sethoflagos

4 hours ago, joigus said:

Absolutely. Sorry I missed this very good argument for so long. It's only because of what you say that different molecules have different specific heats as a function of temperature. The internal degrees of freedom are totally relevant. This is exactly the reason why different molecular components have different specific heats. What other reason could there be for different gases to display different specific heats if only the CoM DOF were relevant?

Quite a different matter is how quantum mechanics introduces a cutoff for short-length degrees of freedom (independently of how poly-atomic a gas is), and how this played a crucial role in the dawning of quantum mechanics itself. (Birth of the old quantum theory as a mechanism to freeze the short-wavelength DOF.)

Glad someone was listening 🙂

2 hours ago, joigus said:

Recently, a key to why CO₂ (kinda mysterious, as it's just a boring non-polar linear molecule) is such an important agent in global warming has been found to have a root in resonances of such non-obvious normal modes due to Fermi resonances:

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

1 hour ago, KJW said:

Yes, pressure and temperature are statistical quantities. I never said that non-translational motion had no effect on each individual collision. But the universality of the ideal gas law is a testament to the statistical independence of pressure and temperature on non-translational motion.

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:

C_VT = C_PT - PV which is equivalent to U = Q + W.

This demonstrates that it's simply a convenient reformulation of the First Law. Obviously, C_V and C_P include all available thermal degrees of freedom on an equivalent footing.

1 hour ago, KJW said:

Why are you saying that constant volume is a theoretical very special case?

All practical thermal processes involve bulk expansion or compression. A truly constant volume operation would be rather difficult to achieve in practice.

1 hour ago, KJW said:

Can you elaborate on this?

Gas processes operate within a spectrum that ranges between two idealised endpoints: the isothermal (PV = constant) and the isentropic (PV^k = constant) where k is the ratio of specific heats C_P/C_V. 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.   

2 hours ago, KJW said:

If pressure is independent of non-translational motion...

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.

21 minutes ago, KJW said:

One other thing: In the ideal gas law, pressure, which is proportional to temperature

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. 

3 minutes ago, swansont said:

Seems to me there's no unambiguous argument in either direction, because the equipartition force the energy to be shared between the modes. I see nothing in literature making the distinction that it's only translational KE in systems with additional degrees of freedom. Nothing shows up in the equations, and IMO it's confusing to make that distinction when it doesn't show up in or matter to the calculation.

Exactly!

1 hour ago, KJW said:

But this conflicts with the equipartition theorem.

No it doesn't. It just conflicts with your rather unusual interpretation.

1 hour ago, KJW said:

The more degrees of freedom, the more energy. But this requires that only the ever-present three translational degrees of freedom contribute to the temperature.

As @exchemist, points out, your unusual interpretation collapses for cases where there are no translational degrees of freedom. 

34 minutes ago, KJW said:

All degrees of freedom do contribute to the entropy. 

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

49 minutes ago, KJW said:

I was actually thinking the same question. The answer I came up with was that vibrational motion within crystals is translational motion of individual molecules. The modes that do not correspond to temperature are rotations of individual molecules, vibrations...

T = dq_rev/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?

1 hour ago, martillo said:

Right. The temperature is related to the thermal energy of the system but is not a direct relation, they verify Stefan-Boltzmann Law.

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).

1 hour ago, KJW said:

One thing should be mentioned: Only the translational modes of molecular motion contribute to the temperature.

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.

1 hour ago, martillo said:

Seems to me temperature can be explained in both ways, with or without vibrating atoms. I would prefer the second one with no vibrations.

 

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.

On 10/16/2023 at 12:20 PM, Genady said:

It is obvious why bees and butterflies are attracted to flowers. But why do humans find flowers attractive?

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

10 hours ago, joigus said:

For a while I felt nervous about zitterbewegung and bremsstrahlung, but it grows on you.

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.

17 hours ago, Otto Kretschmer said:

I am not that well versed in the evolution of cats.

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.

1 hour ago, Otto Kretschmer said:

Did large cats get larger over the course of evolution or did the small cats get smaller?

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?

1 hour ago, WillyEngland said:

Did you come to a conclusion? 

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.

4 hours ago, Externet said:

What good or effect will the second bee provide with its 'better/foreign/varied' pollen to the flowers that were already self-pollinated by the first bee ?

I'll stand to be corrected but my understanding is that apples cannot self-pollinate.

4 hours ago, Externet said:

If a branch with a dozen flowers, each gets a different bee carrying one of a dozen different variety pollens, will that produce a dozen different fruits in that same branch ?

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.

It's focused somewhere but with a very shallow depth of field. So most of the image is oof 

The focal plane doesn't appear all that planar. Is it taken through an astigmatic lens?

29 minutes ago, MasterOgon said:

The Navier-Stokes equation is solved in a vector grid in a Cartesian coordinate system. That is, rectangular.

... or cylindrical (commonest in my line of work) or even spherical from time to time.

31 minutes ago, MasterOgon said:

But does a rectangular mesh relate to what happens in a gas or liquid, and is it better to use a triangular mesh?

False premise (see above) and no. If coordinate axes are not mutually perpendicular, how do you even separate the vectors into independent axial components?

52 minutes ago, MasterOgon said:

Undoubtedly, it is incredibly difficult to take into account all the factors even in a triangular or tetrider coordinate system, which is difficult even for visual perception.

Difficult for verbal perception too if you're going to use made up words.

53 minutes ago, MasterOgon said:

And in its direct form such a solution is impossible.

Then what use is it?

56 minutes ago, MasterOgon said:

But it is precisely this system that allows the logical formation of figures that we can see in water - a ring vortex or torus,

Where are the triangles in a torus?  

1 hour ago, MasterOgon said:

snowflake

Fluid?

1 hour ago, MasterOgon said:

Let's imagine a homogeneous medium that consists of individual particles.

Navier-Stokes is a continuum model, not a particle model.

This is a rather fundamental distinction and renders the rest of your post somewhat off-topic as far as solving Navier-Stokes is concerned.

1 hour ago, Photon Guy said:

Bellend One

Have you considered investing in this bold new venture?

8 hours ago, CharonY said:

Well, not only that, it also takes time and genetic isolation between populations. Even extreme inbreeding would not result in genetic isolation within a generation (or at least I cannot think of a scenario at the top of my head).

Dawkins has used hypothetical cases such as this as a reductio ad absurdum criticism of the Linnaean classification system. In particular, that intermediate evolutionary forms must be shoehorned into either a parent or daughter species at some arbitrary single point mutation event. 

The reality is of course, that genetic isolation etc allow the transition to occur over many generations of intermediates.

The OP is simply an attention seeking gross misrepresentation of Dawkins' argument. 

5 hours ago, Photon Guy said:

Well by the same token I think a good moon rock or mars rock would be a very valuable commercial property yet we don't see much if any commercial demand for the space program. NASA is entirely government funded and we don't have any private space companies that go into space. If we can create a demand for paleontology with fossils perhaps we can create a demand for the space industry. The problem with something being government funded is that if we are to increase funding the only ways we can do that is if we were to cut back on other stuff that's government funded or by raising taxes, neither of those are popular choices. 

I responded to your question about the funding of palaeontological studies in good faith only to discover that your OP was more of a vehicle to peddle conservative fiscal propaganda. Or at least take its dogmatic assumptions at face value. 

Okay then:

In general, private commercial enterprise requires a supply of well-educated young recruits (including palaeontologists and rocket scientists) but is too short-sighted and avaricious to fund public education themselves.

Relying on the population to fund their own individual education creates fundamentally unstable, self-perpetuating tiered societies where the majority are denied access to good education and the better-paid jobs that follow on from that due to lack of means.

Most of the more successful economies fund universal education programmes through progressive taxation policies leveraging preferentially on commercial profits and the wealthier sections of society to maximise the opportunities for all to realise their full potential.

This latter option carries the additional benefit that a better-educated majority is more likely to appreciate the fairness and political stability of such a system, and less likely to indulge in armed insurrection for example.

Of course, there are those who prefer the privileges they gain from less fair systems of wealth distribution. Funding for palaeontological studies for example is under constant pressure from religious fundamentalists for example as its findings tend to belie their underlying mythologies.