Thornton & Rex, 4th ed. Fall 2018 Prof. Sergio B. Mendes 1

Transcription

1 Modern Physics for Scientists and Engineers Thornton & Rex, 4th ed. Fall 2018 Prof. Sergio B. Mendes 1

2 CHAPTER 1 The Birth of Modern Physics Fall 2018 Prof. Sergio B. Mendes 2

3 Topics 1) Classical Physics of the 1890s 2) Kinetic Theory of Gases 3) Atomistic Theory of Matter 4) Mechanical Waves 5) A Few Dark Clouds Fall 2018 Prof. Sergio B. Mendes 3

4 1) Classical Physics of the 1890s Mechanics Electromagnetism Thermodynamics The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote Our future discoveries must be looked for in the sixth place of decimals. - Albert A. Michelson, 1894 Fall 2018 Prof. Sergio B. Mendes 4

5 Mechanics Fall 2018 Prof. Sergio B. Mendes 5

6 Contributions from: Galileo Galilei Kepler Isaac Newton Euler Lagrange Hamilton Fall 2018 Prof. Sergio B. Mendes 6

7 Newton s Laws Newton s First Law: FF = 0 aa = 0 aa aa Newton s Second Law: FF = mm aa Newton s Third Law: FF AA BB = FF BB AA Summer 2018 Prof. Sergio B. Mendes 7

8 Electricity and Magnetism = Electromagnetism Fall 2018 Prof. Sergio B. Mendes 8

9 Contributions from: Coulomb ( ) Oersted ( ) Young ( ) Ampère ( ) Faraday ( ) Henry ( ) Maxwell ( ) Hertz ( ) Fall 2018 Prof. Sergio B. Mendes 9

10 Maxwell s Equations and Lorentz Law Gauss s law (Φ E ): (electric field) SS EE rr. ddaa = ii = iiiiiiiiiiii qq ii εε 0 = QQ iiiiiiiiiiii εε 0 Gauss s law (Φ B ): (magnetic field) SS BB rr. ddaa = 0 Faraday s law: Ampère s law: (generalized) CC CC EE rr. ddss = ddφ BB dddd BB rr. ddss = μμ oo II + μμ oo εε oo ddφ EE dddd Lorentz law: (force) FF = qq EE + qq vv BB Fall 2018 Prof. Sergio B. Mendes 10

11 Thermodynamics Fall 2018 Prof. Sergio B. Mendes 11

12 Contributions from: Benjamin Thompson ( ) (Count Rumford) Sadi Carnot ( ) James Joule ( ) Rudolf Clausius ( ) William Thompson ( ) (Lord Kelvin) Fall 2018 Prof. Sergio B. Mendes 12

13 Key Concepts Temperature, internal energy, heat, work, and entropy. Introduces the concept of internal energy. Temperature as a measure of internal energy. Establishes heat as energy transferred due to temperature difference. Thermal equilibrium: a state in which the macroscopic properties (p, V, and T) no longer change with time if the system is mechanically and thermally isolated. Summer 2018 Prof. Sergio B. Mendes 13

14 The Laws of Thermodynamics The zeroth law: two systems in thermal equilibrium with a third system are in thermal equilibrium with each other. First law: The change in the internal energy ΔU of a system is equal to the heat Q added to a system plus the work W done by the system ΔUU = QQ + WW Fall 2018 Prof. Sergio B. Mendes 14

15 Second law (a): It is not possible to convert heat completely into work without some other change taking place. Impossible!! Possible!! ee WW QQ h = 1 TT cc TT h Second law (b): It is not possible to fully transfer heat from a cold to a hot reservoir without work. Impossible!! Possible!! Third law: It is not possible to achieve an absolute zero temperature (TT > 0 KK). Fall 2018 Prof. Sergio B. Mendes 15

16 2) Kinetic Theory of Gases Fall 2018 Prof. Sergio B. Mendes 16

17 Contributions made by: Robert Boyle ( ) Jacques Charles ( ) Joseph Louis Gay-Lussac ( ) Culminated in the ideal gas equation for n moles of a simple gas: P V = n R T (where R is the ideal gas constant, 8.31 J/mol K) Fall 2018 Prof. Sergio B. Mendes 17

18 Additional Contributions Amedeo Avogadro ( ) John Dalton ( ) Daniel Bernoulli ( ) Ludwig Boltzmann ( ) James Clerk Maxwell ( ) J. Willard Gibbs ( ) Summer 2018 Prof. Sergio B. Mendes 18

19 Main Results The average molecular kinetic energy is directly related to the absolute temperature: KK = 3 kk TT 2 The internal energy is equally distributed among all degrees of freedom (f ) of the system: UU = NN ff kk TT 2 Summer 2018 Prof. Sergio B. Mendes 19

20 The molar heat capacity at constant volume (c V ) is given by: cc vv = = ff 2 RR The molecular speed distribution f(v) is described: Summer 2018 Prof. Sergio B. Mendes 20

21 3) Atomistic Theory of Matter Fall 2018 Prof. Sergio B. Mendes 21

22 Contributions from: John Dalton advances the atomic theory of matter to explain the law of definite proportions Robert Brown observes microscopic random motion of suspended grains of pollen in water Albert Einstein ( ) uses molecules to explain Brownian motion and determines the approximate value of their size and mass Jean Perrin ( ) experimentally verifies Einstein s predictions J.J. Thomson Summer 2018 Ernst Rutherford Prof. Sergio B. Mendes 22

23 4) Mechanical Waves longitudinal displacement transverse displacement Fall 2018 Prof. Sergio B. Mendes 23

24 Wave Equation ψψ = pppppppppppppppp 2 ψψ xx 2 = 1 2 ψψ vv 2 tt 2 ψψ = heeeeeeeee yy xx 2 yy(xx, tt) xx 2 = 1 vv 2 2 yy(xx, tt) tt 2 yy xx, tt = ff(xx vv tt) Fall 2018 Prof. Sergio B. Mendes 24

25 Wave Speed FF nnnnnn 2 FF θθ FF = mm aa mm 2 θθ RR μμ aa = vv2 RR 2 FF θθ 2 θθ RR μμ vv2 RR vv = FF μμ Summer 2018 Prof. Sergio B. Mendes 25

26 The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote Our future discoveries must be looked for in the sixth place of decimals. - Albert A. Michelson, 1894 Summer 2018 Prof. Sergio B. Mendes 26

27 5) A Few Dark Clouds two clouds on the horizon, Lord Kelvin, 1900 Fall 2018 Prof. Sergio B. Mendes 27

28 From the electromagnetic theory, one can derive a wave equation for the electric and magnetic fields: 2 EE xx 2 = 1 2 EE cc 2 tt 2 cc = 1 εε oo μμ oo Where is the medium that carries the electromagnetic wave? 2 BB xx 2 = 1 2 BB cc 2 tt 2 Are the laws of electromagnetism valid for only one particular inertial frame of reference? Fall 2018 Prof. Sergio B. Mendes 28

29 Electromagnetic Radiation in Thermal Equilibrium: Blackbody Radiation Classical theory predicts an infinite energy for short wavelengths, UV catastrophe Summer 2018 Prof. Sergio B. Mendes 29

30 Consider the simplest atom (H): From Coulomb s law, we know that opposite charges attract each other. Why don t the proton and the electron collapse into each other? Why is the hydrogen atom (and other atoms) stable? Summer 2018 Prof. Sergio B. Mendes 30