exchemist

No. The uncertainty principle comes from QM, not relativity, and relates to non-commuting operators or, in the wave formalism, to certain pairs of properties being related to each other through Fourier transforms, whereby increasing precision in one leads to loss of precision in the other. QM is applied to physical systems - objects, if you like - rather than to spacetime.

I don't know the first thing about this program, but it sounds to me as if it may use some sort of method of iterative approximation that converges towards a final value. If that is so it may be programmed to stop iterating when the difference between successive iterations falls below a preset level, or something. Could that makes sense?

Yes, so I discover.

Rotons go very well with "p"s, I find.

Well it's multiple choice, so all you need do is choose an answer that seems sensible. What % of the enzyme is bound to the substrate at the Km value? You should know this from the definition of Km. So then you can ask yourself whether the actual concentration of substrate is higher or lower than this - and choose an appropriate answer accordingly. (At least, that is how it seems to me. Being a chemist, I didn't know what Km was, so I've had to to look it up. But I think I could now choose the correct answer.)

Bacteria have a length of the order of 1 micron. The honing pattern in the cylinder liner of an engine, which is a pattern you can see but can't easily feel with your fingers, has grooves about a micron in depth. So if the scratches you are talking about are of this magnitude there will not be space for a colony of bacteria to hide in them. But as @Peterkinsays, there are some bacteria on all surfaces that have not just been sterilised and there will no doubt be a few in the scratches too. This is not a concern. The vast majority are not harmful and even for those that can be, our bodies are adapted to dealing with the sorts of low levels of them we are likely to encounter in daily life.

There are intermolecular forces acting between the molecules in the liquid, which have to be overcome in order for molecules to slide past one another. At higher temperatures, a greater proportion of the molecules have enough kinetic energy to overcome at least some of these forces, reducing the resistance to them moving relative to one another.

It looks as if this is part of a general mathematical course. Learning basic differential calculus is relatively easy and doesn't require much of all that stuff. I learned it when I was 15, as part of the old UK O-Level syllabus. I don't think statistics helps much with learning calculus. You just need to draw functions as a graph and see how you can make approximations to the slope of the line that, in the limiting case, give you an exact value. There are various videos on this. Looking at them quickly I thought this one was fairly clear. The chief mathematical idea is the idea of limits, what happens to an algebraic quantity when one variable gets smaller and smaller and tends to zero. But then the power of knowing the slope of a function at any point on its graph is that that represents its rate of change. This leads onto all sorts of applications. For example the rate of change of distance with time is velocity and the rate of change of velocity with time is acceleration. Also, the point a slope becomes zero is a maximum or a minimum (or sometimes a point of inflexion) of the curve, so you can find maximum and minimum values of functions this way. And there are lots more applications of course. Integral calculus is the inverse process, in effect calculating the area under a portion of a curve. There are teaching modules on that too. So I think you should be able to short-circuit the modules of the Khan Academy course and go directly to calculus, provided you are OK with algebra and graphing functions and can understand limits. (I speak as a chemist rather than a mathematician. It may be that a proper mathematician would disapprove of the short cuts I am suggesting.)

Not sure, but it could be. Salt marsh seems to be what they are advocating. But actually this marsh stuff is different from your original link, which was about things like kelp and sea grass i.e. actual seaweed, growing under salt water.

Thanks, that is more informative. I notice however that the emphasis is on conserving existing littoral ecosystems, i.e. preventing their loss, rather than developing them as new carbon sinks to sequester more carbon from the atmosphere.

The article seems pretty poor at explaining it. There is a handwaving mention of kelp and seagrass but no discussion of the associated carbon cycle. These are plants with finite life. What happens to the carbon when they die? Maybe someone here can comment.

I've a feeling I've seen this silly question before, somewhere.

Surely the relevant question is how high this lake or tarn is above the generating station, i.e. the head available for power generation. In the Highlands, one of the things that is free is height.

Indeed. If you read my description of the inductive mechanism in the OP, it explains how that can take place.

Yes Trevor it was stimulated by the research I did on this arising from your question on the other forum. There are more scientists here, so there is more of a chance of getting further with the topic. Suggest you read and learn, and refrain from outlandish speculations.

Curiously, Maynard's name does not appear in the review of the various models that I linked in the OP. A lot of work has been done since the 1960s, so it may have been superseded. Rather than sending me 10 pages by PM, is it possible for you to post a short summary of its key features?

Nice. This seems to be the inductive model, more or less.

I think it best to keep in mind what is happening physically, to ensure your answer makes sense. If there is a volume reduction, the atmosphere is compressing the system. Then as @sethoflagossays, that adds internal energy, so if what you get out as heat is less than this, the net internal energy must have gone up, so ΔU has to be +ve. But I confess I too was thrown by the term "expansion work" when in fact what happens is the opposite, viz. compression work - at least from the system's point of view. It may be that the learning point for both of us is what @sethoflagos says about "expansion work" being used to denote any form of PdV work, regardless of whether it is expansion or compression of the system. I was never taught this terminology. We always spoke of "PdV work" and left it at that, which is far less confusing in my estimation.

What does this tell us about the mechanism by which charge separation takes place in thunderclouds?

I wonder if this is to do with the wording. They say 22kJ is expansion work done "on the system". They don't say 22kJ of expansion work is done by the system. Presuming "the system" means the reactant and products, I'm confused as to whether the atmosphere does work on the system, i.e. the volume decreases in the course of the reaction, or whether the system does work pushing back the atmosphere, i.e. the volume increases. If the volume increases, then I agree the internal energy change must be enough to supply that work AND still give you a measured heat output of 15kJ.

From my experience in the oil industryI'm aware of static generation in insulating liquids flowing in a pipe or in charged droplets in water sprays, used in tank cleaning etc, but I don't believe I've come across the idea that liquid falling through air does this to a significant extent.

Cloud to cloud discharges are extremely common in thunderstorms. But my interest is in the charge separation mechanism. Handwaving about the triboelectric effect (which by the way also seems poorly understood) doesn't seem to help very much. Regarding cloud to ground discharges, my understanding is that it is the charge separation within the cloud which causes a polarisation of the earth beneath and that is what leads to a lightning strike. I've never heard of any triboelectric effect involving the earth (what would "rub" against the earth and how would that work?).

It may be but it seems to address a different issue, viz. how the lightning discharge occurs. Does it actually discuss the mechanism of charge separation? I'm not going to waste time watching a video that may be irrelevant to what I'm trying to understand.

Due to a question asked on another forum, I tried to look into the mechanism by which charge separation takes place in thunderclouds. To my surprise it seems we still don't know how it happens. I found this paper, summarising the various hypotheses and the drawbacks of each: https://www.researchgate.net/publication/227134643_Charge_Separation_Mechanisms_in_Clouds Apparently the leading hypotheses are an inductive mechanism, relying on polarisation of liquid water droplets and one involving charge transfer between "graupel" (soft hail) and ie crystals. The inductive hypotheses relies on the idea that the electric field within the cloud (+ve at the top and -ve at the bottom) polarises the larger droplets, which are falling under their weight, so that they become positively charged at their base. When they encounter small droplets, which are rising due to the convective updraught in the cloud, they abstract electrons, leaving the small droplets with a +ve charge. So this leads to a further accumulation of +ve charge at the top and -ve at the bottom, further strengthening the electric field and so on. The ice one was more intriguing. Experiments at Manchester University have apparently shown that when falling lumps of graupel contact ice crystals, charge tends to be transferred, the extent and polarity of the transfer depending on the temperature. I found myself wondering why there should be a difference in tendency to lose electrons - or protons - (it is unclear which are the charge carriers in the interaction) - between crystalline ice and the presumably more amorphous ice in graupel. I wonder if it may be to do with the edges and vertices of crystals. There will be unsatisfied valencies there, since the molecules at such locations are not fully bound into the lattice in all directions. The paper doesn't go into this, being more concerned with the physics of the overall process. Anyway, it seemed interesting that this is not yet well understood. I wondered if anyone here might know more about the subject.

Metallic gallium seems to have low toxicity. From what I read it behaves more or less like Fe in biological systems. I don't think handling a bit of it will do any harm.