studiot

Don't stand there thinking too long or the tide will ave ee.

Does that make a difference to a theoretical system or the laws themselves? Where do any of the laws of thermodynamics declare zero friction impossible? Even if we have never observed it can we not treat zero friction by the time honoured method of asymptotic approach? I don't follow how your next two lines are compatible. Don't they contradict each other as underlined? The same laws of thermodynamics are supposed to apply to all systems. I merely said one can propose a system where entropy does not increase. In the case of the universe we have a few dilemmas to resolve. We do not know if the uiverse is finite or infinite. If it is infinite, does it not possess infinite entropy? If so how can entropy increase? If it is finite then what is beyond the finite? Could not some agent there move the piston? After all, what started the Big Bang if there was one? So you see there are quite a few (apparently) conflicting principles to reconcile. As a matter of interest, what is your prognosis for the future history of my piston-in-cylinder system, once activated?

Since the question was so pleasantly asked for I will tell you. Consider a sealed cylinder of ideal gas containing a frictionless adiabatic piston, dividing it into two chambers, A and B. If the piston is mechanically displaced and then released. the entropy change is zero as (say) chamber A is compressed and chamber B expanded.

I don't think John's cartoon suggests this at all, although it does examine the case as hypothetical.

When I was a pushy youngster I had a (friendly) argument with my brother about the cost of the space race. I was all for the glamour of the rocketry, despite the cost. My brother supported spending the money on something more directly useful instead. His example was improving agriculture to feed the burgeoning world population. "But," I said, "the space race yields spin-off, for example the thermal blanket." (GPS was not even a twinkle in swansont's eye in those days). Yes, said my brother, "But all R&D will have spin off. Agriculture research spin off would be different, but it would be there and we would also have improved agriculture." You never know what will come up.

Did you mean silicon? Did you also mean silicon trioxide? Chemistry is all about answering questions like these, as well as your own in the quotes. But it is much more complicated that asking how much does 1 litre of oil weigh, which can be obtained from a simple arithmetical formula. First you need to know some chemistry. The law of definite proportions. Pure substances (including elements) always combine in the same or definite proportions. So as a first approximation we can say X amount of sulphur will combine with Y amount of oxygen to form sulphur dioxide; the ratio X/Y, is always the same. But will silicon or sulphur form trioxide or dioxide? Well secondly you need to know some chemistry, specifically elementary valency. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=valency&gbv=2&oq=valency&gs_l=heirloom-hp.3..0i131j0l9.1656.4172.0.6047.7.7.0.0.0.0.234.1000.0j5j1.6.0....0...1ac.1.34.heirloom-hp..1.6.1000.KgauRuffOzE (Did you look up my last reference?) This will help you form proposed chemical reactions, according to the rules of valency. Having got your stoichiometery (proportions) correct you can ask Is the reaction possible? To address this question you need to know some more chemistry, chemical thermodynamics or chemical energetics. The reaction could proceed if it releases energy in doing so. But some proposed reaction, correct on valency rules, cannot proceed without energy being added. So you have to heat up the reagents. Even if the reaction is energetically favourable, it may proceed rapidly or slowly or even so slowly as to be be negligable. To understand this you need to know some more chemistry. Rates of reaction are covered in chemical kinetics, but this mathematics may be offset by passivation or other interfering layers. So hopefully you can begin to see why chemistry is a very large and rich subject.

Your waves sound like a lot of energy, Mike. But consider these figures. Burning 1kg of petrol releases 4.6 x 107 Joules of energy.(yes 46 megaJoules) source: National Physical Laboratory tables. Raising 1kg of petrol up 100 metres takes about 103 Joules. Yes one thousand Joules. So the hydro potential energy available due to 1kg of water falling 100 metres is 103 Joules. So the enenergy density for combustion is several thousandfold greater than for gravitational potential. Collection and concentration is the key issue in alternative energy.

What about spin-off?

What if they don't react? Are they still reactants? Chemistry is not a branch of Mathematics (nor Mathematics a branch of chemistry), but both are useful to the other. You need chemical knowledge as well as the mathematical kind. In the case of sulphur and oxygen you should look up Activation Energy. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=activation+energy&gbv=2&oq=Activation+Energy&gs_l=heirloom-hp.1.0.0i131j0l9.1031.4672.0.6938.17.13.0.3.3.0.203.1423.0j8j1.9.0....0...1ac.1.34.heirloom-hp..5.12.1549.fcOjfyfhZs4

Hi ydoaPs, did you mean this?

It is important to realise that the second law does not say entropy always increases. It says entropy never decreases, which is not the same. It is possible to offer theoretical systems where entropy does not change, but other thermodynamic variables do.

Thank you Acme, but it doesn't always work. That is the problem. There are some issues out of control of this (or any) website due to scripting in adverts (which arise offsite). Sometimes I can't scroll properly without turning all scripting off. Then I loose some site functionality, but at least I can read the posts.

I have had this problem sometimes. It seems to depend upon which browser and operating system you are using and what the settings are, particularly older ones. So please tell us what system and browser you are using.

Can you give some examples? I would say that perhaps you mean the difference is that sometimes the equation gives the conditions of the reactants and products, for example in solution, where the solvent does not participate in the reaction but needs to be present for the reaction to proceed. for example [math]N{a_2}C{O_3}(aq) + CaC{l_2}(s) \to CaC{O_3} \downarrow + 2NaCl(aq)[/math] But what happens if you just mix solid sodium carbonate and solid calcium chloride together? Both are white powders. Note 'balancing' a chemical equation only makes sense if there is a chemical reaction and there are some products different from the reactants. In the above you could say that the chemical reaction consists of dissolving calcium chloride in a solution of calcium carbonate and that calcium carbonate is precipitated from the solution, without quantities as I have done. Or you could just say the chemical reaction in words eg a more general one Acid + Base = Salt plus Water

You don't say what sort of project. So I suggest thinking about a 'light cone' and basing your project on this. https://en.wikipedia.org/wiki/Light_cone The picture at the beginning of Wiki lends itself to A sculputure An SF short story A factual essay Drawings, sketches, discussions. Also look up Tachyons.

Both issues already answered.

I've never read Mr Greene , and from your quotes, I never want to. However I would imagine he is referring to the spacetime interval, ds, which is invariant (the same for all observers) under the Lorenz transformation. It is, however, the summation of the squares that is important. ds2 = c2(dt)2 - (dx)2 - (dy)2 - (dz)2

How is it greener than the energy supplied by the existing plant?

Flat means that there is an isomorphism to Euclidian space.

More to the point would have been to have read it thoroughly. I was and always heave been discussing the replacement of one nuclear power station by another nuclear power station. I even wrote it out at similar length in post#8, for emphasis. The promise of nuclear power plants, since their inception, has always been falling power costs. There is no doubt in my mind this that project is another over-expensive white elephant, that forms one of the main reasons behind why the UK government cannot fund its proper programmes.

Thank you, billiards and overtone for that explanation. I hadn't considered that aspect. However that will not prevent the warmest salty water rising to the top of the saline layer, where it will be in direct contact with the colder fresh water. So heat will still be transferred over by conduction at this junction. So it does not prevent the heat rising and merely slows the transfer to the top layer which is the definition of an insulator.

Thanks, good catch +1

Yes I agree it is not the only consideration, but the question asked specifically "Why are we spending money...?" this was the principal clause in that sentence. One of the main justifications for the nuclear plant I mentioned is that it does not produce carbon dioxide or the other noxious pollutants from coal fired stations. However the financial facts are that it will cost considerably more than the nuclear designs it replaces and produce considerably more expensive energy. So it will be considerably financially inferior to a simple like-for-like replacement of the existing nuclear installation, which has performed extremely well over decades. So my comment stands.

Unfortunately you have not asked a simple question and both you and Strange have mixed up ideas about curvature. So here is an extract from the linked website, which is about as simple as I can find. I have underlined the relevant parts of the passages in both posts and added numbers to refer to them http://settheory.net/curvature Two types of curvature are recognised, extrinsic (2) and intrinsic (3). The statement in your post (1) refers to extrinsic curvature which is always embedded in a higher dimension, hence my query about which direction. The 'curvature' of spacetime in relativity refers to Gaussian curvature which is intrinsic (3). Intrinsic curvature is additive in regard to the principle curvatures and thus has the property that the curvature achieved by the addition has the same dimension as the principal curvatures, ie the reciprocal of length. Thus it can be expressed as a radius. Intrinsic edit extrinsic curvature has the property that Strange mentioned in that it is independent of the higher dimension that contains it (4), and can be detected by measurements purely in the dimension of interest (our 4D spactime) and is the type used for relativity without embedding. This does not mean to say that the higher containing dimension does not exist, just that it is not required for the mathematics. However intrinsic curvature is a product of principal curvatures and thus its reciprocal does not have the units of length and cannot therefore be expressed by a 'radius'. The curvature that Strange refers to is the extrinsic Riemanian curvature (5), but is this the one you want ? Here is a simpler example of the use of Gaussian curvature. Consider a sting of beads. Each bead is coloured half red and half blue. Imagine the string is laid out in a circle on a sheet of paper and each bead is oriented so that it appears either all red or all blue from each side of the paper. A flatland being on that paper could walk round the string and detect the sequence of colours of the beads and could use a primitve rotation function to describe this and could detect torsional rotations about the string axis. This example appears in nature in the orientation of the parts of long chain molecules. It would be really great if ajb were able to offer answers in this post. Differential geometry is his speciality.

Welcome back +1