IS CLASSICAL THERMODYNAMICS THE UNIQUE PHYSICAL THEORY WHICH WILL NEVER BE REFUTED?

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1 IS CLASSICAL THERMODYNAMICS THE UNIQUE PHYSICAL THEORY WHICH WILL NEVER BE REFUTED? Temur Z. Kalaov Home o Physical Problems, Pisatelskaya 6a, Tashket, Uzbekista tzkuz@yahoo.com, t.z.kalaov@mail.ru, t.z.kalaov@rambler.ru Abstract: A ew theoretical aalysis o the geerally accepted oudatios o classical thermodyamics is proposed. The priciple o the uity o ormal logic ad ratioal dialectics is a methodological basis o the aalysis. The result is as ollows: the oudatios o classical thermodyamics (i.e., the irst ad secod laws, equatio o state, cocepts o iteral eergy, o heat eergy, o etropy, o temperature cotai logical errors. The existece o logical errors is irreutable proo o icorrectess o thermodyamics. The correct statistical oudatios are proposed. Keywords: classical thermodyamics, statistical thermodyamics, quatum theory PACS umbers: a INTRODUCTION As is kow, thermodyamics is a brach o physics which deals with the heat eergy ad work o a system. It is a udametal part o the physical sciece. The results o thermodyamics are essetial or other ields o physics ad or chemistry, chemical egieerig, cell biology, biomedical egieerig, ad materials sciece. The startig poit or most thermodyamic cosideratios are our laws o classical thermodyamics: about iteral eergy, heat eergy, etropy, ad temperature. These laws do ot deped o the details o the iteractios or the systems beig studied ad postulate that: (a eergy ca be exchaged betwee physical systems as heat ad work; (b there exist a quatity amed etropy. The mai cocepts iteral eergy, heat eergy, etropy, ad temperature are ot deied withi the ramework o thermodyamics. Thereore, classical thermodyamics a pheomeological theory should be scietiically grouded ad explaied by molecular-kietic theory ad statistical physics. Statistical iterpretatio o the secod ad third laws o thermodyamics is a object o statistical thermodyamics: the statistical iterpretatio is to derive all macroscopic properties rom the statistical properties o movig costituet particles ad the iteractios betwee them. The result o great eorts putted ito substatiatio o the oudatios o thermodyamics i 20th cetury ca be expressed by A. Eistei s words: Classical thermodyamics is the uique classical physical theory which will be ever reuted. However, this statemet was recetly reuted: it was show [1-9] or the irst time that the oudatios o classical thermodyamics ad statistical physics cotai logical errors. Cosequetly, there is the problem o truth i thermodyamics ad statistical physics. From the ormal-logical poit o view, thermodyamics ad statistical physics caot be compared with each other i there is o logical relatios (idetity, subordiatio, collateral subordiatio, partial coicidece, discrepacy betwee thermodyamic ad statistical cocepts. Thereore, substatiatio ad explaatio o thermodyamics meas establishmet o 1

2 logical relatios betwee thermodyamic ad quatum-statistical cocepts: Geeral relatioship betwee eergy ad temperature ca be uderstood oly with the help o probabilistic cosideratio. The problem o temperature coects very closely with quatum hypothesis (M. Plack. The correct base or compariso o the cocepts is Gibbs quatum caoical distributio, ad the priciple o the uity o ormal logic ad o ratioal dialectics represets the methodological basis o the aalysis. I coectio with [1-9], the critical aalysis o the geerally accepted oudatios o classical thermodyamics (i.e., the irst ad secod laws, equatio o state, cocepts o iteral eergy, heat eergy, etropy, temperature are proposed i this work. The purpose o the aalysis is to prove that the stadard oudatios cotai logical (mathematical errors ad to oer the correct ormulatios. 1. METHODOLOGICAL BASIS FOR THE THEORETICAL ANALYSIS Moder theoretical physics cosists o the set o theories but does ot cotai criterio o the truth o physical theories. I my opiio, lack o the criterio o the truth o theories i theoretical physics is explaied by the act that the system o physical (i.e. special scietiic cocepts ad laws is icomplete: it does ot iclude may uiversal (i.e. the geeral scietiic cocepts ad laws. The complete system the system o physical cocepts ad the laws supplemeted with the system o uiversal cocepts ad laws would represet ot oly basis o physics but also methodological basis or the deductive aalysis o physics. From this poit o view, the uiied criterio o the truth o physical theory should be ormulated as ollows: a physical (i.e. special scietiic theory must ot cotradict the system o the uiversal (i.e. geeral scietiic cocepts ad laws. The system o the uiversal cocepts ad laws represets a uity o ormal logic ad o ratioal dialectics. Ad this uity is a sciece o most geeral laws o developmet o the Nature, huma society, ad correct thikig. Cosequetly, this system is a methodological basis or a critical aalysis o physical theories. The mai dialectics priciple is the priciple o objectivity o huma kowledge. It is ormulated as ollows: objective laws ad truth must be ivariat uder choice o meas ad methods o cogitio, i.e. uder chage o properties o system o reerece (i particular, objective laws ad truth must ot cotai reereces to devices, procedure ad accuracy o measuremet or o calculatio. Thus, the priciple o the uity o ormal logic ad o retioal dialectics is the correct methodological basis or the proposed theoretical aalysis o thermodyamics. 2. CORRECT FORMULATION OF THE FIRST LAW OF THERMODYNAMICS As is kow, the geerally accepted irst law o thermodyamics reads as ollows: the chage i the iteral eergy o a closed thermodyamic system is equal to the sum o the amout o heat eergy supplied to the system ad the work doe o the system. The irst law is give by the dieretial expressio du = dq + where U, Q, W are iteral eergy, heat eergy, ad o-heat eergy o the system, respectively. But this expressio does ot take ito cosideratio the empirical act that there is mutual trasormatio o heat eergy ad the work i practice. Oe should take ito cosideratio this empirical act i the ollowig way. From mathematical poit o view, quatities U, Q, W are i the ollowig relatio: U is a uctio o two idepedet variables, Q, W. Thereore, the correct ormulatio o the irst law must be based o the cocepts o uctio ad dieretial o uctio. Really, i iteral eergy U o system is a uctio o two idepedet variables, Q = Q(t (describig o the heat orm o eergy ad W = W (t dw 2

3 (describig o-heat orm o eergy, the the correct ormulatio o the irst law o thermodyamics is du ( Q, W U = dt Q W dq U + dt W U U where t ad η are time ad measure o mutual trasormatio o orms o W Q Q W eergy, respectively. (For example, the eergy o the molecules which absorbs laser radiatio is a o-heat orm o eergy. Cosequetly, the geerally accepted ormulatio o the irst law o thermodyamics represets a logical (mathematical error because its cotet (i.e. special assertio is ot a law (i.e. geeral assertio. 3. CORRECT FORMULATION OF THE SECOND LAW OF THERMODYNAMICS As is kow, the geerally accepted secod law o thermodyamics reads as ollows: the total etropy o ay isolated thermodyamic system teds to icrease over time, approachig a maximum value. The secod law is give by the dieretial expressio ( thermodyamic dq( thermodyamic T ( thermodyamic Q dw dt ds =, 0 < T (thermodyamic < where Q ( thermodyamic, S ( thermodyamic, T ( thermodyamic are the thermodyamic heat eergy, the thermodyamic etropy, ad the thermodyamic temperature o the system. I order to research this expressio, oe should establish logical relatios betwee cocepts thermodyamic heat eergy, thermodyamic etropy, thermodyamic temperature ad cocepts statistical heat eergy, statistical etropy, statistical temperature. Correct solutio o this problem is based o Gibbs quatum caoical distributio which represets the correct ad complete quatumstatistical descriptio o isolated macroscopic system ideal gas o molecules (quatum particles i thermodyamic equilibrium. Gibbs quatum caoical distributio is cosequece o the ollowig set o priciples [10-12] ad premises: (1 The priciple o motio o quatum particle: the motio is the orm o existece o quatum particle; the motio represets uity o iteral ad exteral (i.e. traslatory motios. E, = 0, 1, 2, K (where (2 The priciple o eergy o quatum particle: the eergy is the eergetic quatum umber is ialieable property o a quatum particle. Eergy levels o the quatum particle arise ad disappear oly as a result o absorptio ad emissio o other quatum particles, respectively. (Cosequetly, the problem o quatizatio o eergy is ot the Shrödiger problem o eigevalues. (3 The priciple o equivalece o eergy E ad requecy eergy E is related to requecy hν by the ormula E hν hν o quatum particle: ν are the where h ad Plack costat (i.e. quatum o actio ad the requecy o the periodic process o mutual trasormatio o the iteral ad exteral motios, respectively. The cocepts o eergy E ad o requecy hν are idetical oes. Multiplicatio o the quatities h ad ν is permitted by logic law o idetity i h is a oscillatig quatity. 3

4 (4 The priciple o speed o traslatory motio o quatum particle: the speed v is deied by the ormula v λν where λ is the size (the diameter o the particle. The λ equals the distace traveled the particle or the oscillatio period τ 1ν. This traslatory motio is a result o cotractio ad extesio o the size (diameter o the particle. Thereore, the traslatory motio o the quatum particle relative to a reerece system is a absolute oe. The absolute motio is ivariat uder choice o a reerece system. This statemet meas that the velocity additio theorem or quatum particle is ot valid. (5 The priciple o mass ad mometum o quatum particle: the mass m ad the 2 2 mometum p are deied by the ormula E ( E v 2 v m v p v. The cocept o 2 mass m ad the cocept o eergy E are ot idetical oes. Thereore, the ormula E m v does ot express the priciple o equivalecy o mass ad eergy. (6 A molecule o isolated ideal gas is idividual quatum particle. The eergy o the molecule represets discrete radom quatity sice molecules collide with each other i a radom way. (7 The radom quatity takes o the values E, = 0, 1, 2, K where E 0 = 0 is origi o coutig o the radom quatity; (8 is probability that molecule is i eergetic quatum state ad has eergy E. The probabilities give complete quatum-statistical descriptio o the ideal gas o molecules. (9 Rule o additio o probabilities has the ollowig orm: = 0 = 1 where 0 < < 1, lim ( 1 < 1. (10 Rule o combiatio (multiplicatio o probabilities or idepedet radom evets has the ollowig orm: + =, m m where E + E, m is combied probability that two molecules have eergy m the expoetial uctio (A. Cauchy, 1821:. I this case, is = exp( β E 0 where 1 β is a statistical parameter o molecule. The parameter 1 β is itroduced or mathematical reasos: quatity β E must be dimesioless oe. This parameter is cosequece o existece o eergy spectrum o quatum particle (atom, molecule ad does ot deped o structure o eergy spectrum. I the parameter was depedet o it would represet value o some (ideiable radom quatity. 4

5 (11 The parameter 1 β = E l ( 0 or (i other orm 1 β = ( E + E l ( represets physical-statistical property o molecules o gas ad has both mathematical ad physical meaig. From mathematical poit o view, 1 β is a cotiuous ad limited variable. From physical poit o view, 1 β is the physical quatity which has eergy dimesio. Zero is origi o coutig o this physical-statistical quatity ad is the same or molecule o ay kid. Rage o existece o this parameter is deied by the relatioship 0 < 1 β < E. Quatum-statistical descriptio o ideal gas o molecules loses statistical meaig outside this rage: (a i 1 β = 0, the the eergy o the molecule is ot a radom quatity; (b i 1 β = E, the the set is diverged. = 0 (12 The parameter 1 β has the same value or ay (every molecule o the system. Cosequetly, 1 β is the uiversal statistical parameter (i.e. statistical potetial o the system. This parameter has essetial property o temperature. As is empirically kow, this property is that temperature has the same value or every part (subsystem o system i the system is i a state o heat equilibrium. Thereore, the idetity 1 β T (statistical is the cojecture, the postulate. Owig to this postulate, the uctio is called Gibbs caoical distributio, ad the temperature T is called absolute temperature. The absolute temperature is temperature i the sese o the cocept Gibbs quatum caoical distributio. The absolute temperature does ot deped o the existece o a thermometer (device. It ollows rom above that = exp ( E 0 T (statistical is Gibbs quatum caoical distributio. It has objective meaig because E ad T are idepedet o existece o a thermometer. Gibbs quatum caoical distributio deies the correct relatioship betwee the statistical-average (microscopic eergy E o molecule, the statistical-average (microscopic etropy s o molecule, ad the statistical temperature T o molecule. This relatioship has the orm: E = st (statistical, 0 < s < 1, lim s = 0 T 0 ( statistical 5

6 where E = 0 E, s s, s E T( statistical = l( 0. = 0 Obviously, the heat eergy E is a oliear uctio o the T because etropy s depeds o the T. I the case o biary gaseous mixture, it ollows rom the coditio T = o thermal equilibrium that, geerally speakig, ' ( statistical T(statistical ' E E where E ad the statistical-average eergies o molecules o compoets. The correct relatioship betwee microscopic ad macroscopic quatities has the orm: Q ( macroscohic = S T(statistical, Q( macroscopi c = N E, S = N s, ' E are where N (macroscopic is total (macroscopic umber o molecules i the system. The ollowig statemet ollows rom this relatioship. I: (a the relatioship Q = S ( macroscohic T(statistical is correct; (b the idetities Q( thermodyamic Q, ( thermodyamic S S, T( thermodyamic T(statistical is valid (i.e. thermodyamics cocepts thermodyamic heat eergy, thermodyamic etropy, ad thermodyamic temperature are idetical with the cocepts macroscopic heat eergy, macroscopic etropy, ad statistical temperature, respectively, the the geerally accepted ormulatio o the secod law o thermodyamics is icorrect. Sice the rages 0 T <, 0 < < E < (thermodyamic T o existece o T (thermodyamic ad T dier i degree, there exist partial coicidece betwee cocepts thermodyamic temperature ad statistical temperature. Thus, the geerally accepted secod law o thermodyamics represets a logical (mathematical error. 4. CORRECT FORMULATION OF THE EQUATION OF STATE As is kow, i movemet o molecules (quatum particles is cause o gas pressure, the average pressure p o molecules o gas is deied by the uique relatioship p = µ (macroscopic E where µ ad E are average umber o molecules i uit volume ad average eergy o oe molecule, respectively. This relatioship represets the correct equatio o state o gas. I the case o heat movemet o molecules, average eergy E o oe molecule is E. Puttig 6

7 E = p / µ ito the let part o the relatioship Q =, ( macroscohic S T(statistical oe ca express equatio o state i the heat orm: p V Q =, i.e. T(statistical = p V, S where macroscopic V N ( / µ, V N µ are volume o molecular gas ad total umber o molecules i gas, respectively. I E 1 = E ad E 1 T << 1, the value o etropy at the high-temperature limit is approximately equal to (statistical oe, s 1, ad heat equatio o state takes the ollowig liear orm: p V N T. (statistical Distictio betwee this orm ad stadard thermodyamic equatio o state, p V = N T, ( thermodyamic is ot oly distictio i degree, but also distictio i kid. I order to explai qualitative ad quatitative determiacy o the T (thermodyamic, oe should cosider the gas system i developmet. As is kow, the ratioal dialectics priciple reads as ollows: oe should cosider the system i developmet. I accordace with this priciple, oe should cosider the ollowig developmet o the gas system absorbig eergy without limitatio: (gas o molecules (gas o atoms (gas o elemetary particles. The system gas o elemetary particles does ot obey Gibbs quatum caoical distributio. Cosequetly, the elemetary particles (photos, electros etc. have o statistical temperature, ad the system is ot i heat equilibrium. Moreover, the system have o thermodyamic temperature because there is o the heat orm o eergy i this system. There exist the cocept o average eergy o elemetary particle oly: E ( photo, E ( electro etc.. I oe measures the average eergy with the help thermometer, the thermometer will read the temperature: T ( photos, T ( electros etc.. Temperature (i.e., physical property o the thermometer, the device, cotactig the gas exists oly as measure o the thermometer, i.e. as the uity o qualitative ad quatitative determiacy o the thermometer, as the ordered set o the thermometer states (thermometer 7

8 readigs. The cocept o temperatures T ( photos, T ( electros is the covetioal cocept coectig with the existece o the cocept o thermometer (device. From ormal-logical poit o view, it meas that the cocept o thermodyamic temperature coects iseparably with the cocept o thermometer: the cocept thermodyamic temperature exists as cosequece o the cocept thermometer. Cosequetly, cocepts thermodyamic temperature ad statistical temperature are ot idetical oes, ad the cocept thermodyamic temperature has o objective meaig. Thus, the expressio Q = p (macroscopic V is the uique correct ormulatio o the equatio o statistical state. The geerally accepted ormulatio o equatio o thermodyamic state represets a logical (mathematical error because, irstly, T (thermodyamic has o qualitative determiacy at T ad, secodly, the cocept o thermodyamic (thermodyamic temperature is logically erroeous ad o-objective oe. 5. DISCUSSION As is kow, ormal logic is a sciece o the laws o correct thikig. Oe o its mai priciples is that deiitio o scietiic cocept must be exact ad complete. However, classical thermodyamics does ot satisy this priciple: withi the ramework o classical thermodyamics a pheomeological theory, oe caot give exact ad complete deiitio o the thermodyamic cocepts (i.e. cocepts o iteral eergy, o heat eergy, o etropy, o temperature. I order to deie thermodyamic cocepts oe should iclude the cocepts o thermodyamic istrumets (thermometer, calorimeter etc. ad o measuremet i the theory. Theory icludig cocepts o istrumet (device ad o measuremet is o-objective, ad a pheomeological theory excludig these cocepts has o scietiic meaig. This is the qualitative determiacy o ay pheomeological theory. Thereore, the pheomeological, oobjective theory (classical thermodyamics must be scietiically grouded ad iterpreted by the objective theory (statistical physics which has the same object o scietiic research. However, a part o results o the pheomeological theory loses scietiic meaig at the groudig ad iterpretig. CONCLUSION Thus, the correct theoretical aalysis shows that classical thermodyamics a pheomeological theory is ot a objective theory. Its oudatios (i.e., the irst ad secod laws, equatio o state, cocepts o iteral eergy, o heat eergy, o etropy, o temperature cotai logical (mathematical errors. The existece o logical errors is irreutable proo o icorrectess o classical thermodyamics. These errors are explaied by the global cause: the errors are a collateral ad ievitable result o iductive method o kowledge o the Nature, i.e. result o movemet rom ormatio o separate cocepts to ormatio o system o cocepts. The iductive way o developmet i physics is characterized, or example, by A. Eistei s words: (a there has bee ormed a view that the oudatios o physics were ially established ad the work o a theoretical physicist should be to brig a theory i correspodece with all the time icreasig abudace o the ivestigated pheomea. Nobody thought that a eed or radical rebuildig o the basis o all physics could arise; (b but the progress o sciece will cause revolutio i its oudatios. Our otios o physical reality ever ca be ial oes. We should be always ready to chage axiomatic basis o physics to substatiate acts o perceptio i logically most perect orm. It ollows rom these words that the progress i (iductive sciece is the uderliig o diiculties (N. Bohr. Ad o-objective, icorrect theories should be replaced by objective, correct theories. 8

9 ACKNOWLEDGMENT The books Surprises i Theoretical Physics (1979 ad More Surprises i Theoretical Physics (1991 by Sir Rudol Peierls stimulated my work. REFERENCES [1] T.Z. Kalaov, "Correct quatum-statistical descriptio o ideal systems withi the ramework o master equatio". Proc. XXVth ICPIG, Nagoya, Japa---Ed. By Toshio Goto / Japa: Nagoya Uiv., 2001, Vol. 3, p [2] T.Z. Kalaov, "O a solutio o the problem o uitarizatio o the elemetary priciples o statistical physics ad physical kietics", Bull. Am. Phys. Soc., Vol. 47, No. 2 (2002, pp [3] T.Z. Kalaov, "O the mai errors uderlyig statistical physics", Bull. Am. Phys. Soc., Vol. 47, No. 2 (2002, p [4] T.Z. Kalaov, "O the correct ormulatio o the irst law o thermodyamics", Bull. Am. Phys. Soc., Vol. 51, No. 2 (2006, p. 60. [5] T.Z. Kalaov, "The secod law o thermodyamics: Mathematical error", Bull. Am. Phys. Soc., Vol. 51, No. 2 (2006, p. 60. [6] T.Z. Kalaov, "Bose's method: A logical error", Bull. Am. Phys. Soc., Vol. 51, No. 2 (2006, p. 61. [7] T.Z. Kalaov, "Dirac's theory o physical vacuum: Cotiuatio o Bose's logical errors", Bull. Am. Phys. Soc., Vol. 51, No. 2 (2006, p. 61. [8] T.Z. Kalaov, "Bose-Eistei statistics ad Fermi-Dirac statistics: A logical error", Bull. Am. Phys. Soc., Vol. 51, No. 2 (2006, p. 61. [9] T.Z. Kalaov, "O the correct aalysis o Maxwell distributio", Bull. Am. Phys. Soc., Vol. 51, No. 2 (2006, p [10] T.Z. Kalaov, "O a ew basis o quatum theory", Bull. Am. Phys. Soc., V. 47, No. 2 (2002, p [11] T.Z. Kalaov, "The correct theoretical aalysis o the oudatios o quatum mechaics", Joural o Ultra Scietists o Physical Scieces (Idia, V. 16, No. 2 (2004, pp ( [12] T.Z. Kalaov, "O the correct theoretical aalysis o the oudatios o quatum mechaics", Bull. Am. Phys. Soc., V. 50, No. 2 (