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Network Solutions recommends I place text here regarding my location, but you are already here. How convenient.
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To your right, an image of a place not where you are and not where I am. Chaos on Europa. (photo by NASA)
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| Conamara Chaos region on Jupiter's moon, Europa |
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Network Solutions recommends I enter my address in this text block, but all you have to do is look up.
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Orientation
(to Chaos)
(Helpful)
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| Screen Print from "Chaos Demonstrations" by J.C. Sprott and George Rowlands, in case you are seaching for quantification of the reigning disorder and entropy |
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The point is to move from Chaos to Lex. Identifying the chaos is key. If the etymology did not help (see home page) there is a magazine called Chaos. Written by physicists, it is probably too complicated for you.
The good people at the University of Texas have offered up What Is Chaos? An Interactive Online Course for Everyone that may be of more use to anyone who's wandered onto this page. (Firmly entrenched in the chaos camp, they dub chaos one of "the most exciting topics in physical science.")
From their instructive explanations:
"To a physicist, the phrase "chaotic motion" really has nothing with whether or not the motion of a physical system is frenzied or wild in appearance. In fact, a chaotic system can actually evolve in a way which appears smooth and ordered. Rather, chaos refers to the issue of whether or not it is possible to make accurate long-term predictions about the behavior of the system."
(The ideal soundtrack here might be Cole Porter's "Don't Fence Me In.") (But that is way beyond this website's capabilities.)
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| Photo from Butterfly Events, a butterfly farm on the web specializing in wedding releases (of butterflies). (Note to webmaster: perhaps a whole other page on chaos and weddings.) |
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| Even though everyone from Ashton Kuchner (sp?) to Venus Williams knows about the Butterfly Effect, this famed metaphor for chaos cannot be excluded from our helpful orientation.
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| The Butterfly Effect is imagistic shorthand (yes, a poem) for "the sensitive dependence on initial conditions."
"The sensitive dependence on initial conditions" is the essence of chaos according to physicists, one of the two groups whose business is chaos. (Obviously, the other group is poets.) (Relax, this is not a poetry website.) The term became official in 1973, when a fellow named Edward Lorenz gave a talk entitled, "Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?" Delivered at the December convention of the American Association for the Advancement of Science, his answer was, suffice it to say, predictable.
The butterfly effect has also become a meteorological term. (Meteorologists are not, as a group, interested in chaos.) (They hate it.) (But it beats them at every turn.) In fact, Mr. Lorenz stumbled upon the whole notion back in 1963, when trying to write a computer program predicting the weather.
Wikipedia, which is an absolute incarnation of Ab Chaos Lex, has a decent entry on the butterfly effect here.
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The unknown compression process, from T1V1 to T2Vo, obviously was done both by applying work, to decrease the volume AND heat to increase the temperature (work doesn't show in the TS-diagram). The total resulting increase of internal energy is given under the Vo-curve between T1 and T2 (the granulated area). This energy is released, when the gas is cooled down at constant volume Vo.Let's illustrate this with the following example in a TS-diagram, there we want to calculate the change of entropy for a system's (gas) change of condition. (Mind that Vo < V1 < V2 . Normally the TS-diagram is used with similar curves for constant pressure and those count upwards for higher values). Originally the system was in the coordinates T1V1 and by some unknown process compressed to the present condition T2Vo. How can we calculate the change of entropy of this by using dS = dQ/T and integrating afterwards? The change of internal energy DU = m.Cv.(T2-T1), is the (granulated) area under the curve Vo and between the lines for S2 and T1. However, if we cool the gas down to T1 at the constant volume Vo, we are not back in the original coordinates T1V1. Hence, the change of entropy cannot have been a differentially calculated: m.Cv.ln(T2/T1).
The only way to correctly calculate the change of entropy, is by first expanding adiabatically to the original temperature, T1, and then compressing isothermally to the original volume V1. The total change of entropy for the gas becomes then: DS = m.R.ln(V2/V1). As this occurs between the same isentropes S1 and S2, as the previous unknown process from T1V1 to T2Vo, the according change of entropy is the same.
We can make a simple analysis to compare this step-method with the 'reversible' differential one, for a change of condition at constant volume, from coordinates T1Vo to T2Vo. In that case, DQ = DU and we can write as follows:
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