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Max Planck

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Demokryt (460 - 370 pne) -światło i ciepło są odmianami tej samej substancji.

http://en.wikipedia.org/wiki/Atomism 

 

"W połowie XVII wieku panował pogląd, że światło jest bezbarwne, a barwy widzimy dzięki temu, że światło w jakiś sposób wydobywa je z przedmiotów i przekazuje oku. Natomiast Izaak Newton uważał, że światło białe, słoneczne jest mieszaniną wielu barw - jest kolorowe. 

 Zdaniem Newtona jednobarwne promienie światła otrzymane przez rozszczepienie pryzmacie są czymś w rodzaju  atomów świetlnych,  których nie można już ani rozdzielić, ani w żaden sposób zmienić.

Newton twierdził, że białe światło jest mieszaniną wszystkich barw widma, choć twierdzenie to przeczyło całej tradycji liczącej dwa tysiące lat ...."

więcej: http://www.izaaknewton.ovh.org/optics/optics.html

 

200 lat później

Według przekonań fizyków przełomu XVIII i XIX wieku, podobnie jak ciepło, światło miało być fluidem. W 1789 Lavoisier umieścił je w tablicy pierwiastkówJędrzej Śniadecki przetłumaczył to pojęcie jako świetlik [2]. /http://pl.wikipedia.org/wiki/%C5%9Awiat%C5%82o/

 

100 lat później

James Clerk Maxwell wykazał, że teoretyczne fale elektromagnetyczne będą przemieszczać się w przestrzeni ze stałą prędkością zależną od współczynników kierunkowych ε iμ, co okazało się być zgodne z uprzednio zmierzoną prędkością światła. Na tej podstawie Maxwell stwierdził, że światło jest formą promieniowania elektromagnetycznego (1873 Treatise on Electricity and Magnetism) - znane jako równania Maxwella . 

źródło: http://en.wikipedia.org/wiki/Light#Historical_theories_about_light.2C_in_chronological_order 

 

Słabością teorii falowej było, że fale świetlne, podobnie jak fale dźwiękowe, potrzebują medium do rozprzestrzeniania się. 

Istnienie substancji hipotetycznego świetlnego eteru proponowane przez Huygensa w 1678 roku,

 zostało  ZAKWESTIONOWANE  pod koniec XIX wieku przez

 INTERPRETATORÓW  eksperymentu Michelsona-Morleya .


http://en.wikipedia.org/wiki/Light#Quantum_theory

 

 

i się zaczęło ;D

Teoria kwantowa

W 1900 roku Max Planck , próbując wyjaśnić promieniowanie ciała doskonale czarnego zasugerował, że choć światło jest falą, to fale te mogą zyskać lub stracić energię tylko w ograniczonej ilości, związanej z ich częstotliwością. Planck nazwał te porcje  "kwantami energii światła" (z łacińskiego słowa oznaczającego "ile"). W 1905 roku Albert Einstein za pomcą idei  kwantów światła wyjaśnił efekt fotoelektryczny , i zasugerował, że te kwanty światła są "prawdziwe".  /http://en.wikipedia.org/wiki/Light#Quantum_theory/


Zauważyłem, że Waldemar.m polecił Robaxsowi do przeczytania oryginalną prace Plancka z grudnia 1900, w której Planck podaje swoje rozumowanie i na jego podstawie wyprowadza matematyczną formułę, wyrażająca jego słynne prawo.  Jeden artykuł, który obszernie omawia historię odkrycia i tłumaczy w nieco wiekszych szczegółach matematyke z tej pracy z grudnia 1900, można przeczytać tutaj  /SNAFU  13.07.2014 11:06/

 

To, że poleciłem tą właśnie pracę, jest zasługą jednego z komentatorów mojej notki. To on zamieścił adres do tej pracy Plancka na moim blogu, a ja go tylko poleciłem Robaksowi. Liczyłem na to, że dowiem się w jaki sposób Planck zasłużył sobie tą pracą z 1900 r. na miano ojca Mechaniki Kwantowej /waldemar.m  13.07.2014 17:18/ 

 

 Faktycznie tak było, że źródło do pdf

http://www.ffn.ub.es/luisnavarro/nuevo_maletin/Planck%20%281900%29,%20Distribution%20Law.pdf

 podał  jeden z komentatorów  a chodzi o tłumaczenie

— — ¦♦¦ — —

English translation from “The Old Quantum Theory,” ed. by D. ter Haar, Pergamon Press, 1967, p. 82.

— — ¦♦¦ — —

 

Oto ten tekst w wersji html


M. Planck, Verhandl. Dtsch. phys. Ges.,2, 237                                          1900

 

On the Theory of the Energy Distribution Law of the Normal Spectrum

M. Planck

Berlin

(Received 1900)

 

GENTLEMEN: when some weeks ago I had the honour to draw your attention to a new formula which seemed to me to be suited to express the law of the distribution of radiation energy over the whole range of the normal spectrum [1], I mentioned already then that in my opinion the usefulness of this equation was not based only on the apparently close agreement of the few numbers, which I could then communicate, with the available experimental data,1 {1 Verh.Dtsch. Phys. Ges.Berlin 2, 237 (1900)} but mainly on the simple structure of the formula and especially on the fact that it gave a very simple logarithmic expression for the dependence of the entropy of an irradiated monochromatic vibrating resonator on its vibrational energy. This formula seemed to promise in any case the possibility of a general interpretation much rather than other equations which have been proposed, apart from Wien’s formula which, however, was not confirmed by experiment.

 

Entropy means disorder, and I thought that one should find this disorder in the irregularity with which even in a completely stationary radiation field the vibrations of the resonator change their amplitude and phase, as long as considers time intervals long compared to the period of one vibration, but short compared to the duration of a measurement. The constant energy of the stationary vibrating resonator can thus only be considered to be a time (str.1) average, or, put differently, to be an instantaneous average of the energies of a large number of identical resonators which are in the same stationary radiation field, but far enough from one another not to influence each other. Since the entropy of a resonator is thus determined by the way in which the energy is distributed at one time over many resonators, I suspected that one should evaluate this quantity in the electromagnetic radiation theory by introducing probability considerations, the importance of which for the second law of thermodynamics was first of all discovered by Mr. Boltzmann[3]. This suspicion has been confirmed; I have been able to derive deductively an expression for the entropy of a monochromatically vibrating resonator and thus for the energy distribution in a stationary radiation state, that is, in the normal spectrum. To do this it was only necessary to extend somewhat the interpretation of the hypothesis of “natural radiation” which is introduced in electromagnetic theory. Apart from this I have obtained other relations which seem to me to be of considerable importance for other branches of physics and also of chemistry.

 

I do not wish to give today this deduction – which is based on the laws of electromagnetic radiation, thermodynamics and probability calculus – systematically in all details, but rather to explain as clearly as possible the real core of the theory. This can be done most easily by describing to you a new, completely elementary treatment through which one can evaluate – without knowing anything about a spectral formula or about any theory – the distribution of a given amount of energy over the different colours of the normal spectrum using one constant of nature only and after that the value of the temperature of this energy radiation using a second constant of nature. You will find many points in the treatment to be presented arbitrary and complicated, but as I said a moment ago I do not want to pay attention to a proof of the necessity and the simple, practical details, but to the clarity and uniqueness of the given prescriptions for the solution of the problem.

 

Let us consider a large number of monochromatically vibrating resonator – N of frequencyν (per second), N’ of frequencyν’ , N’’  of frequencyν’’, ..., with all N large number – which are at large distances apart and are enclosed in a diathermic medium with light velocity c and bounded by reflecting walls. Let the system contain a certain amount of energy, the total energy Et (erg) which is present partly in the medium as travelling radiation and partly in the resonators as vibrational energy. The question is how in a stationary state this energy is distributed over the vibrations of the resonator and over the various of the radiation present in the medium, and what will be the temperature of the total system.

 

To answer this question we first of all consider the vebrations of the (str.2) resonators and assign to them arbitrary definite energies, for instance, an energy E to the N resonatorsν , E’ to the N’ resonatorsν’ ,... . The sum

E + E’ + E’’ + ...= E0

must, of course, be less than Et. The remainder Et − E0 pertains then to the radiation present in the medium. We must now give the distribution of the energy over the separate resonators of each group, first of all the distribution of the energy E over the N resonators of frequencyν . If E considered to be continuously divisible quantity, this distribution is possible in infinitely many ways. We consider, however – this is the most essential point of the whole calculation – E to be composed of a very definite number of equal parts and use thereto the constant of nature h = 6.55 × 10− 27 erg · sec. This constant multiplied by the common frequencyν of the resonators gives us the energy elementε in erg, and dividing E byε we get the number P of energy elements which must be divided over the N resonators. If the ratio is not an integer, we take for P an integer in the neighbourhood.

 

It is clear that the distribution of P energy elements over N resonators can only take place in a finite, well–defined number of ways. Each of these ways of distribution we call a ”complexion”, using an expression introduced by Mr. Boltzmann for a similar quantity. If we denote the resonators by the numbers 1, 2, 3, ... , N , and write these in a row, and if we under each resonator put the number of its energy elements, we get for each complexion a symbol of the following form

1 2 3 4 5 6 7 8 9 10

7 38 11 0 9 2 20 4 4 5

We have taken here N = 10, P = 100. The number of all possible complexions is clearly equal to the number of all possible sets of number which one can obtain for lower sequence for given N and P . To exclude all misunderstandings, we remark that two complexions must be considered to be different if the corresponding sequences contain the same numbers, but in different order. From the theory of permutations we get for the number of all possible complexions

N ( N + 1) · ( N + 2) ... ( N + P − 1) / 1 · 2 · 3 ...P = ( N + P − 1)! / ( N − 1)! P !

or to a sufficient approximations,

= ( N + P )^(N + P) / N^NP^P.(str 3)

 

We perform the same calculation for the resonators of the other groups, by determining for each group of resonators the number of possible complexions for the energy given to the group. The multiplication of all numbers obtained in this way gives us then the total number R of all possible complexions for the arbitrary assigned energy distribution over all resonators.

 

In the same way any other arbitrarily chosen energy distribution E, E’ ,E’’ ... will correspond to a definite number R of all possible complexions which is evaluated in the above manner. Among all energy distributions which are possible for a constant E0 = E + E’ + E’’ + ... there is one well– defined one for which the number of possible complexions R0  is larger than for any other distribution. We look for this distribution, if necessary by trial, since this will just be the distribution taken up by the resonators in the stationary radiation field, if they together possess the energy E0 . This quantities E, E’, E’’,... can then be expressed in terms of E0. Dividing E by N, E’ by N’ ,... we obtain the stationary value of the energy Uν , U’ν, U’’ν’’ ... of a single resonator of each group, and thus also the spatial density of the corresponding radiation energy in a diathermic medium in the spectral rangeν toν + dν ,

uνdν = 8πν2/ c3 · Uνdν,

so that the energy of the medium is also determined.

 

Of all quantities which occur only E0 seems now still to be arbitrary. One sees easily, however, how one can finally evaluate E0 from the total energy Et , since if the chosen value of E0 leads, for instance, to too large a value of Et , we must decrease it, and the other way round.

 

After the stationary energy distribution is thus determined using a constant h , we can find the corresponding temperatureθ in degrees absolute 2 {2 The original states “degrees centigrade” which is clearly a slip [D. t. H.]} using a second constant of nature k = 1.346 × 10^(−6)erg · degree((-1) through the equation

1 /θ = k d ln R0 /dE0.

 

The product k ln · R0 is the entropy of the system of resonators; it is the sum of the entropy of all separate resonators.

 

It would, to be sure, be very complicated to perform explicity the above– mentioned calculations, although it would not be without some interest to test the truth of the attainable degree of approximation in a simple case. A more general calculation which is performed very simply, using the above (str.4)prescriptions shows much more directly that the normal energy distribution determined in this way for a medium containing radiation is given by expression

Uν dν = 8πν3 /c3 · dν / (e^hν/kθ − 1)

which corresponds exactly to the spectral formula which I give earlier

Eλdλ = c1λ^(−5) / (e^c2/λθ −1) dλ.

 

The formal differences are due to the differences in the definitions of uν and Eλ . The first equation is somewhat more general inasfar as it is valid for arbitrary diathermic medium with light velocity c . The numerical values of h and k which I mentioned were calculated from that equation using the measurements by F. Kurlbaum and by O. Lummer and E. Pringsheim.3 { F. Kurlbaum [4] gives S100 − S0 = 0.0731 Watt cm^(−2), while O. Lummer and E. Pringsheim [5] giveλmθ = 2940μ ·degree.}

 

I shall now make a few short remarks about the question of the necessity of the above given deduction. The fact that the chosen energy elementε for a given group of resonators must be proportional to the frequencyν follows immediately from the extremely important Wien displacement law. The relation between u and U is one of the basic equations of the electromagnetic theory of radiation. Apart from that, the whole deduction is based upon the theorem that the entropy of a system of resonators with given energy is proportional to the logarithm of the total number of possible complexions for the given energy. This theorem can be split into two other theorems: (1) The entropy of the system in a given state is proportional to the logarithm of the probability of that state, and (2) The probability of any state is proportional to the number of corresponding complexions, or, in other words, any definite complexion is equally probable as any other complexion. The first theorem is, as for as radiative phenomena are concerned, just a definition of the probability of the state, insofar as we have for energy radiation no other a priori way to define the probability that the definition of its entropy. We have here a distinction from the corresponding situation in the kinetic theory of gases. The second theorem is the core of the whole of the theory presented here: in the last resort its proof can only be given empirically. It can also be understood as a more detailed definition of the hypothesis of natural radiation which I have introduced. This hypothesis I have expressed before [6] only in the form that the energy of the radiation is completely ”randomly” distributed over the various partial vibrations present in the (str.5) radiation.4  {4When Mr. Wien in his Paris report about the theoretical radiation laws did not find my theory on the irreversible radiation phenomena satisfactory since it did not give the proof that the hypothesis of natural radiation is the only one which leads to irreversibility, he surely demanded, in my opinion, too much of this hypothesis. If one could prove the hypothesis, it would no longer be a hypothesis, and one did not have to formulate it. However, one could then not derive anything new from it. From the same point of view one should also declare the kinetic theory of gases to be unsatisfactory since nobody has yet proved that the atomistic hypothesis is the only which explains irreversibility. A similar objection could with more or less justice be raised against all inductively obtained theories.} I plan to communicate elsewhere in detail the considerations, which have only been sketched here, with all calculations and with a survey of the development of the theory up to the present.

 

To conclude I may point to an important consequence of this theory which at the same time makes possible a further test of its reliability. Mr. Boltzmann [7] has shown that the entropy of a monatomic gas in equilibrium is equal toωR ln P0 , where P0 is the number of possible complexions (the “permutability”) corresponding to the most probable velocity distribution, R being the well known gas constant (8.31 × 10^7 for O = 16),ω the ratio of the mass of a real molecule to the mass of a mole, which is the same for all substances. If there are any radiating resonators present in the gas, the entropy of the total system must according to the theory developed here be proportional to the logarithm of the number of all possible complexions, including both velocities and radiation. Since according to the electromagnetic theory of the radiation the velocities of the atoms are completely independent of the distribution of the radiation energy, the total number of complexions is simply equal to the product of the number relating to the velocities and the number relating to the radiation. For the total entropy we have thus

f ln (P0 R0) = f ln P0 + f ln R0,

where f is a factor of proportionality. Comparing this with the earlier expressions we find

f =ωR = k,

or

ω = k R = 1.62 × 10^(−24),

that is, a real molecule is 1.62 × 10^(−24)of a mole or, a hydrogen atom weighs 1.64 × 10^(−24)g, since H = 1.01, or, in a mole of any substance there are 1/ω = 6.175 × 10^23 real molecules. Mr. O.E Mayer [8] gives for this number 640 × 10^21which agrees closely. (str6)

 

Loschmidt’s number L , that is, the number of gas molecules in 1 cm3 at 0º C and 1 atm is

L = 1 013 200 / R·273·ω = 2.76 × 10^19.

Mr. Drude [9] finds L = 2.1 × 10^19.

 

The Boltzmann-Drude constantα , that is, the average kinetic energy of an atom at the absolute temperature 1 is

α = 3/2ωR = 3/2 k = 2.02 × 10^(−16).

Mr. Drude [9] findsα = 2.65 × 10^(−16).

 

The elementary quantum of electricity e , that is, the electrical charge of a positive monovalent ion or of an electron is, ifε is the known charge of a monovalent mole,

e =εω = 4.69 × 10^(−10)c.s.u.

Mr. F. Richarz [10] finds 1.29 × 10^(−10)and Mr. Thomson [11] recently 6.5 × 10^(−10).

 

If the theory is at all correct, all these relations should be not approximately, but absolutely, valid. The accuracy of the calculated number is thus essentially the same as that of the relatively worst known, the radiation constant k, and is thus much better than all determinations up to now. To test it by more direct methods should be both an important and a necessary task for further research.

 

References

[1] M. Planck, Verh. D. Physik.Ges. Berlin 2, 202 (1900) (reprintedas Paper 1 on p. 79 in the present volume).

[2] H. Rubens and F. Kurlbaum, S.B. Preuss. Akad. Wiss. p. 929 ( 1900);

[3] L. Boltzmann, S.B. Akad. Wess. Wien 76, 373 (1877);

[4] F. Kurlbaum, Ann. Physik 65, 759 (1898);

[5] O. Lummer and E. Pringsheim, Verh. D. Physik. Ges. Berlin 2, 176 (1900);

[6] M. Planck, Ann.Physik 1, 73 (1900);

(str.7)

[7] L. Boltzmann, S.B. Akad. Wiss. Wien 76, 428 (1877);

[8] O.E. Mayer, Die Kinetische Theotie der Gase, 2nd ed., p. 337 ( 1899);

[9] P. Drude, Ann. Physik 1, 578 (1900);

[10] F. Richarz, Ann. Physik 52, 397 (1894);

[11] J.J. Thomson, Phil. Mag. 46, 528 (1898). 

(str.8)


 

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Wniosek:

Chcąc zrozumieć co napisał Planck trzeba rozumieć co znaczy słowo OPIS.

Bez tego każdy tekst to tylko "mielenie ozorem"  :)

complexion = karnacja

Edward Robak* z Nowej Huty   ۞   Technik Elektronik :) 

 

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