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What is temperature? Peter Hänggi Universität Augsburg In collaboration with Dr. Gerhard Schmid Temperature sensation • Subjective temperature sensation • Memory effects • Measuring the heat flow • Heat – substance ↔ CldCold – substance What is temperature? Early temperature measurements No scale for measuring temperature between some reference points a thermoscope 1592: first documented (gas‐) thermometer invented by Galileo Galilei Galileo Galilei (1564 – 1642) First thermometer & temperature scales 1638: Robert Fludd – air thermometer &scale ~1700: linseed oil thermometer by Newton 1701: red wine as temperature indicator by Rømer 1702: Guillaume Amontons: Absolute zero temperature? 1714: mercury and alcohol thermometer by Fahrenheit DfiitiDefinition of tttemperature scales Olaf Christensen René Antoine Sir Isaac Newton Daniel Gabriel AdAnders CliCelsius Römer Ferchault de (1643 – 1727) Fahrenheit (1701 – 1744) (1644 – 1710) (1686 – 1736) Réaumur (1683 – 1757) Absolute Zero Ideal gas law: p V = NkB T V V =0,T=0 1848: Kelvin postulates an absolute zero temperature William Thomson ― Lord Kelvin T (1824 – 1907) 273.15 ◦C − It is impossible by any procedure to reduce the temperature of a system to zero in a finite number of operations. Absolute temperature scale Kelvin –scale (SI) Reference: absolute zero temperature & triple point of water (273.16K; 611.73 Pa) Scale division: 1K is equal to the fraction (273.16)‐1 of the thermodynamic temperature of the triple point of water ∆T =1K 1˚C (degree Celsius) ≡ How to determine the absolute thdhermodynamic temperature t dv T dt dt log = p dt T0 t0 ¡ ¢ Z v + cp0 dp ³ ´ t : arbitrary temperature scale v :volume cp0 : specific heat at constant pressure “ ... wo nun wieder unter dem Integralzeichen lauter direkt und verhältnismäßig bequem meßbare Größen stehen. ...” M. Planck Low temperature milestones Heike Kamerlingh 1908: liquid helium; 5 K Onnes (1853 – 1926) 1995: Bose‐Einstein‐ Condensate; 20 nK Eric A. Cornell Wolfgang Ketterle Carl E. Wieman 2003: BEC; 450 pK – W. Ketterle Temperature Extrema p + n ‐> quark gluon plasma with gold ion collisions in Relativistic Heavy Ion Collider (RHIC) 4 x 1012 °C Planck units Constant Symbol Value in SI units Speed of light c 299 792 458 m s‐1 Gravitational constant G 6.67429 ∙ 10‐11 m3 kg‐1 s‐2 reduced Planck’s constant¯h 1.054571628 ∙10‐34 J s 1 3 ‐2 ‐2 Coulomb force constant (4π²0)− 8 987 551 787.368 kg m s C ‐23 ‐1 BltBoltzmann constttant kB 1. 3806504∙10 J K Name Expression SI equivalents 5 1 2 32 Planck temperature TP = √¯hc G− k− 1.41168∙ 10 K Planck length3 1.61625∙ 10‐35 m lP = √¯hGc− 1 ‐8 Planck massmP = √¯hcG− 2.17644∙ 10 kg 5 ‐44 Planck timetP = √¯hGc− 5.39124∙ 10 s Planck units Name Expression SI equivalents 5 1 2 32 Planck temperature TP = √¯hc G− k− 1.41168∙ 10 K Planck length3 1.61625∙ 10‐35 m lP = √¯hGc− 1 ‐8 Planck massmP = √¯hcG− 2.17644∙ 10 kg 5 ‐44 Planck time tP = √¯hGc− 5. 39124∙ 10 s … ihre Bedeutung für alle Zeiten und für alle, auch außerirdische und außermenschliche Kulturen notwendig behalten unnd welche daher als natürliche Maßeinheiten bezeichnet werden können … … These necessarily retain their meaning for all times and for all civilizations, even extraterrestrial and non‐human ones, and can thhferefore be ddiesignated as natural units … (Planck, 1899) The highest temperature you can see Lightning: 30 000 °C Fuse soil or sand into glas Thermometers Gas Thermometers Idea l gas: V T = p Nk µ B ¶ Galilei Thermometer Volume change of water Upon increasing T → 4°C Water volume shrinks Linneaus thermometer Carl von Linné (1707 – 1778) RdthClilReversed the Celsius scale 1744: broken on delivery 1745: botanical garden in Uppsala Anders Celsius Noise Thermometer Johnson – Nyquist noise r oo V PSDV (ω)=2kBT R Resist -- classical regime only -- hmic OO PSDV : power spectral density of the voltage signal kB : Boltzmann constant R : resistance Quantum fluctuation‐dissipation theorem ¯hω PSD (ω) =¯hω coth ReY (ω) I 2k T µ B ¶ ¯hω ¯hω = 2 + ReY (ω) 2 exp(β¯hω) 1 µ − ¶ k T ¯hω B kBT ¯hω À ¿ P SDI (ω) = 2kBT ReY (ω) P SDI (ω) = ¯hω ReY (ω) Black body radiation 8πhc 1 Planck’ s law [1901]: u(λ, T ) = λ5 exp( hc ) 1 λ kBT − u(λ,T) : spectral energy density λ : wavelength h : Planck constant c : speed of light kB : Boltzmann constant Stefan – Boltzmann law: E T 4 ∝ Thermometer ! Small system – single realizations 1-st.1‐st law: law: ∆Eω = Qω + Wω ! random quantities ¡ 4 4 ... ∆U = Q + W h i ⇒ 4 4 Note: Q = ∆U W ∆U =? & W =? 4 − 4 4 weak coupling: Q = Qbath 4 − 4 REV Q 2‐nd law: ∆SA B 4 → ≥ T IRREV REV Q ∆SA B = 4 + ( 0) → T ≥ ∆U XW IRREV = − 4 + T Q IRREVX = − 4 bath + ; for weak coupling T X Cosmic background temperature T = 2.725 ±…. K Four Grand Laws of Thermodynamics Zeroth Law Transitivity ! A in equilibrium with B: fAB(pA, VA; pB, VB, ...) = 0 B in equilibrium with C: fBC(pB,VB; pC,VC,...)=0 A in equilibrium with C f (p , V ; p , V ,...) = 0 ⇒ ⇔ AC A A C C Allows the formal introduction of a temperature: T = TA(pA,VA; ...)=TB(pB,VB; ...)=TC(pC,VC; ...) First Law Julius Robert James Prescott Hermann von von Mayer Joule Helmholtz (1814 – 1878) (1818 – 1889) (1821 – 1894) Firs t Law – Energy CtiConservation ∆U = Q + W ∆U change in internal energy Q heat added on the system 4 W work done on thesystem 4 H. von Helmholtz: “Über die Erhaltung der Kraft” (1847) ∆U = (T ∆S)quasi-static (p∆V )quasi-static − Second Law Rudlfdolf Julius Emanuel Clilausius William Thomson alias Lord Kelvin (1822 – 1888) (1824 – 1907) Heat generally cannot No cyclic process exists whose sole spontaneously flow from a effect is to extract heat from a material at lower temperature to single heat bath at temperature T a materilial at hig her temperature. and convert it entilirely to work. δQ = T dS (Z¨urich, 1865) Theeodyarmodynamic Teepeauemperature δQrev = TdS thermodynamic entropy ← S = S(E,V,N1,N2, ...; M,P,...) S(E,...): (continuous) & differentiableand monotonic function of the internal energy E ∂S 1 = ∂E T µ ¶... Entropy S – content of transformation „Vdlt“Verwandlungswert“ d S = δQrev T ; δQirrev < δQrev V2,T2 δQ Γrev Γirrev 0 C T ≤ I 1 C = Γrev− + Γirrev V1,T1 δQ S(V ,T ) S(V ,T ) 2 2 − 1 1 ≥ T ∂S ZΓirrev δQ 0 NO ! S(V ,T ) S(V ,T )= 2 2 − 1 1 T ∂t ≥ ZΓrev Perpetuum mobile of the second kind ? One heat reservoir Two heat reservoirs NO ! Third Law Approaching zero temperature Famous exception of the 3rd law … and Planck’s version THIRD LAW AND PLANCK 1913 Beim Nullpunkt der absoluten Temperatur besitzt die Entropie eines jeden chemisch homogenen festen oder flüssigen Körpers den Wert Null. ∂E ¯hω ¯hω Specific heat: CE = , E = 0 + 0 ∂T 2 exp (¯hω0β) 1 − Quantum harmonic Oscillator: the limit ω 0 does NOT yield the specificheatCE = k /2 0 → B of the free particle 1 NiilthNo virial theorem ! E = k T No equipartition th.! 6 2 B Specific Heat E = E exp( βE ) exp( βE ) i − i − i i i X ± X E dE 2 1 2 C = =(k T )− (E E ) > 0 ! dT B h i − h ii i ∂S ∂2S 1 Note also: =1/T , = - ∂E ∂E2 CET 2 S CE<0 CE>0 E Temperature Fluctuations – An Oxymoron Ch. Kittel, Physics Today, May 1988, p. 93 1 Nano‐system β = BATH kBT T does NOT fluctuate! ∆U ∆β =1 ∆U ∆T = k T 2 NO! | || | ↔ | || | B “…Tempppyyyerature is precisely defined only for a system in thermal equilibrium with a heat bath: The temperature of a system A, however small, is defined as equal to the temperature of a very large heat reservoir B with which the system is in equilibrium and in thermal contact. Thermal contact means that A and B can exchange energy, although insulated from the outer World. …” Molecular Dynamics • Every quadratic term in the Hamiltonian 1 contributes kB T to the internal energy 2 • Classical systems: VIRIAL THEOREM n n [Hi q or p Ei = kBT/n] ∝ i i ⇒ h i • Classical harmonic Oscillator p2 1 1 h i i = m v2 = k T 2m 2 h i i 2 B 1 1 mω2 x2 = k T 2 h i i 2 B NOT SO FOR A QUANTUM OSCILLATOR Specific heat paradox (microcanonical) R. Em den (1907); A. S. Edding ton (1926); D. Lynden-Bell & R. Wood (1968); W. Thirring (1970); W. Thirring, H. Narnhofer & H. A. Posch (2003) Coulomb: Φi = kBT CLASSICAL ! h i − 1 Tkin = Φtot =3NkBT/2 −2h i 2Tkin + Φtot =0=E + Tkin h i dE dT CE = = kin = 3Nk /2 < 0 dT − dT − B Relativistic Regime Σ(u = 0) Σ0(u = 0) −→ 6 x0 = γ(u) (x u t) − · 2 t0 = γ(u) t ux/c − 1/2 ¡ u2 −¢ with γ(u)= 1 − c2 µ ¶ 2 2 2 2 2 2 x c t = (x0) c (t0) − − Note: thermodynamic observables are NONLOCAL J. Dunkel & P.H., Relativistic Brownian motion, Phys. Rep. 471, 1 - 73 (2009) Maxwell‐Boltzmann distribution velocity distribution: m 3/2 v2 + v2 + v2 f (v ,v ,v )= exp x y z ~v x y z 2π k T − 2 k T/m µ B ¶ à B ! 25 °C James Clerk Maxwell Ludwig Eduard Boltzmann (1831 – 1879) (1844 – 1906) ! v < c violated ! Diffus ion classical relativistic Author's personal copy Author's personal copy J. Dunkel, P. Hänggi / Physics Reports 471 (2009) 1–73 5 J. Dunkel, P. Hänggi / Physics Reports 471 (2009) 1–73 45 that point on, nonrelativistic statistical mechanics emerges without much difficulty [287,288].
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  • The Links of Chain of Development of Physics from Past to the Present in a Chronological Order Starting from Thales of Miletus

    The Links of Chain of Development of Physics from Past to the Present in a Chronological Order Starting from Thales of Miletus

    ISSN (Online) 2393-8021 IARJSET ISSN (Print) 2394-1588 International Advanced Research Journal in Science, Engineering and Technology Vol. 5, Issue 10, October 2018 The Links of Chain of Development of Physics from Past to the Present in a Chronological Order Starting from Thales of Miletus Dr.(Prof.) V.C.A NAIR* Educational Physicist, Research Guide for Physics at Shri J.J.T. University, Rajasthan-333001, India. *[email protected] Abstract: The Research Paper consists mainly of the birth dates of scientists and philosophers Before Christ (BC) and After Death (AD) starting from Thales of Miletus with a brief description of their work and contribution to the development of Physics. The author has taken up some 400 odd scientists and put them in a chronological order. Nobel laureates are considered separately in the same paper. Along with the names of researchers are included few of the scientific events of importance. The entire chain forms a cascade and a ready reference for the reader. The graph at the end shows the recession in the earlier centuries and its transition to renaissance after the 12th century to the present. Keywords: As the contents of the paper mainly consists of names of scientists, the key words are many and hence the same is not given I. INTRODUCTION As the material for the topic is not readily available, it is taken from various sources and the collection and compiling is a Herculean task running into some 20 pages. It is given in 3 parts, Part I, Part II and Part III. In Part I the years are given in Chronological order as per the year of birth of the scientist and accordingly the serial number.