studiot

OK, I'm glad you have done a cooling curve. This makes things easier. I am going to talk about a heating curve because it makes the explanation flow better. Heating curves are just the reverse of cooling ones. You can go up and down them as many times as you want. So if you heated some water (ice) up in a beaker and measured temperature v time and then cooled it down again you would get the similar curves. The heating one would be quicker simply because you are supplying heat with a burner so can change the temperature more quickly. OK so if we set the burner so it heats the beaker constantly. That is we are supplying a constant amount of heat per second to first the ice and then the water. We ensure this constancy by adjusting the burner then leaving it. Understanding this is quite important and it is easier to do with heating than cooling. So looking at my curve, We see that the temperature remains constant from A to B, then rises steadily from B to C then remains constant from C to D and if we are able to measure in the steam it rises again more steeply from D to E. Looking first at the section B to C (I'll come back to AB) We have ensured that the amount of heat input per second is constant. (We could easily measure this with an electric heater instead of the burner) Now I have drawn BC as a straight line and in a real experiment it would be very nearly so. This means that the temperature rise is proportional to time and therefore to the total heat input. The temperature rise = a constant times the total heat input. If we turn this round we can also say that the total heat input = a constant times the temperature rise. (Where the second constant is the reciprocal of the first) If we divide through by the mass of water we are heating we get an important constant called the specific heat. The specific heat and tells us the amount of heat needed to raise the 1 kilogramme of water temperature 1 degree. Now along the line AB we note that the temperature is not rising. Yet we are inputting heat, which we can calculate in the same way as we did for the specific heat. We should also notice that the temperature does not start rising until all the ice has melted. This tells us that the heat we are putting in is doing something different from the specific heat. Indeed it is the heat we have to put in to turn a solid into a liquid and is called the latent heat of fusion. We would get this heat back if we froze water at 0o Section CD of the curve represents a similar situation with boiling. This is the latent heat of evaporation (or sometimes condensation). This represent the heat we must put in to change a liquid into a gas. Can this latent heat be considered potential energy? That is a good question since we need to put it in to melt or boil and can recover it by freezing or condenstation. We can do this repeatedly so it is a reliable store for energy. So yes in that sense it is potential energy. However getting energy by freezing water is less useful at normal temperatures than storing energy in steam (which is hotter than ambient) and using it to drive machinery, by allowing it to cool all the way abck to liquid. This is actually done in modern central heating boilers known as condensing boilers to make them more efficient by recovering the latent heat as well as the other forms of energy due to the combustion of the fuels.

It wasn't a trick question, but I said nothing about direct current. I asked about conventional current and showed (part of) a circuit with two sources. The AC source 'sees' a capacitor in series with two resistors in parallel with each other and circulates an (alternating) current through that circuit. Which way does convention state that current to flow?

That's a fair question so perhaps you would like to tell me which way the conventional current flows through the capacitor in fig1, ie which direction is the direction of conventional current around loopABCD? Is it flowing from positive to negative or negative to positive? Now reverse the power supply to the resistor chain, as in fig2 and answer the same question.

Using writings and pictures from that time as 'evidence' is fraught with difficulty. I understand there were many pictures of men and animals with wings and men with animal heads. But that does not mean I condemn them as unenlightened superstitious savages. Just that I am cautious about attempting to interpret their relics. Now a thought to me occurs in relation to the water trough around and perhaps under the pyramids. You have repeatedly mentioned how horizontal the coursing is, and I have observed how stable the structure has been over the last 5000 years or so. So how did they achieve horizontal? I know that the Romans used (and chronicled) water levels and were able to build their aqueducts to a sophistication unavailable to the Egyptians. Well perhaps the water troughing was a primitve precursor of the Roman water level, to enable the horizontal to be established over such a large area. The pyramid site area is substantial after all. In a way they did better than some have managed in modern times and I could tell you a story of this I have personal experience of.

I think I've made my point and we needn't discuss ramps further. Equally I'm tired of Egyptologist bashing. So after 132 posts, can we limit discussion to the mechanics of the interestesing proposition you have put forward that some form of cable haulage using counterweighted water buckets to haul stones up and perhaps into place? How was movement controlled? Particularly of the buckets to prevent water slopping out - a potential disaster for such a system. Do you have any idea about impulsive forces in cables used in this manner and the sort of cables that would be needed to carry these loads?

This is a prime example of why folks find discourse with you so difficult. Why did you totally ignore the fact that I specificlly excluded the pyramids from my question?

Where do you get the notion the OP was about the general case for electrons? He specified 'electron cloud' I admit I also jumped to the QM conclusion as can be seen from my first response, althought the term is more of a Chemists' one so I gave well respected Chemical references (from Cambridge University Press). However I later realised that electron cloud could aldo refer to 'situations where electrons congregate'. The space charge is one such and I'm sure anyone could dig up umpteen references to this effect from DeForest on. I have detailed analyses in my EUP book Principles of Electronics by Gavin and Houldin (They devote a whole chapter to it) Electronic Fundamentals and applications by Ryder (who specifically refers to the 'space charge cloud on p93 in his treatment of the space charge equation.

Why do you consider vacuum diodes obscure?

Setting aside the building of the pyramids for the moment. Do you honestly believe that the Ancient Egyptians had no ramps whatsover anywhere at all?

Oh come on, I hope you are just having an off day as this is a pretty condescending response. Especially as your thesis is not even true. We have all assumed that the 'electron cloud' has to to with quantum mechanics. But in fact electron clouds do exist and such clouds provide one of the few analytical solutions we have managed to make for the solution of Poisson's equation. (The field equations for a vacuum diode, including the space charge).

Are you saying that this is independent of any (potential) observer. Would that not imply a prefered or absolute reference frame since the t coordinate in one reference frame will be different in another?

We can, however agree that, as you said, translation is very difficult because it has to be not only from their language to ours, but their culture to ours. For my part I would have caught on much more quickly if the translation had been vessel instead of boat. We clearly have a greater range of words available and it is the skill of the translator to get the meaning across by selecting the appropriate modern word or phrase rather than disgorging the dictionary. Translating poetry is even more difficult.

I agree language is a problem. But there is also an underlying problem in our analysis. In using (x,y,z,t) we are implicitly accepting the 'block universe' concept. To be precise there is something missing. What is missing is that which connects parts of a physical object and makes it an entity.

Hello Tony, before I answer this can you tell me if you have done a cooling or melting curve experiment? That is plotted the Temperture v Time graph of some ice or wax as it melts and then warms up or some water or oil as it cools and solidifies?

Well one way to solve a pair of simultaneous equations is by substitution. This means using the second equation to find one unknown in terms of the other and then replacing it in the first equation. This will obtain a single equation in one unknown for you. Edit x and y are not variables they have particular values in your problem. But they are unknown until you calculate them

But, as elfmotat has pointed out that implies simultaneity, which depends upon the observer.

No offence but this is still rather contorted? Agreed, but what is the same time? Which makes the point, Mig and I were trying to put and explore the significance of this statement, given this is a thread about time. That's not actually what I said, but since you introduce world lines, do you consider it necessary to move the entire wordline in time for time travel to occur?

That's a bit harsh. You will find many so called "charge cloud" representations of molecules and atoms in monchrome in that classic textbook form Cambridge University Stranks et al : "Chemistry A Structural View" And a really beautiful colour one of uranium acetate on the front cover of Petrucci : "General Chemistry"

Surely that is prohibited by special relativity of simultaneity?

I suppose you could say it depends since 'chaos' is a collective term for a number of different effects. Some systems are constrained so that the chaos cannot 'grow'. Example of this would be the path of a metal ball hung above four magnets. In chemistry the Belousov-Zhabotinskii reaction. In other systems the 'chaos' can grow without limit even to the destruction of the system. Examples of this would be Euler instability of motion. Audio or video feedback. I agree with ajb that chaos and randomness are different phenomena. But also note that a small amount of initial randomness can lead to signification variation of system future history (called trajectory). There may, as ajb says, be entirely predictable equations that the trajectory follows. Any the chaos arises from (small) random variations in initial conditions. The course of this trajectory will depend upon the system as I said, but the instability that allows chaos is to grow or not, is inherent in the system, not the process. Euler instabilty is one such example. So called 'frequency doubling chaos', on the other hand contains the seeds of its own expansion in the process. Feedback comes to mind here. I expect this thread will develop further and I would be happy to expand on any of these points. I would be wary of using the term degree of chaos to measure it since fractals are often included in the basket of effects and the the term degree could be confused with the Hausordf Dimension, responsible for this phenomenon.

Note the formulae up to now have been about rotation about different axes. Your book may have been looking at volumes of revolution in different ways. Here is the same volume generated by rotation about the y axis in both cases. The area bounded by the curves x2=4y and y=2x is rotated about the y axis. Find the volume generated. solving the two equations simultaneously yields x = 0 and 8 ; y = 0 and 16 So the method on the left is as per my simple formula and the shaded area is rotated about the y axis [math]V = \int\limits_0^{16} {\pi \left( {x_1^2 - x_2^2} \right)} dy[/math] and for the second method we integrate with respect to x using vertical strips of area (y2-y1)dx which rotate about the y axis on a circle of of radius x . [math]dV = 2\pi x\left( {{y_2} - {y_1}} \right)dx[/math]

For volumes the corresponding formulae are [math]V = \int\limits_a^b {\pi {y^2}} dx[/math] for rotation about the x axis from x = a to x = b [math]V = \int\limits_c^d {\pi {x^2}} dy[/math] for rotation about the y axis from y = c to y = d

I was coming to that but I was waiting for you to answer my last comment because it is important. I just noticed that you said rotates about the y axis. For the formula I have given and you have used the rotation is about the x axis. For the formula elfmotat has given rotation is about the y axis, as he correctly states.

Are you sure your textbook says about the y axis?

You will also need to watch this when you come to multiple integrals, the limits become functions, not just simple numbers, and this catches many (including me when I first saw it)