Weblog on Physics

Friday 24 May 2013

Il ciclo di Carnot

Al link
http://books.google.it/books/about/R%C3%A9flexions_sur_la_puissance_motrice_du.html?id=YcY9AAAAMAAJ&redir_esc=y
il libro di Carnot dove descrve il ciclo.

Alcune pagine di una versione inglese del 1897

Nicolas Léonard Sadi Carnot

http://en.wikipedia.org/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot

Carnot's Reflections on the Motive Power of Fire

When Carnot began working on his book, steam engines had achieved widely recognized economic and industrial importance, but there had been no real scientific study of them. Newcomen had invented the first piston-operated steam engine over a century before, in 1712; some 50 years after that, James Watt made his celebrated improvements, which were responsible for greatly increasing the efficiency and practicality of steam engines. Compound engines (engines with more than one stage of expansion) had already been invented, and there was even a crude form of internal-combustion engine, with which Carnot was familiar and which he described in some detail in his book. Although there existed some intuitive understanding of the workings of engines, scientific theory for their operation was almost nonexistent. In 1824 the principle of conservation of energy was still poorly developed and controversial, and an exact formulation of the first law of thermodynamicswas still more than a decade away; the mechanical equivalence of heat would not be formulated for another two decades. The prevalent theory of heat was the caloric theory, which regarded heat as a sort of weightless and invisible fluid that flowed when out of equilibrium.

Engineers in Carnot's time had tried, by means such as highly pressurized steam and the use of fluids, to improve the efficiency of engines. In these early stages of engine development, the efficiency of a typical engine — the useful work it was able to do when a given quantity of fuelwas burned — was only 3%.

The Carnot Cycle

Carnot sought to answer two questions about the operation of heat engines: "Is the work available from a heat source potentially unbounded?" and "Can heat engines in principle be improved by replacing the steam with some other working fluid or gas?" He attempted to answer these in a memoir, published as a popular work in 1824 when he was only 28 years old. It was entitled Réflexions sur la Puissance Motrice du Feu ("Reflections on the Motive Power of Fire"). The book was plainly intended to cover a rather wide range of topics about heat engines in a rather popular fashion; equations were kept to a minimum and called for little more than simple algebra and arithmetic, except occasionally in the footnotes, where he indulged in a few arguments involving some calculus. He discussed the relative merits of air and steam as working fluids, the merits of various aspects of steam engine design, and even included some ideas of his own regarding possible improvements of the practical nature. The most important part of the book was devoted to an abstract presentation of an idealized engine that could be used to understand and clarify the fundamental principles that are generally applied to all heat engines, independent of their design.

Perhaps the most important contribution Carnot made to thermodynamics was his abstraction of the essential features of the steam engine, as they were known in his day, into a more general and idealized heat engine. This resulted in a model thermodynamic system upon which exact calculations could be made, and avoided the complications introduced by many of the crude features of the contemporary steam engine. By idealizing the engine, he could arrive at clear and indisputable answers to his original two questions.

He showed that the efficiency of this idealized engine is a function only of the two temperatures of the reservoirs between which it operates. He did not, however, give the exact form of the function, which was later shown to be ^{(T₁−T₂)}⁄_T₁, where T₁ is the absolute temperature of the hotter reservoir. (Note: This equation probably came from Kelvin.) No thermal engine operating any other cycle can be more efficient, given the same operating temperatures.

The Carnot cycle is the most efficient possible engine, not only because of the (trivial) absence of friction and other incidental wasteful processes; the main reason is that it assumes no conduction of heat between parts of the engine at different temperatures. Carnot knew that the conduction of heat between bodies at different temperatures is a wasteful and irreversible process, which must be eliminated if the heat engine is to achieve maximum efficiency.

Regarding the second point, he also was quite certain that the maximum efficiency attainable did not depend upon the exact nature of theworking fluid. He stated this for emphasis as a general proposition: "The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which the transfer of caloric takes place." For his "motive power of heat", we would today say "the efficiency of a reversible heat engine," and rather than "transfer of caloric" we would say "the reversible transfer of heat." He knew intuitively that his engine would have the maximum efficiency, but was unable to state what that efficiency would be.

He concluded:

The production of motive power is therefore due in steam engines not to actual consumption of caloric but to its transportation from a warm body to a cold body.

—Carnot 1960, p. 7

and

In the fall of caloric, motive power evidently increases with the difference of temperature between the warm and cold bodies, but we do not know whether it is proportional to this difference.

—Carnot 1960, p. 15

The Second Law of Thermodynamics

In Carnot's idealized model, the caloric heat converted into work could be recovered by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Nevertheless, Carnot further postulated that some caloric is lost and not converted into mechanical work. Hence, a real heat engine could not realize the Carnot cycle's reversibility and would consequently be less efficient.

Though formulated in terms of caloric, rather than entropy, this was an early rendition of the second law of thermodynamics.

Reception and later life

Carnot’s book received very little attention from his contemporaries. The only reference to it within a few years after its publication was in a review in the periodical Revue Encyclopédique, which was a journal that covered a wide range of topics in literature. The impact of the work had only become apparent once it was modernized by Émile Clapeyron in 1834 and then further elaborated upon by Clausius and Kelvin, who together derived from it the concept of entropy and the second law of thermodymics.

Adiabatica

Cosmic Microwave Background Radiation
http://www.nicadd.niu.edu/~bterzic/PHYS652/Lecture_19.pdf by Balša Terzić
"The CMB radiation is a prediction of Big Bang theory. According to the Big Bang theory, the
early Universe was made up of a hot plasma of photons, electrons and baryons. The photons were
constantly interacting with the plasma through Thomson scattering. As the Universe expanded,
adiabatic cooling caused the plasma to cool until it became favorable for electrons to combine
with protons and form hydrogen atoms. This happened at around 3,000 K or when the Universe
was approximately 380,000 years old (z ≈ 1100). At this point, the photons scattered oﬀ the
now neutral atoms and began to travel freely through space. This process is called recombination
or decoupling (referring to electrons combining with nuclei and to the decoupling of matter and
radiation respectively). The photons have continued cooling ever since; they have now reached 2.725 K and their temperature will continue to drop as long as the Universe continues expanding. Accordingly,
the radiation from the sky that we measure today comes from a spherical surface, called the surface of last scattering. This represents the collection of points in space (currently around 46 billion light years from the Earth) at which the decoupling event happened long enough ago (less than 400,000 years after the Big Bang, 13.7 billion years ago) that the light from that part of space is just reaching observers."

Sul LAVORO in termodinamica

Lavoro in termodinamica

In termodinamica, il lavoro viene scomposto per comodità in due contributi: un contributo relativo alla variazione di volume (lavoro di volume) e un contributo indipendente dalla variazione di volume (lavoro isocoro).

Lavoro di volume

In termodinamica un gas esercita una pressione P interna sulle pareti del recipiente in cui è contenuto. Se una di queste pareti (di area A) è mobile e si sposta di una quantità infinitesima dl sotto l'azione di questa pressione, allora il lavoro infinitesimo compiuto dal gas è dato da:

$\delta L = P A dl = P \cdot dV$ .

dove dV = A dl è la variazione del volume corrispondente. Questo è vero se la trasformazione è reversibile, infatti solo se il sistema è in equilibrio termodinamico è possibile conoscere il valore della pressione P interna al contenitore. La notazione $\delta L$ è usata per indicare che il lavoro in fisica non è una funzione di stato, ed invece dipende dalla particolare trasformazione eseguita sul sistema. Se il sistema termodinamico subisce una trasformazione dove non si consoce p, quindi in una tarsformazione irreversibile, il lavoro lo possiamo determinare sfruttando il primo principio della termodinamcia, conoscendo calo scambiato e variazione d'energia interna. Possiamo ancora quantificare il lavoro fatto dal gas o dal sistema comeì:

$\delta L= P_e A dl = P_e \cdot dV$ ,

lavoro fatto contro la pressione esterna $P_e$ , se ammettiamo di consocere la pressione esterna.

La termodinamica non è fatta solo di sistemi P,V,T (fluidi) e quindi ci può essere un lavoro "isocoro"

Lavoro isocoro

Sotto il termine di lavoro isocoro si annoverano tutti i tipi di lavoro che non si riflettono in una variazione di volume, ad esempio: il lavoro elettrico.

Lavoro elettrico: In un circuito elettrico il lavoro infinitesimo compiuto dalla batteria che genera la differenza di potenziale E per far circolare una corrente elettrica I per un tempo infinitesimo dt è data da , il segno di tale lavoro sarà positivo o negativo a seconda che rispettivamente la pila eroghi o assorba corrente. Il valore del lavoro elettrico scambiato tra il tempo t₀ e il tempo t₁ si può ottenere integrando l'equazione precedente, dalla quale si ottiene:

$L = \ \int^{t_1}_{t_0} EI\, dt$

nel caso in cui la differenza di potenziale E rimanga costante durante l'intervallo di tempo considerato, si può scrivere:

$L = E \ \int^{t_1}_{t_0} I\, dt = E \cdot Q_{el}$

essendo:

L il lavoro elettrico (in joule);
E la differenza di potenziale elettrico (in volt);
I l'intensità di corrente elettrica in (in ampere);
t il tempo (in secondi);
Q_el la quantità di carica elettrica circolata durante l'intervallo di tempo considerato (in coulomb).

Saturday 18 May 2013

The spinning top

Rotate vs revolve

Rotate versus revolve, from http://www.worldwidewords.org/nl/uifj.htm
by MICHAEL QUINION

Q From Brian Miller, Australia: A loosely organised group of eccentric friends and wine lovers meets each week. The question arose, does a lazy Susan revolve or rotate? What about the plates on it?

A That’s an interesting question, which lacks a simple answer. If anybody’s not sure about a lazy Susan, by the way, it’s a device on a table which turns to give easy access to plates and condiments.

... The two words are used so interchangeably in the sense of spinning round that for most purposes they’re synonyms and they’re treated as such in thesauruses. To take an example, does a wheel rotate or revolve? Most people would say it can do either.

If you’re arguing from etymology (always risky), it can only rotate, since that term is from the Latin verb rotare, to turn in a circle, whose root is rota, a wheel. But you might argue that it revolves, because that verb is from the Latin volvere, to roll (in this case, the re- prefix implies repetition of the action) and a wheeled vehicle certainly does roll along.

Strictly speaking, there is a difference, which is most noticeable in the terminology of astronomers. For them, the earth rotates every 24 hours but takes a year to revolve around the sun. The rule about which verb to use is based on the position of the axis of rotation. If the body turns on an axis within itself it rotates but if the axis is outside it revolves. Following this definition, a wheel can only rotate (hooray for etymology).

The strict answer to the question, therefore, is that the lazy Susan rotates. However, because the plates on it orbit or circle around an axis outside themselves, they revolve. Do not insist on this careful distinction during the later stages of a dinner party or the lazy Susan may become a spinning projectile aimed at you.

As I say, the rule is rarely observed outside science and the two words have been hopelessly muddled for centuries. A revolving door actually rotates; a rotating shaft makes revolutions. You might argue that a revolver ought to be a rotator but it depends whether you are thinking of the cartridges or the cylinder that holds them.

Friday 17 May 2013

La trottola

Da "Semplicemente fisica. Fraintendimenti, bugie, buchi neri nell'apprendimento scolastico della fisica", di Giovanni Tonzig, Maggioli Editore, 2010 - 227 pagine