for generating black body radiation is via the acceleration of charged particles, and as @swansont has pointed out, this can be many orders of magnitude below the internal energy of the matter phase. There is interchange between the matter phase and proton gas phase, and this can have effects during dynamic changes in thermal equilibrium. Off the top of my head, it's one reason we can never quite achieve the theoretical adiabatic combustion temperature in fuel burning processes. But if you only start getting a glimpse of a phenomenon at >1500 K, there really are no grounds whatsoever for claiming it to be a dominant process at normal, lower temperatures.

Glad someone was listening 🙂 Worth a +1 just for the mention. Hope someone else is listening.

This simply doesn't follow. The IDE is not universal, particularly for higher pressures, and says nothing of the nature of particla collisions. A bit of algebraic rearrangement gives: CVT = CPT - PV which is equivalent to U = Q + W. This demonstrates that it's simply a convenient reformulation of the First Law. Obviously, CV and CP include all available thermal degrees of freedom on an equivalent footing. All practical thermal processes involve bulk expansion or compression. A truly constant volume operation would be rather difficult to achieve in practice. Gas processes operate within a spectrum that ranges between two idealised endpoints: the isothermal (PV = constant) and the isentropic (PVk = constant) where k is the ratio of specific heats CP/CV. As a general rule, the faster a process occurs, the more nearly it approaches the isentropic endpoint. This is a strong indicator that all thermal degrees of freedom are immediately available to momentum exchange. Everybody needs some kind of mental picture to help get their heads around such physical processes, and as you've pointed out, equipartition allows estimation of pressure and temperature from consideration of linear momentum alone. But to extrapolate from this an independence of rotational and vibrational modes is to confuse correlation with causation I think. At least it rattles the mental pictures others have which may be no bad thing, but you're going to get some kickback for that.

@KJW. I understand that you regard my last few posts as too much of a waste your precious time to be worth responding to. But I trust that in turn, you will not object to me regarding your silence, particularly wrt the non-conservation of linear momentum in general gas collisions, as concessions to the arguments presented. Live long and prosper.

But it isn't. The 'boink' of each collision that creates the emergent property of pressure is in itself the vector sum of translational, rotational and vibrational momentum changes along the axis of point contact. The 'independence' you claim relies on the fact that statistically the rotational and vibrational transfers average out to zero over a sufficiently large number of collisions. It's a mathematical artefact. Imagine being hit by a spinning dumbell. It makes a difference which end hits you.

Only in one very special case: that of a theoretical constant volume thermodynamic process. More general cases show P, T dependence involving the ratio of specific heats, (~7/5 for diatomic gases) which per force requires consideration of all available thermal degrees of freedom, not just the three translational ones. Exactly!

No it doesn't. It just conflicts with your rather unusual interpretation. As @exchemist, points out, your unusual interpretation collapses for cases where there are no translational degrees of freedom.

Therefore all degrees of freedom contribute to equilibrium system temperature. This is the traditional thermodynamic definition of temperature.

T = dqrev/dS (constant V, N) What's going to your calculation of T if you decide to ignore some of the degrees of freedom that contribute to system entropy?

And yet when we measure temperature gradients between systems at different temperatures, in non-extreme conditions they are generally linear in agreement with the dominant mechanism for transfer of heat being by momentum exchange. If the dominant mechanism were EMR as you suggest, then the measured gradients would be highly non-linear (cubic in delta T I think). I understand your POV but I think it's a misleading one. Particle collisions in gases that support rotational and vibrational modes only follow conservation of linear momentum on average. In the general case, some momentum is transferred via the other modes.

Preference? We know that metals expand appreciably with increasing temperature, so some of the thermal energy is absorbed in the 'static' phenomenon of increased interatomic bond lengths. But this isn't thermal energy anymore and doesn't contribute to the temperature. You can't discard lattice vibrations just because you don't like them. And I think you'll struggle to explain the typically high thermal conductivity of most metals if you ignore the free electrons.

Maybe we're just drawn by curiosity to things that stand out from the background.

At least they sound more impressive than their literal English translations ('jitter motion' and 'braking radiation'). I'd not call it a 'pet peeve' as such but I've learnt to always bear in mind that translations of foreign technical documents are rarely error free. I had a salutory lesson during design work for a couple of utillties supply facilities in Malaysia. I requested some local groundwater analyses from the client, and when they arrived I learnt that the Malay word for water is 'air'. That caused a stir of interest at the hazard and operability review.

After 25 years in Nigeria, fufu (go Google) remains a step too far for me. I try it from time to time but come away from the experience understanding that I'm evolved to find a good crusty loaf my carbohydrate of choice. Mrs Seth loves it and total respect to those who can share in that pleasure, but it is a taste I have yet to acquire.

The.ramp slope should be no more than what is needed to get the pellet rolling. Too steep and the pellet will slide rather than roll smoothly. Assuming a true conical profile, the pellet will follow a track bounded by two circular arcs of radius length x 6 / (6 - 4.5) mm and length x 4.5 / (6 - 4.5) mm. You might consider embedding photo detectors.in the ramp just outside these bounds to detect out of tolerance pellets coupled to a deflector arm or similar to dispose of them.

Evolution in cat size tends to be governed by niche partitioning: cat species don't thrive when in direct competition with other carnivores of similar size. In much of southern Amazonia there are six 'common' cat species. In size order: jaguar, puma, ocelot, jaguarundi, margay and oncilla. They each avoid direct competition by feeding on different prey appropriate to their size. However, the jaguarundi and similar sized margay avoid competition by one being diurnal, the other nocturnal. If they'd diverged in size instead, they'd encroach on niches already occupied by ocelot and oncilla. So the whole cat guild can be viewed as coevolving in such a way so as not to step on each other's toes.

Why do you omit the cases of large cats getting smaller or small cats getting larger, both of which are supported by the fossil record?

The Na:K mass ratio order of magnitude appears to be established by the ~11:1 ratio in the Earth's mantle. This probably manifests predominantly as hydrothermal vents entering the oceans at mid-oceanic ridges. Beyond that it gets complicated as the elements take different routes in their respective cycles. However, a huge amount of ancient marine potassium has become preferentially locked up in the granites of the Earth's continental crust which must account for some significant depletion of the residual potassium in the ocean relative to sodium. It isn't the complete picture but it may be a good part of it.

I'll stand to be corrected but my understanding is that apples cannot self-pollinate. Cultivated apple trees are cloned varieties grafted onto an appropriate root stock. All fruit on a tree is true to the grafted cultivar, but the seeds will not sprout true to type - you'll get all sorts coming up, even from a single fruit.

So you dispute the law of conservation of quantum information, which is a consequence of the no-hiding theorem. This is in turn considered rigorously proven by many authorities. Your argument by common sense seems to fall a little short in comparison. Google is your friend. The wiki page for 'no hiding theorem' addresses most of your misunderstandings. Even the black hole stuff.

I'm guessing you are referring to the apparent 'furrow' running roughly E-W from the SE end of Cuba to the coast of Belize. Compare with a tectonic map of the Caribbean area The feature clearly aligns with the northern boundary of the Caribbean plate, comprising two E-W transform faults flanking a small N-S trending rift zone. Yes, it looks like a furrow. But it's tectonic, not extraterrestrial in origin.