Boşluktan Taneciklere Yolculuk
Transkript
Boşluktan Taneciklere Yolculuk
Boşluktan Taneciklere Yolculuk Veysi Erkcan Özcan 22 Haziran 2015 Hedef Madde ve boşluğun, uzay ve zamanın antik felsefecilerden 21. yüzyıla uzanan tarihçesi. Maddenin kütlesinin evreni saran alanlarla ilişkisi. Kuantum fiziği ve özel göreliliğe giriş. Böylesi soruların yanıtlanmasında çağımızda kullanılan yöntemlerin tanıtılması, örneğin CERN’deki Büyük Hadron Çarpıştırıcısı ve benzeri hızlandırıcıların teknolojisi. Higgs bozonu ve diğer temel parçacıklar için çıkılan define avı. 2 Nasıl Öğrenmeli? Okuma tavsiyesi: “Two Approaches to Learning Physics”, David Hammer, Physics Teacher, Aralık 1989. 5 sayfa, 10 dakikalık bir okuma (maalesef İngilizce). “I look at all those formulas...” “I am trying to imagine…” Elinizi kirletmeden olmaz! 3 Particle Phys. Nuclear Phys. Cosmology Astronomy Condensed Matter P. Geophysics Chemistry-Biology Mechanics Astrophysics Zm Fizik = Doğayı Anlama Ym Insan gozu en ufak neyi gorebilir? Baska yer belirtecleri olmadan hangi uzakliklari tahmin edebilir? 10^-4’den 10^4 metreye. Legolas’in gozleri. Bizim gozumuz arastirdigimiz olcegin cok azini aliyor. Diger tum duyularimiz da. O zaman arastirdigimizda ortaya cikanlar bize tuhaf gelebilir. Ama ne kadar ilginctir ki, insan dillerinin ifade etmekte yetersiz kalabildigi kavramlari cozumleyecek ve tum bu skaladaki olgulari anlatabilecek matematik diye bir dil icat edebiliyoruz. Insan beyninin bu cesit bir becerisi olmasi ilginc degil mi? => Wigner. 17 denklem: 7-8’i calculus uzerine. Bunu ogrenmeden olmaz. Guzel denklem ne demek? (1) Zor olmali, zanaat. (2) Sade, estetik olmali. Euler özdeşliği, 5 ana sabiti birbirine bagliyor. e sayisi nedir? bilesik faizi tartisalim. 12 ay yuzde 10 mu daha iyi, yoksa iki kere 6 ay yuzde 5 mi? 1.05’in karesi mi buyuktur, 1.10 mu? Iki tarafi da 100x100 ile carpalim. 105x105 mi buyuktur, yoksa 110x100 mu? Elimizde belli uzunlukta cit olsun, o citlerle tarlamizi belirleyeceksek, hangi cesit dikdortgen en cok alani verir? Cevabin kare cikmasi neden? Seklin “ozel” olmasi bize ne verir? a*(210-a) nerede max olur? Parabol cizebiliriz. (1+x)^2 = 1+2x+x^2 Sonsuz kisa vadede sonsuz bilesik faiz yaparsak ne kadar kazaniriz? e^0.10 = 1.10517 (Limit ve convergence’a geri gelmek olabilir?) 5 graph buyemYazFizik { node [style="setlinewidth(0)"]; sr [label="ozelGörelilik"]; gr [label="genelGorelilik"]; gravity [label=yercekimi]; higgs; mass [label="kütle"]; field [label=alan]; sb [label="simetriKirilmasi"]; qft [label="kuantumAlani"]; light [label=isik]; wave [label=dalga]; EM [label="elektromanyetizmaMaxwell"]; mechanics [label=mekanik]; optics [label=optik]; diffraction [label=kirinim]; MM [label=MichelsonMorley]; fma [label="F=ma"]; inertia [label=eylemsizlik]; higgs -- mass; qft -- field; higgs -- sb; higgs -- qft; Einstein -- sr; gravity -- mass; field -- Faraday; Faraday -- EM; EM -- light; light -- optics; light -- wave; EM -- wave; wave -- mechanics; wave -- diffraction; optics -- MM; diffraction -- MM; mass -- inertia; inertia -- Galileo; Galileo -- Kepler; Kepler -- Newton; Newton -- mechanics; Kepler -- epicycle; fma -- inertia; Newton -- gravity; gravity -- gr; gr -- sr; Newton -- fma; Einstein -- light; } 6 Dünyayı değiştiren 17 denklem 7 Dünyayı değiştiren 17 denklem ⑇ ✓ ✓⑇ ⑇ ✓ ✓ ✓ ✓ 101 102 201 202 7 Nasıl? “Kuramınızın ne kadar da güzel olduğu, sizin ne kadar da zeki olduğunuz falan farketmez. Eğer deney ile uyuşmuyorsa, yanlıştır.” - Richard Feynman (1965 Nobel F.) “Matematiğin fen bilimlerindeki inanılmaz verimi/başarısı” - Eugene Wigner (1963 Nobel F.) “…, denklemlerinizin güzellik barındırması, onların deneye uyumlu olmasından daha önemlidir…” - Paul Dirac (1933 Nobel F.) Ölçüm (gözlem, deney) + matematik model (kuram). 8 Gerçek Güzellik! Bunun için biraz sabır gerekiyor. 9 Pisagor Fayans Kaplama 10 Pisagor Fayans Kaplama 10 1845 Mechanical Equivalent of Heat Mechanical equivalent of heat 11 Von Mayer independently got the same result. Phase Diagram • • • • Tube data: height = 580mm, diameter = 105mm, m(CO2) = 2kg Volume = πr2h = 5.0 L n = 2kg / (12+16+16 g/mol) = 45 mol If C02 were only in gas form, the pressure in the can at room temperature would be: • P = nRT/V = 22.1 MPa = 218 atm • From the phase diagram, we see that at that pressure & room temperature, it is not possible to have C02 only in gas form. • Actually, the vapor pressure at 25°C is about 63atm. 12 Consider a CO2 filled fire-extinguisher tube. CO2 is mostly in liquid form initially. When it is activated with the opening of the tube, it starts boiling and maintains an essentially constant gas pressure significantly above 1atm. This goes on until almost all of the liquid CO2 turns into gas. Joseph Black Discovers and names “latent heat” Talks about “heat capacity” and points out that different substances have different “specific heat”s. Also: One of the “discovers” of carbon dioxide. 13 1750s (≤1762) Mpemba Effect In 2013, Royal Society of Chemistry held a competition. Nikola Bregović’s explanation: 1969 Phys. Educ. 4 172 Convection and supercooling were the reasons of the effect. 14 Heat Capacity Ratio molar specific heat under constant pressure molar specific heat when volume is kept constant For monoatomic ideal gases it is about: 1+2/3 = 5/3 For diatomic ideal gases around room temperature it is about: 1+2/5 = 7/5 f = number of degrees of freedom (ie. number of parameters to characterise the status of a given molecule) 15 Monatomic Gas In a Box px = N = number of molecules 2mvx 2mvx px / t = = 2L/vx < fx >= mvx2 /L P = Fonwall /L2 = N m < vx2 > /L3 < vx2 >=< vy2 >=< vz2 >=< v 2 > /3 P L3 = N < mv 2 > /3 PV = PV = 16 2 1 N < mv 2 > 3 2 2 N < KE >= N kB T 3 Monatomic Gas In a Box px = N = number of molecules 2mvx 2mvx px / t = = 2L/vx < fx >= mvx2 /L P = Fonwall /L2 = N m < vx2 > /L3 < vx2 >=< vy2 >=< vz2 >=< v 2 > /3 P L3 = N < mv 2 > /3 PV = PV = CV dT = dQ CV = d(NA < KE >)/dT = < KE >= 3 R 2 16 2 1 N < mv 2 > 3 2 2 N < KE >= N kB T 3 3 kB T 2 Temperature is really the name of the average kinetic energy of the molecules! Equipartition Theorem In 3D, we found the average kinetic energy of a monatomic 2 2 2 molecule as 3kBT/2. The factor 3 came from vx , vy and vz . If we were in a 2D universe, we would find the average kinetic energy as 2kBT/2, so the cV would be R. For a diatomic gas in 3D space, energy of the gas molecules would not just be the tranlational KE. It would also be rotational (2 degrees of freedom) and vibrational (2 additional degrees of freedom). So cV becomes (3+2+2)R/2 = 7R/2. γ=9/7 17 Equipartition = equal division of energy amongst different degrees of freedom Heat Engine / Heat Pump First law of thermodynamics, ie. conservation of energy: QH=W+QC efficiency of heat engine: ε=W/QH coefficient of performance of a heat pump: COP=Qrequired/W Heater: COP=QH/W (mathematically equal to 1/ε) Refrigator or air-conditioner: COP=QC/W 18 A Simple “Hypothetical” Engine (c) Calculate the efficiency of the engine. 19 Efficiency of Human “Engine” Report from the “Physics at the British Association”, published in Nature, September 29, 1898! “…the law of conservation of energy is found to be true…” “ratio of mechanical work by a man to the total energy supplied to him, …, is usually about 7%, and may be as high as 10%…” “higher than perfect heatengine” For more information (like the energy content of feces, the calories of food stuffs, and how the apparatus works), see “The Elements of the Science of Nutrition”. 20 Atwater-Rosa Respiration Calorimeter “The apparatus represented technical perfection, as was evidenced by the fact that when a measured amount of heat was generated by an electric current within the box it was determined as 100.01 per cent, of the actual value. This test of accuracy is called an electric check. Also, when a known quantity of alcohol was oxidized, the carbon dioxid recovered amounted to 99.8 per cent, and the heat to 99.9 per cent, of the theoretic value.” - From The Elements of the Science of Nutrition, 3rd edition (1917), by Graham Lusk. Read more: https://archive.org/stream/ elementsscience02luskgoog#page/n63/mode/2up Figure from: http://chestofbooks.com/health/ nutrition/Science/Principle-Of-The-AtwaterRosa-Benedict-Respiration-Calorimeters.html 21 Carnot 1824 Carnot’s theorem: for heat engines between two heat reservoirs, the efficiency: ε ≤ 1 − TC/TH. Max eff. when reversible engine <=> Carnot cycle. 22 Carnot Cycle PV=constant reversible adiabatic PVγ=constant PVγ=constant reversible adiabatic PV=constant This is an idealised cycle, it would take infinite time to complete. 23 Clausius 1850-1865 Common form of 2nd law of thermodynamics: “Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.” Definition of “change in entropy” as a thermodynamic quantity. ΔS over a full reversible cycle is zero. 24 Reversible Engine Consider a reversible heat engine (ex. Carnot cycle) Note: Idealization, no real heat engine is completely reversible. We can run it backwards as a heat pump. If two copies are running together in “opposite directions”, zero net flow of energy. Imagine a hypothetical heat engine with higher efficiency connected to our reversible engine. ε=W/Qh > εr=W/QhC QhC > Qh Given the conservation of energy, this means we are extracting energy from the cold reservoir and heating up the hot reservoir. ==> Not allowed! ==> No engine can have higher efficiency than Carnot’s. 25