studiot

Phosphorus, ground state. 1s22s22p63s23p33d0 So phosphorus has 5 electrons in the third shell. This makes the empty 3d orbital available for hybridsation. This is called the expanded octet. In the case of POCl3 the octet is expanded to 10 this way. Note that resonance is possible with alternate partially polar forms of bonding and an octet.

Both of these are inherently inefficient. It's all to do with timing. Although the waves move more or less continuously for longish periods of time, they will only contact the periphery of the wheel for a short time since they are irregularly spaced out in time and distance. It would be much more efficient if you could ge the paddles and the waves to mesh like a worm gear wheel. The tides overtopping your wall will flow continuously but only for about 1/8 of any day, again making the process inefficient. Further the process is capital (£, $) inefficient because you are proposing large structures that must be built before any £return can be made. This is actually what kills most hydro power schemes. The most attractive from an engineering point of view, taking into account geographic, mechanical and financial considerations is to realise that tides not only go up and down the also flow backwards and forwards. And this is a relatively continuous movement 24/7. So if we plant a single turbine generator on the seabed it will 1) Stay submerged and clear of traffic and other installations. 2) Produce continuous power from installation. 3) Not require massive investment in initial support works. 4) Can be added to with a second, third etc turbine as finances allow.

Just to be crystal clear. Velocity is a vector quantity. This is it has both speed and direction. Change either and it is an acceleration. Acceleration is also a vector quantity, with magnitude and direction. It take energy to change the speed but no energy to change the direction. But in both cases a force has to be applied to cause this. Can you see why? Can you see the connection to the definition of work?

It's the same method, just he used u for substitution, then found that u appears in the normal parts formula and regretted it. That was why I suggested t. Have a good exam.

http://www.youtube.com/watch?v=P-o6iFzJLpw

Thank you for this quote Gopher T (Post #622 in this thread here http://forum.allaboutcircuits.com/showthread.php?t=60389)

Substitute t = root(x) Then integrate the resulting integral in t by parts.

Following swansont's Popeye challenge, I challenge anyone who believes that only material things are real to use one of these without a real hole in the middle.

I ran a little spreadsheet to test values. If there was a misprint so that the lefthand chamber pressure was 1.8 bar instead of 8 bar then the equal chamber pressure would be 1.32 and the max right chamber pressure I make 1.45 bar, pretty close to the 1.6 bar stated. A left hand pressure of 0.8 or 2.8 diverges further from that offered.

Don't you mean having too much 'vodka craft'?

I will see what figures I come up with over the weekend. You do not have to arrive at the chamber volumes by trial and error. Boyles law works even better. Because the cylinder must have constant cross section the volume is proportional to the piston displacement. You can easily calculate the piston start position geometrically. Boyles law again will give the equal pressure volumes (or any other) and thus the piston displacement. So calculating the piston position at any moment is easy. If you like you can form an equation for the work done on the piston in terms of the pressure difference force and the displacement, but it is a quadratic fraction that must be integrated. As regards the book answer, perhaps there was an error which is why Endy couldn't find it in his later edition of the book in post#3? One final thought. Say the piston was 0.1 metres long then its volume is (0.1 x 0.1) m3 (note the superscript and subscript icons in the toolbar here) = 0.01m3 So I wonder what the authors think this piston is made of? Gold is heavy stuff of density 19000kg/m3, so my gold piston has a mass of 190kg. Any longer piston would make nonsense of the rest of the calcs since the cylinder is only 2.5 m (plus piston) long.

There is already a rich mathematics extending complex numbers to as many dimensions as you like, called quaternions. http://en.wikipedia.org/wiki/Quaternion

This question was inspired by the recent silly argument over Zeno. I heard on the news today that if you reduce your calories intake by half you will increase your life expectancy by 10%. So if I reduce my intake by half, then half again, then half again, then half again................................. Will I live forever?

This is interesting because I tend to space out much of my stuff double as I find it more readable that way, on screen. I have had many comments, on more than one forum, to the effect that my readers, anyway, prefer this. This is in no way a criticism of your opinion.

First I have a confession. I wrote this down the wrong way round by mistake in my post#2. It should of course be an adiabatic piston and non adiabatic (diathermal) walls. OK I also get equal chamber pressures at 3.8 bar. It is, perhaps, a good idea to convert the bar to Pascal (N / m2) so that work and energy calculations will come out in Joules. Now since the expansions and contractions are isothermal it is easy to work out the isothermal work in each of the two sealed chambers to the equal pressure point. since in this case all expansions and compressions are positive displacement ie there is no free expansion. [math]W = PV\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right) = PV\ln \left( {\frac{{{P_1}}}{{{P_2}}}} \right)[/math] Where the Boyle's constant = PV for any pair of pressure and volume points, such as the given initial ones. In an isothermal expansion of an ideal gas there is no change in internal energy. All the work done is balanced by heat drawn from or rejected to the surroundings. This is why the cylinder walls must be non adiabatic, but the piston must be adiabatic, so there is no heat transfer between the chambers. So the left hand chamber gas draws in heat from the surroundings equal to the work on the piston and the right hand chamber gas, whilst maintaining its temperature and internal energy constant. Similarly the right hand chamber gas accepts work in compression and rejects an equal amount of heat to the surroundings to maintain its constant temperature and internal energy. Therefore the difference in the work done by the left hand chamber gas and the work accepted by the right hand chamber gas equals the work done on the piston in accelerating it from rest and moving it to the equal chamber pressure position. This must therefore be equal to the energy of the piston, which at maximum velocity is all KE. This is the energy that further compresses the gas in the right hand chamber until the piston is stationary, at which point the right hand chamber is at maximum compression. This presents a problem since you say the book claims the maximum pressure to be around half that of the equal chamber pressure. Are you sure it did not ask for the minimum? Perhaps you could post the question verbatim?

I look forward to reading this book when it comes out. Hopefully it will include some of the tall tales from the forum campfire.

You seem to have written agreat deal, without comment on any of my thoughts about the problem. Yes I agree the PE of the piston in its momentarily still position equals its potential energy. This also equals the work done in compressing the gas in the right chamber minus the work done expanding the gas in the left, beyond the point where the chamber pressures are equal. It should be elementary to calculate the point where the chamber pressures are equal.

Oxford comma? Swans, you should have looked up your examples before the G&T not after. It needs a list of three items or more. But it is so last century anyway. If I want to enhance the separation in a list I use semicolons, not commas.

It's called the continuity equation. https://www.google.co.uk/search?hl=en-GB&source=hp&q=continuity+equation&gbv=2&oq=continuity+eqa&gs_l=heirloom-hp.1.0.0i10.1172.5203.0.7703.14.13.0.1.1.0.188.1624.1j12.13.0....0...1ac.1.34.heirloom-hp..0.14.1656.ekvxV8MoHaw

I suspect more miscommunications arise from the parties concerned using different definitions of a key word, phrase or construct, than from any other source. Adherence to precision greatly reduces the scope for this form of miscommunication, so is to be recommended. However there is some difference of usage in different branches of the English language that may or may not impede communication. You say that the reader has exclusive rights of deciding what is distracting. If I find american spelling of say sulphur distracting when I read it, should I therefore enjoin all americans to change their spelling or should I put up with it. Or should I follow the words of that famous scholar of English and say "That is something up with which I will not put"? How about that old and very common chestnut AC current or AC voltage?

So what was you question or point about this statement, which is not wrong?

Mitch you cannot progress if you just design your own questions, ignoring a large part of what is said to you. I laid out a list of areas or subjects you should enquire into to help you find out more. I am happy to say more about any of these. But I do not know you or what you already know, so I have kept it short to start with. Do you understand that there is a dividing line in the physics of matter when we talk about particles bigger than an atom or smaller than an atom.

Sorry to disagree with you Mordred, but your four states of matter refer to the physics definition. Chemists recognise quite a few more. Mitch The study of these four states and their properties lies within the realms of classical physics, 'particle' sizes that are atomic or greater. We further distinguish between pure substances and mixtures of several pure substances, because many properties are different for mixtures. In fact there are more modes of motion available to solid substances than to the other three fluid states because fluids do not support shear stresses. The study of modes of motion is called mechanics and the particular branch of mechanics that is relevent here is called continuum mechanics. Here, Euler's equations of motion play a greater part than Newton's (They amount to the same thing, it's just that Euler wrote them in a more convenient manner for internal motions within solids and fluids) The study of atomic packing is called crystallography. Here the atoms are regarded as "balls" with definite radii. That is size and shape are taken intio account. Possible crystal structures are studied by (mathematical) processes equivalent to placing marbles in a box or jar. If you do this you will see that there is a great deal of empty space between marbles. Mixtures can be packed together much more tightly, that is in fact the theory of concrete mix design, but empty space cannot be completely eliminated without an infinite range of aprtcle sizes. Quantum tunnelling is apparent in modern physics where sub atomic particles can penetrate through apparantly solid other particles by a process known as quantum tunnelling. The electronics driving you computer and mine use this effect. So particle size and shape are important. Does this help?

Mitch, I didn't ask Mordred, I asked you, and you have no right to assume my question was in any way linked to any of Mordred's posts. So I ask you again. Studiot What would prevent motion? Particles were not mentioned in your question, nor in my response. Since you mention them now, please specify the shape and scale of the these 'particles'. Classical particles (atoms and larger) are subject to packing laws, which generally leave lots of empty space. Subatomic particles exhibit quantum tunnelling.

Has this really made it any clearer? I recommend using brackets as shown by mathematic in post#2. Then there can be no ambiguity. But thank you for coming back to us with some feedback. Don't hesitate to post more questions in future.