studiot

Please explain this sentence.

And as I said, adiabatic.

It would also be helpful if you completed your old threads before starting new ones. You might learn something that way and others might be more inclined to answer new questions.

Newton's first Law requires the body to continue movement in a straight line unless acted on by an external force. In the case of circular motion, that force is called centripetal force. Because centripetal force is a real force something has to provide it. That something can be the tension in a string or the force of gravity or an electromagnetic force or a sideways push (reaction) on a moving fluid from a pipe or many other mechanisms. Each one has the general term centrifugal but also a particular name depending upon its source.

Centripetal force is not balanced and an object executing circular motion is not in equilibrium.

I don't have thermodynamic (enthalpy) data for the B-Z reaction and the only source I could find wants $40 for the information. http://www.sciencedirect.com/science/article/pii/004060319180455R Most articles concentrate on the chemical and ensuing rate non linear differential equations that cause the oscillations rahter than addressing the calorimetry. So if any professional chemist can supply this data it would be vary helpful to progress calculations. Meanwhile here is an outline of a mechanical system that acts as you describe up to the underlined part of my quote in post4. Consider a sealed adiabatic cylinder, C, separated into two chambers A (equilibrium volume Va) and B (equilibrium volume Vb) by a frictionless system. Both chambers are filled with inert ideal gas. Cylinder C forms a system but to analysise its action we must split it into two sub systems A and B. Let us start with the piston at the equilibrium position and imagine it drawn slightly aside and then released. Note no heat has entered the system and no heat can transfer from one chamber to the other. If Sa is the original entropy of A then [math]d{S_a} = \frac{{d{U_a}}}{{{T_a}}} + \frac{{{P_a}}}{{{T_a}}}d{V_a}[/math] In the absence of heat transfer [math]d{U_a} = - Pd{V_a}[/math] Substituting leads to [math]d{S_a} = 0[/math] Similarly for chamber B. Thus the overall system entropy change is Sc = Sa + Sb = 0 Since we have specified no dissipative forces system C will oscillate forever as specified, using the input mechanical energy as the source of the oscillation energy. If we now connect an adiabatic rod to the piston and use the motion to extract work via some external system D, the oscillation will die away as the work is extracted. There will be no entropy change as a result of this for systems A, B and C or for the wrok extracted. However entropy will increase in the surroundings and possibly D.

This is why I keep banging on about neighbourhoods. A set is said to be dense (in itself) if every punctured neighberhood of every element in the set intersects the set itself. Alternatively if between any two members of the set we can insert a third the set is dense. So for the rationals p and q the rational (1/2)(p+q) is another rational between p and q. There is not necessarily such an integer available between integers i and j ; 1/2(i + j) , is not necessarily an integer Countability/cardinality is a different concept and the apparent peculiarity you noted is one of the oddities of infinite sets.

That rationals are dense in R http://web.mat.bham.ac.uk/R.W.Kaye/seqser/density.html

To expand on this nonsense. I'm sorry to be blunt but that is what it is. One of the axioms of a metric or distance function d(a, b) is For any two points a, b in a set d(a, b) = 0 iff (if and only if) a = b It follows by axiom that there are no points b of zero distance from a in any set. That is why we have the concept of a neighbourhood. A neighbourhood is another set, the set of all points within a given distance from 'a'. Note the general statement includes zero distance and thus a itself. Several types of points and types of neighbourhood are distinguished. A 'punctured neighbourhood' excludes the zero distance case and thus excludes 'a' itself. Types of neighberhood are used to identify different types of points. Of particular interest are those called limit points, cluster points or accumulation points (these are all names for the same idea). Points which are not cluster points are called isolated points. Comparing neighberhoods for different points allows us to examine set properties such as connectedness, compactness (or dense) and discreteness. A definition A discrete set has no cluster points so every point in the set is isolated. Example the integers form a discrete set, but the rationals and the reals do not.

nonsense. I'm sorry to be blunt but that is what it is. You say you have not studied set theory yet you are prepared to ignore what others tell you about it. When asked for a definition of ideas and terms you use you cannot supply one. How exactly do extract a distinct and identifiable member of set from a continuum? A while back I suggested you look at connectedness, compactness, completeness and coverings in relation to set theory as they are relevant. How would you define a connected set? This is what I thing you are striving towards. But there are pitfalls. Would you say that the set of all x2 - y2 < 0 is connected or disconnected? x,y contained in R.

? Does this also show how the water gets under the piston to lift it?

Thanks Xerxes +1, I was relying on you and uncool to do the algebra.

I used the word discrete in inverted commas because I meant using pengkuan's description, which is more akin to connected. It is important to distinguish between the set along with its properties and the members of the set, along with their properties. One required property of all members of all sets is that each member should be distinct (or distinguishable from any other member). There is no general requirement about their juxtaposition is real or phase space. Indeed I see difficulties discussing juxtaposition without a metric.

Surely all sets are 'discrete' by definition. What is your definition of a member of a set?

There's been a lot of talk of uncertainty. This is my last post on the subject because it really is off topic as it makes no difference if you cool something to absolute zero. That takes time. In fact the third law says infinite time. but you can warm it back up again also in time. So zero time is not involved. All those introducing uncertainty should calculate it, remembering that we are talking about the movement of massive objects like atoms or molecules, not electrons. What is the uncertainty relative to the size of the atom and its uncertainty?

Until we know exactly what process moreno has in mind, how can we decide if it is reversible or not?

Yup it takes a supernova to make the heavy elements. Cain't be did in ordnary stars.

Acid + Base = Salt + water. But the salt is soluble so stays in solution.

One further comment to add to Ophiolite's ecstacy. The so called packing fraction curve determines that energy will be released by fusion for elements up to iron in the periodic table, and that causing fission of these elements requires an input of energy. This is the normal process within stars. The building up of lighter elements to heavier ones as far as iron. Conversely beyond iron in the table the positions are reversed. Fission now releases energy and fusion requires energy input. So to build up the elements heavier than iron (a great deal of) energy input is required. This is achieved in supernovae, not ordinary stars. When the supernova explodes its material over a region of space, the material then contains the heavier radioactive elements which seed the resulting stellar and planetary systems.

the drakensbnerg

Agreed in QM. But classically the Third Law sets S=0 at T=0 so that the integration of TdS from zero to any desired temperature may be perfomed to obtain the so named absolute entropy. In those calculations zero point energy is not included. Further discussion here https://van.physics.illinois.edu/qa/listing.php?id=22970

To reinforce John's comment. The statement that motion ceases at absolute zero is disingenuous because the full statement is The vibrational motion of the atoms of a perfect crystal approaches zero as the temperature approaches absolute zero. That is not to say that other forms of motion is forbidden, even for instance simple translational motion of the crystal itself.

A Wave is global. That is it extends to or is defined for a very significant part of space or even all space. A Particle is local. That is the particle and all its properties only extend over a very small region of space, perhaps even just a point. The whole dichotomy is that real world objects seem to exhibit both of the mutually exclusive characteristics in some measure. Normally one of these characteristics dominates the other so we call the real world object a wave or a particle to suit.

I don't think this thread is meant to be about the proof or substantiation of the Second Law. I don't know what moreno really wants since although he has been back to this thread he has chosen not to clarify his original post as I invited him to do. The Wiki quote is inapplicable to classical themodynamics, which was clearly stated for a cyclic process only. Further the Wiki statement, which is basically the inequality of Clausius, is useless in cases where q = 0. Discussion about entropy in these cases is like discussing the direction the zero vector points in. Moreno's proposed a case which can be theoretically realised in the mechanical world (q=0) and I am happy to delve more deeply into the thermodynamic mathematics of this so long as he is not asking us to do all the work.

I suppose that your route to the second law must depend upon which formulation you want to reach. But I don't see this question is really about Maxwell's demon. In any event, thank you for the reference I might look at it as it seems interesting. But there are quite a few books about the philosophical underpinnings of the second law. Professor's Atkins little book, Four Laws that Drive the Universe, is particularly good as it does this for all four of them.