studiot

Matters are more subtle than this, although personally keeping cool when it is very hot is no subtle matter. Standard body temperature is 37 degrees centigrade. So for ambient below this temperature the body has to burn ingested fuel to stay alive Conversely, above this temperature survival requires the body has to reject heat. Having lived and worked in places where this barrier is regularly crossed for extended periods I can attestify that crossing this temperature barrier makes quite a difference.

No offence meant. but does T stand for ( the biblical) Thomas? Nothing I like more than to think my reply will be received with an open mind. OK On your wrist you have a gadget that performs exactly this miracle every hour. Let us take a line and connect the ends together into a circle. Now I can divide the line into (as many) infinitely small bits as I like, but the end result is still a finite circle, with a finite circumference. If I were to say I could not draw my circle or my watch hand could not pass the 12 because if I assemble an infinite number of these infinitely small bits of circumference will take an infinite amount of time, would I be right? Now extend that idea to the infinite number line. This time the circumference is infinite, but any point (as King Arthur said) on a round table can be taken as the start point, and is also the end point. So I can see both ends of my infinite number line. So there you have infinity without the maths. This was a very quickly dashed off exposition since It is well past my midnight and I am toddling off now. Final point the last step in an infinite sequence that reduces to zero must have zero length. I do not need to be able to count to infinity to know that. I did ask, a while back, that since your original post did not contain a question, whether you wanted to discuss infinities or the deficiencies in Zeno's logic. The deficiencies are not about infinities.

Confusion over terms seems rather common.

Well surely that has also to depend upon where your place your generator? solar is not much use at the North Pole, but then again wind is not much good in the doldrums nor is wave power in the Sahara.

Whilst I have offered you alternatives to thinking about infinities and you have eschewed them, the above is not true. So it is up to you if you wish to know more about what I mean or just continue to condemn the thought processes of others.

No of course not, why should I ? But I would contend that a block of pure steel containing a motor is different from one that does not. Just as any object with a hole is different from a similar one without. Of course the hole has defining limits. The ones I offered before have material boundaries. Various attempts have been made to create sustained artificial fusion reactors. Do you know of any where the containment was within a material body? In this case the containment (hole) was non material. But thank you for your thoughts.

The general cubic y = x3 + ax2 + bx + c is shown below for various values of coefficients a, b & c. For values of x that are very large and positive [math]y \mapsto \left( { + \infty } \right)[/math] For values of x that are very large and negative [math]y \mapsto \left( { - \infty } \right)[/math] So it must cross the x axis at least once on its continuous journey from negative infinity to positive infinity. imatfaal has pointed out that a cubic has three roots so if it crosses the x axis a second time ie left to right or from x negative to x positive it must cross back again to y positive. So a general cubic has one or three real roots. By evaluating the signs at the hinted points you can establish whether there is one or three crossings and where they are, following the same logic within each interval as others have indicated. Should this not be in homework help?

Without the existence of holes, you could not tie a knot and Topology would be a very different branch of Mathematics. Just as number theory would be very different without a solution to the equation x2 = -1

Roughly speaking material is translated as made of matter and no material is made of something else. Perhaps you missed this post in the time thread but here is something made of absolutely nothing (ie non material) If you wish to deny the existence of the hole, try using one without a hole. You didn't say that in your precious post. You need to be accurate and precise in Science. Particularly if you are testing the logic of someone else's deductions or statements.

You asked me what I meant by material and non material and I told you. Since I introduced the terms material and non material into the thread, quite deliberately to distinguish from any terms others might use, I claim the right to define them. We cannot have a conversation about anything I have said subsequent to my definition if you wish to use a different one since anyyhing I have said must be contingent upon my original definition. So are you arguing with my conclusions, drawn commensurate with my definitions, or are you arguing about my definitions? I did indeed, and I have several times in this thread distinguished between real as having existence and imaginary as not having existence. Further I have distinguished between material and non material items, which I have defined as a different concept, as indicated about, to prevent confusion with real v imaginary. I have even accomodated you in altering my use of the term 'object' to item and explained why I did that - again to avoid confusion stemming from conflicting definitions. So are you just palying with words or do you have a substantive point to make? If so, please be good enough to make it properly. Actually this is not strictly true, since there are other circumstances where a soleoid is not inert. If you look more carefully at my statement, I said Now a solenoid possesses calculable self inductance whether or not electric current applied. So once again. are you playing with words or do you have a reasoned objection? If so please state your reasoning.

Useful tips, thanks John, +1

http://www.eeweb.com/toolbox/wire-inductance

For those interested in theoretical thermodynamics (non engineering) I recommend. Elements of Classical Thermodynamics for Students of Advanced Physics : Pippard : Cambridge Thermodynamics and Statistical Mechanics : Wilson : Cambridge Basic Thermodynamics : Carrington :: Oxford Chemical Equilibrium : Denbeigh : Cambridge I do not advise Thermodynamics and and Introduction to Thermostatistics : Callen : Wiley.

Thermodynamics is a very closely defined subject. Unfortunately there is much 'loose talk' about it that leads people into erroneous conclusions. Perhaps the worst for casual aquaintances with thermodynamics is the populist press propagated confusion over order and disorder. For those who study deeper the commonest errors stem from failure to properly specify the full thermodynamic situation (System, boundary and process). I note your original linked article is guilty of this for instance.

But the application of both the first and second laws to an isolated system is trivial since they involve non system quantities (those crossing the system boundary). Both w and q are necessarily zero for an isolated system therefore dU is also zero.

The website prometheus linked to notes that there are several ways to resolve Zeno. In fact you don't need 'infinity' at all when considering the sequence. Further the website makes the usual sleight of hand switch from time to distance in its presentation.

Gosh Tar I thought you were getting somewhere, but you have gone of rambling down the byeways of I know not where again, and overcomplicating things. Quite simply Zeno is correct. Achilles does not catch the tortoise. At least not in the time period that Zeno considers. Zeno's mistake is to think that the interval in time he considers is all of time, whereas all he considers is the period from the satrt of the race to the time when Achilles is abreast of the tortoise (and technically still has not overtaken it). His analysis says nothing about the time after that any more than the time before the start of the race. However, buried in your last two posts you referred to a conjurors switch. This is true. Most descriptions of the analysis start off (correctly) considering time as the independent variable, but suddenly switch to considering distance. You cannot change horses midstream.

You need to understand that the terms order and disorder are statistical statements that refer to probabilities. Try this experiment: Take two dice and roll them. How many ways can their sum equal 2? : This is the lowest sum you can obtain. How many ways can their sum equal 6? In fact form a table from 2 to 12. There is only one configuration that can yield a sum of 2, but there are many that can yield a sum of 6 so 6 is more probable than 2. Now go a step further. How many ways can the two numbers thrown be the same and how many ways can they be different? Call the ways that they can be thrown the same 'order' and the ways they can be different, 'disorder'. Which is more probable? That is all that is meant by the statement disorder is more prebable than order or order tends to disorder. Rewriting it says When (in real life) there are a very large (perhaps infinite) number of states if we take any one state and call it order, then disorder is much more likely.

Your statement makes no sense to me. You must understand the meaning of "material", "non-material" and "existence" in a way I don't understand. Well try it this way. You have made the following statement: So let the two objects both be bar magnets. Certainly they interact to produce an observable 'result'. I am classing the bar magents as material and the interaction between them, however you chose to explain it, as non material. (An example of two material objects interacting to produce a material result would be a lit match, a piece of paper and a fire) I am further suggesting that I may perform this experiment in mind only in which case none of the three objects (physically) exist. Alternatively I might actually perform the experiment with actual bar magnets. In which case both the magnets and their interaction (physically) exist. I am simply trying to choose words to allow for all combinations. There is nothing magic, mystic or intentionally covert about this. Incidentally, with regard to the quote from your goodself. I disagree. An example of where you require only one object to produce an interaction would be the self inductance of a solenoid.

Apologies, I should have said at least three. "things or phenomena" I was simply seeking a generic word to cover all bases in one. I certainly agree that some or all the extra items may be non material. And if the first two possess existence, so must the third, fourth etc. So we have finally come to agreement on that point. Both material and non material items may possess the quality of existence or they may be purely imaginary.

Yeah, Tar you are getting towards your lingual solution. +1 for good thinking. Two key phrases "time and space" Yes there are not one but two infinite sequences involved with finite limits. "The whole infinite set of steps is completed in 10 or 15 seconds," Yes Zeno's analysis only acounts for part of the real number line axis that we call time and to resolve the 'paradox' we need to determine what happens on the rest of it.

The Clausius statement of the second law is:- [math]\oint {\frac{{dQ}}{T}} [/math][math] \le 0[/math] The strict equality holds for reversible systems, the inequality for irreversible systems.

I have a way of describing (the need for) time that might be better placed in the other current thread. It describes a simple experiment with two bar magnets and a compass.

So if I took a mass and elevated it according to that old thermodynamic chestnut of Joules experiment (infinitely slowly) would it gain in mass?

Yes the words order and disorder, in the context of the second law, have particular meanings that are not associated with a housewife's apple pie order or the OP example of perfectly round shapes. The second law holds for both reversible and irreversible cyclic processes. It's use on noncyclic processes can lead to error. Yes it never decreases, but that is not the same as saying evolve towards some maximum entropy. It is possible to construct examples that do not do this.