vttoth — January 30th, 2009
I’m reading a 40-year old book, Methods of Thermodynamics by Howard Reiss. I think I bought it after reading a recommendation on Amazon.com, describing this book as one of the few that takes the idea of axiomatic thermodynamics seriously, and treats it without mixing in concepts from statistical physics or quantum mechanics.
It is a very good book. Not only does it deliver on its promise, it also raises some issues that would not have occurred to me otherwise. For instance, the idea that a so-called equation of state does not fully describe the state of a material, even an ideal gas. You cannot derive U = CvT from the equation of state. You cannot that the internal energy U is a linear function of the temperature T, it has to be postulated.
One thing you can derive from the ideal gas equation of state alone is that an adiabatic expansion must be isothermal. As an ideal gas expands and its volume increases while its pressure decreases, its temperature remains constant. It also made me think again about the cosmological equation of state… cosmologists often play with idealized cases (e.g., dust-filled universe, radiation-filled universe) but until now, I never considered the possibility that even in these idealized cases, the equations of state do not full describe the stuff that they supposedly represent.
Categories: Physics |
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vttoth — January 30th, 2009
Our paper about the thermal analysis of Pioneer 10 and 11 was accepted for publication by Physical Review and it is now on ArXiv.
I think it is an interesting paper. First, it derives from basic principles equations of the thermal recoil force. This is not usually in heat transfer textbooks, as those are more concerned about energy exchange than about momentum. We also derive the infamous factor of 2/3 for a Lambertian (diffuse) surface.
More notably, we make a direct connection between the thermal power of heat sources and the recoil force. The thermal power of heat sources within a spacecraft is usually known very well, and may also be telemetered. So, if a simple formalism exists that gives the recoil force as a function of thermal power, we have a very meaningful way to connect telemetry and trajectory analysis. This is indeed what my “homebrew” orbit determination code does, using Pioneer telemetry and Doppler data together.
No results yet… the paper uses simulated Pioneer 10 data, precisely to avoid jumping to a premature conclusion. We can jump to conclusions once we’re done analyzing all the data using methods that include what’s in this paper… until then, we have to keep an open mind.
Categories: Physics |
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vttoth — January 29th, 2009
In two days, I got two notices of papers being accepted, among them our paper about the possible relationship between modified gravity and the origin of inertia. I am most pleased, because the journal accepting it (MNRAS Letters) is quite prestigious and the paper was a potentially controversial one. The other paper is about Pioneer, and was accepted by Physical Review D. Needless to say, I am pleased.
Categories: Physics |
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vttoth — January 27th, 2009
Long before blogs, long before the Web even, there was an Internet and people communicated via public forums (fora?), Usenet foremost among them.
Yet I stopped using Usenet about a decade ago. Here is a good example as to why. Excerpts from an exchange:
“You will have more success on Usenet if you learn and follow the normal Usenet posting conventions.“
“About posting conventions: where did I stray from them? I do indeed want to respect the list rules.“
“Have a look at <http://cfaj.freeshell.org/google/>“
“Got it: thanks.“
“You failed to appropriately quote the message that you are responding to. See the FAQ and the more detailed explanation of posting style that it links to. Then, if the explanation provided is not sufficiently clear, ask for clarification.“
“I am afraid that you have not yet ‘got it’. You have gone from not quoting the message you are responding to, to top-posting and failing to appropriately trim the material that you are quoting.“
“If you had been told what you did wrong, that would, hopefully, eliminate one class of error from your future posts. You were told where to read about conventions, which *should* eliminate *all* of the well-known errors.“
You are forgiven if you thought that the thread from which I excerpted these snotty remarks was about Usenet’s “netiquette”. But it wasn’t. It was all in response to a very polite and sensible question about ways to implement a destructor in JavaScript.
I guess my views are rather clear on the question as to which people harm Usenet more: those who stray from flawless “netiquette”, or those who feel obliged to lecture them. I have yet to understand why it is proper “netiquette” to flood a topic with such lectures instead of limiting responses to the topic at hand, and responding only when one actually knows the answer. I guess that would be too helpful, and helping other people without scolding them is not proper “netiquette”?
Categories: Internet, Programming |
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vttoth — January 27th, 2009
I’ve read a lot about the coming “digital dark age”, when much of the written record produced by our digital society will no longer be readable due to changing data formats, obsolete hardware, or deteriorating media.
But perhaps, just perhaps, the opposite is happening. Material that is worth preserving may in fact be more likely to survive, simply because it’ll exist in so many copies.
For instance, I was recently citing two books in a paper: one by d’Alembert, written in 1743, and another by Mach, from 1883. Is it pretentious to cite books that you cannot find at any library within a 500-mile radius?
Not anymore, thanks, in this case, to Google Books:
Jean Le Rond d’ Alembert: Traité de dynamique
Ernst Mach: Die Mechanik in ihrer Entwickelung
And now, extra copies of these books exist on my server, as I downloaded and I am preserving the PDFs. Others may do the same, and the books may survive so long as computers exist, as copies are being made and reproduced all the time.
Sometimes, it’s really nice to live in the digital world.
Categories: Books, Internet, Physics, Society, Technology |
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vttoth — January 26th, 2009
The other day, I put my latest (well, I actually did it last summer, but it’s the latest that has seen the light of day) Pioneer paper on ArXiv.org; it is not about new results (yet), just a confirmation of the Pioneer anomaly using independently developed code, and a demonstration that a jerk term may be present in the data.
Categories: Physics |
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vttoth — January 25th, 2009
Often, I wondered: who designed the graphical elements, like the fonts and icons that appear on my computer screen?
Finally, I know the name of one of these people. She is Susan Kare, and her work appeared in the original Macintosh, Windows 3.0, OS/2, even Facebook. I came across her name as I was reading about the 25th anniversary of the Macintosh and clicked a link that took me to a 12-year old article from The New York Times that Ms. Kare has on her Web site.
Categories: Computers |
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vttoth — January 24th, 2009
Once again, I am studying classical thermodynamics. Axiomatic thermodynamics to be precise, none of this statistical physics business (which is interesting on its own right, but it is quite a different topic.)
The more I learn about it, the more I find thermodynamics incredibly fascinating. Why is it so different from other areas of physics? Perhaps I now have an answer that may be trivial to some, but eluded me until now.
Most of physics is described by functions of coordinates and time. This is true even in the case of general relativity, even as the coordinate system itself may be curved, the curvature (the metric) is described as a function of space-time coordinates.
In contrast, there are no coordinates in axiomatic thermodynamics, only states. States are decribed by state variables, and usually you have these in excess. For instance, the state of one mole of an ideal gas is described by any two of the three variables p (pressure), V (volume) and T (temperature); once two of these are known, the third is given by the ideal gas equation of state, pV = KT, where K is a constant.
Notice that there is no independent variable. The variables p, V, and T are not written as functions of time. Nor should they be, since axiomatic thermodynamics is really equilibrium thermodynamics, and when a system is in equilibrium, it is not changing, its state is constant.
So why is it not called thermostatics? What does dynamics have to do with stationary states? As it turns out, thermodynamics is the science of fitting a square peg in a round hole, as having just established that it’s a science of static states, it nevertheless goes on to explain how states can change… so long as all the intermediate states can exist as static states on their own right, such as when you’re heating a gas slowly enough so that its temperature is more or less uniform at all times, and its state is well approximated by thermodynamic variables.
The zeroeth law states that an empirical temperature exists that is associative: systems that have the same temperature form equivalence classes.
The first law defines the (infinitesimal) quantity of heat dQ as the sum of changes in internal energy (dU) and mechanical work (p dV). An important thing about dQ is that there may not be a Q; in the jargon of differential forms, dQ is a Pfaffian that may not be exact.
The second law uses the assumption of irreversibility and Carathéodory’s theorem to show that there is an integrating denominator T and a function S such that dQ = T dS. (Presto, we have entropy.) Further, T is uniquely determined up to a multiplicative constant.
Combined, the two laws can be written in the form dU = T dS − p dV. After that, much of what is in the textbooks about classical thermodynamics can be written compactly in the form of the Jacobian determinant ∂(T, S)/∂(p, V) = 1.
Given that I know all this, why do I still find myself occasionally baffled by the simplest thermodynamic problems, such as convincing myself that when an isolated system of ideal gas expands, its temperature remains constant? (It does, the math says so, textbooks say so, but still…) There is something uniquely non-trivial about axiomatic thermodynamics.
Categories: Physics |
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vttoth — January 22nd, 2009
The other day, arXiv.org split a popular category, astro-ph, into six subcategories. This is convenient… astro-ph, the astrophysics archive, was getting rather large, and the split into sub-categories makes it easier to find papers that are relevant to one’s specialization.
On the other hand… it also means that one is less likely to read papers that are not directly relevant to one’s specialization, but may be interesting, eye-opening, and may help to broaden one’s horizons. Is this a good thing?
There are no easy answers of course… the number of papers just on arXiv.org is mind-boggling (they proudly announced that they’ve passed the half million paper milestone on October, with thousands of new papers added every month) and no one has the time to read them all. Hmmm, perhaps I should have spent more time applauding a recent initiative by Physical Review, their This Week in Physics newsletter and associated Web site.
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vttoth — January 20th, 2009
While we were celebrating President Obama, the Bank of Canada made its move: the Canadian prime rate is now lower than ever, at 1%. The expectation is that the economy will not fare well in coming months.
Being the holder of a variable rate mortgage, I have no reason to complain. Still, it’s an unsettling development.
Categories: Economy |
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