studiot

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.

What would prevent motion?

Do you know about Limit State Design?

Let us say you ask a mechanic or mechanical engineer to fabricate a yacht deck mounting or cleat. The mechanic could go to the metal store, obtain marine grade stainless and make a perfectly satisfactory fixing, possibly a more serviceable one than the engineer could manage. But suppose further that you want it made of some new marine resistant material, then you would need the extra capabilities of the engineer to redesign the shape and size to accomodate the new material properties.

Well it is disappointing for someone to come here for a few minutes post something and not come back, when others have put in significant effort. This is a more interesting problem than most and I said there was a catch.So for the benefit of others who also looked at the problem I have set out my description of what I think happens. It is tempting to assume that the piston is pushed along by the pressure difference until there is the same pressure in both chambers and that the system is then in equilibrium and the question is asking for this pressure. But the question did not ask for this it asked for the maximum pressure in the right hand chamber. The setup described leads to oscillation of the piston. Initially, the difference in pressures between the faces of the piston gives rise to a force on the piston, held back by the latch. Upon release of the latch the piston is accelerated by this force into the right chamber where the pressure is lower. This compresses the gas in the right chamber, raising its pressure, and expands the gas in the left chamber, reducing its pressure. As the piston travels the pressure difference diminishes and with it the force on the piston. So the acceleration continues until the chamber pressures are equal and the piston is now travelling at maximum velocity. The piston continues to compress the right hand chamber and expand the left, suffering a decelerating force as a result of the now reversed pressure difference. This deceleration now continues until the piston stops. This is the point of maximum pressure in the right hand chamber, where the right hand chamber pressure is now greater than the left hand chamber pressure. So the piston is forced to reverse its travel and pass again through the point of equal chamber pressures, this time compressing the left hand chamber above that of the right. And so the oscillation cycle continues.

One of the characteristics of rotational motion is that different parts are moving at different velocities and that somewhere there is a part that has zero velocity. Now the question arises, could we detect such a movement. Well since cosmology is not my field I will leave that answer for Mordred and the Cosmologists, (Are they playing at Glastonbury this year?)

That's the whole point. You have used 'time' by stating that the states have to be 'previous'. Furthermore you assert that time does not exist, yet you tell me that it can be measured. How can it be measured if it does not exist? What do you mean by exist?

There are two sorts of movement. Rotation about its own axis (ie spin) and translation. I am guessing you understand about rotation. Translation means what I think you you mean by movement. This may be straight line movement or along some curved path.

Yes that's right but it still didn't answer my question about what actually happens. I don't understand whether the OP is coming back or not. He was listed as still linked to the question for an hour after I posted my first hints. I think his energy approach, properly implemented, would be easier to calculate, than Newton's laws.

But that piston has mass, and therefore momentum if it is moving. The key is in the question I asked about what you think will happen. .

Just because there is nowhere for the universe to translate to doesn't preclude the universe as a whole possessing rotational motiom.

Will that work?

Why are you considering piston kinetic energy? Start by describing what you think will happen once the piston is released. This is important because there is a catch that I don't think you have picked up. I think the problem (I don't know the book) must also specify adiabatic walls to the cylinder, but not an adiabatic piston?

No this would imply that time is or measures change change. But, as I pointed out earlier, time can also measure lack of change.