sethoflagos

V here really stands for voltage difference, not absolute voltage. So when you say: Your question reads as if the voltage gradient along the wire is zero. Did you intend that the two ends of the wire are maintained at a constant voltage difference? This would make more sense.

I think the correct answer to this rather odd question is yes, though if the wire has any resistance then that uniform current is zero. In the absence of reactive elements (capacitors or inductors) a constant current implies a constant voltage gradient. If the load is purely resistive, then the current is in phase with the voltage. A purely capacitive load will make current lead voltage by 90o. A purely inductive load will cause a 90o lag. Practical loads fall somewhere in between these extremes. The variation 'along the wire length' needs to take into account that the electrical field propagates at some substantial fraction of the speed of light, so the wavelength is oto 4,000 km at 50 Hz.

This reminds me of how pressure is not an 'energy' but mediates the transfer of internal energy of a gas which is a function of temperature alone. However, pressure is a 'force' so that analogy breaks down. I did wonder why electron charge cropped up as a coefficient on both terms of the Lorentz force, both the E and vxB terms. So without q there is no electromagnetic force. Is this what you mean? That the B field is merely a mechanism for transforming dynamic changes to the Coulomb force into a torsional effect?

I suspect that the guarded responses you've received to this query so far are because the simple answer we used to be given at school was bowlocks and sort of implied the existence of magnetic monopoles. Hence no self-respecting physicist will go down that path. As I don't fall into the above category, I'm quite content to picture the energy source as a form of potential energy created by the separation between the nail and the magnet. Much akin to gravitational or (ahem) Coulomb potential. As nail approaches magnet, potential energy begets kinetic energy begets heat (in collision) producing a new magnet that is the sum of its initial magnetic dipole moments, just as a meteor descending to earth creates a new body that is the sum of their individual masses. Now I am expecting this simplistic picture to be shot down in flames, but then I too will be wondering (in the absence of electrical current) where the energy came from.

If all spatial dimensions loop back on themselves seamlessly, so that whichever direction you travel in, after n light years you are back where you started, then what does 'centre' even mean? It's definitely finite with a volume oto (n light years)3. But there is no point more remote from the boundary than any other because there is no boundary. All points within the space are geometrically exactly equivalent.

Pretty sure there's a x-post here with @exchemist so briefly: If we're starting from your declared position of maximum attraction, we're moving against an attraction force for 900; then with a weakened repulsive force (poles wide apart); then against the same repulsive force; then finally with the mirror image of the attraction of the initial power stroke. In the absence of a proper mathematical analysis, by symmetry we have a nett zero sum. And then there's cam friction and the hysteresis braking mentioned earlier. Granted I've ignored secondary effects of the movement of the magnets themselves but frankly, that's beyond my pay scale. Suffice to say, if there was anything to see here, Faraday would have found it back in the day I think. Looks right enough, so you've got the 1800 phase shift covered. Shall we leave the +/-900 phase shifts to the OP?

You're not answering the question I asked. When there is a tab directly between the magnets, are the magnets at minimum separation, maximum separation, or somewhere in between. Just to be absolutely clear on where you want to push and when you want to pull. It makes a difference. Rather like the ignition timing on a combustion engine.

In return, perhaps you could clarify something for me. What is the phase relationship between magnet pole separation and finger position? If we define zero degrees for the disk when a finger is directly between the poles, and zero degrees for the poles as minimum pole separation, then what phase difference between the two should we consider for optimum performance? And how is that optimal phase difference maintained?

Different words, same thing. It's the repulsion of like poles that causes the field rotation I took as a given for sake of brevity.

Perhaps one way of looking at this contraption is to compare it with a Faraday disk (aka homopolar generator). In the latter, both motion and induced current are in the plane of the disk with the magnetic field perpendicular. The OP is rotating this so that motion and magnetic field lines are in the disk plane therefore forcing induced current into the perpendicular. However, different portions of the disk will see different current polarities depending on whether they are moving towards or away from the magnetic poles. In particular, the portion of the disk passing directly between the poles will see a sharp switch in polarity and consequent current flow component appearing in the disk plane. This will in turn deflect the magnetic field lines somewhat out of the disk plane as if attracted by a temporary opposite pole. I don't know whether it's a good picture, but in my mind's eye, I'm seeing this induced temporary pole falling into a potential well only to climb back out as it departs with no nett overall energy change in and of itself. However these circulating currents are a different matter as they will add a time lag to the ideal case making ascent harder than descent, acting as a brake in exchange for simply heating up the disk.

Either of the two main smallpox vaccines can control it, so if it were perceived as important (eg by killing white people instead), it would be easy enough to deal with. We get the odd case here from time to time. Nature's way of telling us not to mess around with rope squirrels (suspected wild reservoir).

Actually both are correct providing dU/dS is evaluated at constant volume and dH/dS is evaluted at constant chemical potential. Look at the wikipedia pages on thermodynamic potential and Maxwell's relations. However, since 2019 the international community has agreed to settle on the former as the official definition of thermodynamic temperature: One thing this equation tells us is that if an amount of energy dU is transferred from a warmer body to a cooler one, the TdS values for each must be equal in magnitude (though opposite in sign). This can only be so if the lower value of T for the cooler body is balanced by a proportionally higher value of dS. Therefore the total entropy change for the two bodies is positive, Howl at the moon as long as you like, your absorbed photons have been dissipated (as phonons in context) and cannot be recovered intact.

Well there's a big mistake here. The vast majority of absorbed photons originate from emitters at a higher temperature because of S-B's T4. Therefore the vast majority of absorbed photons lead to an entropy increase in the emitter/absorber system because dU = TdS. Therefore the reemission of photons you propose would cause an overall system entropy decrease in contravention of the 2nd Law. No amount of arm waving will rescue your hypothesis from this.

But what you don't know is what enthalpy is and where its use is appropriate. It isn't here. Temperature is defined as the inverse partial derivative of entropy with internal energy, not enthalpy. This is just off-topic waffle. Familiarise yourself with Debye's theorem. And why that superseded Einstein's photoelectron model. That should help clarify.

No you can't. That's convection currents.

Enthalpy includes work previously performed on the environment by the system. Since that energy is no longer contained 'in the system' how can it be pertinent to current system temperature? If you ignore all degrees of freedom bar translational, it is a fair approximation for the internal energy of the noble gases. It is simply the wrong expression for enthalpy. A couple of points here. For solids, N refers not to number of molecules, but number of atoms. Secondly, solids support shearing vibrations that gases do not, and therefore have the corresponding degrees of freedom to accommodate this. Of both counts, you are not comparing like with like and therefore your logic has no foundation. Consideration of degrees of freedom explains almost all the differences in expressions for molar heat capacity. Isothermally? Like your last equation. your understanding of thermodynamics needs work.

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.