studiot

There is a certain sense in analysing (1) then (2) then (3) then (4). Note that (4) refers to energy transfer whereas (1) refers to heat only. Failure to make this distinction is a common cause of failure to correctly analyse a thermodynamics problem. Entropy is the ratio of heat transferred to temperature, not the energy. Entropy of what? But no, I would not say that because classical entropy change is defined in terms of cyclic processes and equilibrium states. Can we set entropy aside until the end since it was not mentioned in the question?. The heat engine needs further development to cope with (2) and (3). If you bring bodies A and B (at different temperatures with Ta > Tb) into thermal contact heat will flow directly from A to B. You cannot make this a heat engine ie you cannot extract work from this you have to have an intermediate stage which is why you have to have a working fluid. Incidentally for your issue with (3) Power is the rate of doing work = work/time Note (3) says power, not work. For something that happens infinitely slowly, time = infinity so you are dividing by infinity, which is equivalent to multiplying by zero (in engineering maths not pure maths). So for any finite value of work the power is exactly zero.

You may like to look into 'the LAX heirachy' A good start would be pages 95 to 102 of Cambridge Texts in Applied MAthematics Solitons an Introduction By Drazin and Johnson

What strikes me is that I have made several statements that you haven't asked me about once. For instance I said there are four laws of classical thermodynamics. Each can be stated in several equivalent ways. The most fundamental was introduced after the first law and called the zeroth law. It is the most fundamental because all the other three refer to equilibrium states and there is no point doing this unless you can identify and define an equilibrium state. That is what the zeroth law is about. One version states that heat cannot flow from a colder to a hotter body. So (1) is true but because of the zeroth law, not the second. Any heat pump works like this simple model (there are more complicated ones) There is a working fluid which is cooled by expansion to below the environment temperature. Heat flows from the environment into the working fluid by the zeroth law, cooling the environment and warming the fluid. Because of the zeroth law the fluid cannot become warmer than the environment. The working fluid is then compressed to raise its temperature and pumped to a heat exchanger where it is hotter than the output medium so heat flows from the working fluid to the output medium, again by the zeroth law. The working fluid is pumped back to the environment heat exchanger and expanded to cool it below the environment temperature. This is a cyclic process. At no point is heat transferred directly from a colder to a hotter body.

Was that a freudian slip? As a matter of interest do the students have to pay for this non-teaching?

I'm not sure what your key point is. The use of a first order equation, the use of the Hamiltonian or what? Most uses of H lead to a second order equation and there are many of these in classical physics that have periodic solutions. I pointed to a situiation where H leads to a first order solution in classical physics that is non periodic.

Why does the first order equation have to be linear, and what is A please? For instance how about [math]\frac{{dy}}{{dx}} = \frac{1}{{x\tan y}}[/math]

No I didn't yet answer (3) because I was trying to lead the discussion in that direction. It does worry me that several of your other statements were incorrect and I thought you would appreciate the insight gained by finding for yourself the correct answers. That is why I have only given hints so far. Here are a few more. There are four laws in classical thermodynamics. There are four statements to compare with these laws. Each statement is either correct or incorrect and to do with one or more of the four laws. To reinforce what was said about (3) - How long does it take to complete one single cycle< and what does the second law say about cycles? There is much to be gained from all the answers to this question. We have now dealt with (4), what about (1) and (2)? Does heat flow from a cold body to a hot one in a heat pump? How do you think that happens? Can you offer a heat pump design that achieves this remarkable feat?

The actual form of H in the equation depends upon the situation you are modelling. Several different forms are shown in my reference. Are you referring to the case of a static electric dipole in an electrostaic field as described about 2/3 the way down this Wiki page? http://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics) Since everything is unmoving and unvarying and independent of time there are no space derivatives or time derivatives.

An interesting, but controversial, subject. What are you going to do with the information? In the current education system the only opportunities that I can see for students to receive the wider 'education' ideal of teaching lie in music and sport. Other areas all seem to me to be overdominated by standardisation, with counterproductive effect.

The situation would seem to be as I thought, but you have not read the question correctly. It did not ask which statement was impossible full stop. It asked which statement was forbidden (made impossible) by the second law. For example (4) is a correct statement, ie it is impossible for a physical process to yield more energy that is put in, but just nothing to do with the second law So look again at all 4 statements and see why they are accepted or rejected. Look particularly at the definition of an ideal heat engine. If you were to say that all four statements are poorly worded and somewhat ambiguous, I would agree with you. For example the first statement "it is impossible for heat energy to flow from a colder body to a hotter body" is incomplete so can be taken two ways which make it either possible or impossible,depending upopn how you complete it. However neither interpretation is against the second law.

Then you will have studied operational calculus. The Hamiltonian is an operator. The star is not just a multiplication sign it means that you apply the Hamiltonian operator to the wave variable.

PokePat has noted this is a school project so it is good to pitch the level of answer there. It has been mentioned that the speed of light is the constant for all observers and sources. This is true but it is worth noting that it is a characteristic of (classical) wave motion that the speed of the wave is independent of the source. That is the speed depends only upon the medium. What is different for light is that the speed is also constant for all material observers. The word material is also important. As to why, that is a philosophical rather than a physics question

Yup imatfaal pretty well summed it up, but do you also understand the significance of the RHS? That is the significance of H?

I can't imagine why anyone would want to be a moderator. Constantly having to be involved in someone else's argument instead of doing real science. No thanks. Why do you want to be one?

Like many physical phenomena, osmotic pressure has its origins in humble simple processes. To understand these let us build up one step at a time. Start with a container of liquid solvent. No membrane at this stage. Now add some solute or disperse material to one side only of the container. Coloured ink or Sugar is good. What happens? Well the solute spreads out throughout the whole of the container and pretty soon the concentration is even throught. How come? Well think about the initial stage where there are two regions. A zone of high concentration where you add the solute (left hand side say) and a low of low concentration at the other side where you didn't (right hand side) This means that the % of solute particles on the LHS is greater than the % on the RHS. Since there is no reason to suppose otherwise we assume the particles move equally in all directions. But there are more on the LHS than the RHS So more are travelling from left to right than right to left. This continues until there are the same on both sides when the concentration is even. This applies in reverse to the solvent particles. What we have shown is this evening out of concentration is a powerful tendency in Nature. Now introduce a semi permeable membrane, like a fishing net, across the middle of the container an repeat the experiment. Semi permeable means that the holes in the net will only let the small fish through, but stop the big ones. Usually the solvent particles are small compared to the solute ones, so it is the solute particles that are held back. So the solute cannot spread out, but the system still wants to even out the concentration. So more solvent particles initially pass from right to left than from left to right as before, which reduces the concentration on the LHS. This is the same as if there was a pressure pushing solvent this way, which is why we call it osmotic pressure. This will raise the level of the surface on the LHS relative to the RHS, or increase the pressure within the LHS v the RHS if the container is sealed. Eventually the atmosphere and gravity push back so the net solvent flow from right to left ceases. This happens when the pressures balance. Yes I believe oncotic pressure is an example of this phenomenon with a sealed container (the tumour or whatever) does this help?

It is not clear to me what your question is. Where exactly are you having difficulty with the material you have posted? The part in upright text cannot be complete by itself, was it a multiple choice question, with the underlined part the 'correct' answer? And whose explanation is in italics? Is this the explanation of the 'correct' answer and do you understand why the others are incorrect?

Yes doubtless the spreadsheet could be improved, but I'm glad to see some were interested. It also demonstrates how sometimes you can test out some question by throwing together somehting along these lines, as an alternativwe to more formal analysis.

You might like to play with this spreadsheet. factor.zip

For an isotropic, homogeneous body, surely they will be. dm/dV is just the limit as dV tends to zero and produces the scalar point density finction. Science Student the problem lies in the fact you have differentiated with respect to the wrong variable.However, congratulations for using you scientific acumen to recognise that something was awry. Presumabbly this floows on from your previous question and I will post a more detailed reply in the same vein later.

Gravity is not the source of the energy, that is external to the helicopter-gravity system. The only energy you can get out of the helicopter-gravity system is the potential energy available when the helicopter descends. You can only do this once, unless you input further energy from an external source. Gravity is not an inexaustible source of energy.

Good catch, thanks.

I'm not at all sure what you mean by this question. None of the forces involved exert any moment whatsoever about the top of the boom arm where the shark and tension rope is attached, for the very simple reason that the line of action of all three forces acting passes through this point. Three forces? Yes the boom is a body in equilibrium under the action of three forces, the condiftion for which is that they meet at a point. So MacSwell is correct that the hinge reaction force is along the boom since it must pass through the point where the shark suspension and support rope meet ie the top end. Equally the hinge reaction exerts no moment (american=torque) on the hinge since it passes through it. However the weight of the shark and the support rope tension both exert a moment about the hinge, given by simple trigonometry. Drop perpendiculars from the hinge to the shark (horizontal) and the distance is 4 cos (60) and from the hing to the support rope where the distance is 4sin(80) So the clockwise moments (due to shark weight) are 10000 . 4cos60 = anticlockwise moments (due to rope) Tsin(80) This can easily be solved for T

A cylinder is what is called a volume of revolution or solid of revolution. You get a VOR when you swing a curve (straight line in this case) about a coordinate axis. So a cone, a cylinder, a greek urn, a lampstand or anything you might turn on a lathe are solids of revolution. The volume can be calculated by ordinary single variable calculus. If we rotate the curve f(x) about the x axis the volume from x= a to x = b is given by [math]V = \int\limits_a^b {\pi {{(f(x))}^2}} dx[/math] https://www.google.co.uk/search?hl=en&site=imghp&tbm=isch&source=hp&biw=1280&bih=585&q=volume+of+revolution&oq=volume+of+revolution&gs_l=img.12...0.0.0.2594.0.0.0.0.0.0.0.0..0.0....0...1ac..32.img..0.0.0.aCWGVazA3iA

The 4D spacetime view brings serious and fatal continuity issues.

Someone has given you +1 for this perceptive statement and I have added another. Yes that is what I was trying to prompt MigL towards. However this is your thread and my original reply offered to discuss your understanding of what makes 'order' It is no small task to show if the entropy of the material that makes up a car is greater than or less after manufacture due to change in 'order'. Consider, you take a bunch of iron atoms that are linked to oxygen atoms as ore and convert them to a bunch of iron atoms linked to other iron atoms. You also take a bunch of carbon atoms, linked to other carbon atoms as oil and convert them to a bunch of carbon atoms linked to oxygen and carbon atoms as plastic. Showing this as an increase in order is difficult.