Statistical Mechanics
|
|
- Marshall McDowell
- 5 years ago
- Views:
Transcription
1 Statistical Mechanics
2 Newton's laws in principle tell us how anything works But in a system with many particles, the actual computations can become complicated. We will therefore be happy to get some 'average' or approximate behavior of the system that will be useful for practical purposes Describing this average dynamics is the goal of thermodynamics A microscopic level fundamental understanding of thermodynamics was found later, and this field is called statistical mechanics
3 Average energy Suppose we have probability p i to have energy E i Then the average energy is hei = P i P i E i P i P i Continuous variables: Probability for any given value is zero, but we have a probability for a range P (v) dv v v + dv v
4 v P (v) Area under curve Z P (v)dv =1 v Sometimes we may give the number of particles per unit velocity range N(v)dv particles have momentum between and v v + dv N(v) Area under curve Z N(v)dv = N total
5 GREPracticeBook 56. A sample of N molecules has the distribution of speeds shown in the figure above. P u du is an estimate of the number of molecules with speeds between u and u + du, and this number is nonzero only up to 3u 0, where u 0 is constant. Which of the following gives the value of a? N (A) a 3 u 0 N (B) a 2 u (C) a (D) a N u (E) a N N 2 u 0
6 GREPracticeBook 56. A sample of N molecules has the distribution of speeds shown in the figure above. P u du is an estimate of the number of molecules with speeds between u and u + du, and this number is nonzero only up to 3u 0, where u 0 is constant. Which of the following gives the value of a? N (A) a 3 u 0 N (B) a 2 u (C) a (D) a N u (E) a N N 2 u 0
7 Hot bath, temperature T The particle can get energy from the hot walls when it touches them Basic law of Statistical Mechanics: Probability for the particle to have energy E P / e E kt Here k = JK 1 is the Boltzmann constant
8 77. An ensemble of systems is in thermal equilibrium with a reservoir for which kt = ev. State A has an energy that is 0.1 ev above that of state B. If it is assumed the systems obey Maxwell-Boltzmann statistics and that the degeneracies of the two states are the same, then the ratio of the number of systems in state A to the number in state B is (A) e +4 (B) e (C) 1 (D) e (E) e -4 GRE0177
9 77. An ensemble of systems is in thermal equilibrium with a reservoir for which kt = ev. State A has an energy that is 0.1 ev above that of state B. If it is assumed the systems obey Maxwell-Boltzmann statistics and that the degeneracies of the two states are the same, then the ratio of the number of systems in state A to the number in state B is (A) e +4 (B) e (C) 1 (D) e (E) e -4 GRE0177
10 e E kt E = kt E For each degree of freedom, hei = 1 2 kt A state with lower energy is more likely...
11 First consider the 1-dimensional problem v P / e E kt E = 1 2 mv2 P (v) / e mv2 2kT The most likely speed is v =0
12 Hot bath, temperature T (v 2 x +v2 y ) P / e 2kT v y Many velocities ~v to the same speed v correspond v =0 v x Higher speeds are suppressed because they have more energy Higher speeds are enhanced because there are more possible velocities for higher speeds
13 57. Which of the following statements is (are) true for a Maxwell-Boltzmann description of an ideal gas of atoms in equilibrium at temperature T? I. The average velocity of the atoms is zero. II. The distribution of the speeds of the atoms has a maximum at u = 0. III. The probability of finding an atom with zero kinetic energy is zero. (A) I only (B) II only (C) I and II (D) I and III (E) II and III GREPracticeBook
14 57. Which of the following statements is (are) true for a Maxwell-Boltzmann description of an ideal gas of atoms in equilibrium at temperature T? I. The average velocity of the atoms is zero. II. The distribution of the speeds of the atoms has a maximum at u = 0. III. The probability of finding an atom with zero kinetic energy is zero. (A) I only (B) II only (C) I and II (D) I and III (E) II and III GREPracticeBook
15 For each degree of freedom, hei = 1 2 kt v hei = h 1 2 mv2 i = 1 2 kt Hot bath, temperature T hei = h 1 2 mv2 i + h 1 2 Kx2 i K = 1 2 kt + 1 kt = kt 2 m
16 Hot bath, temperature T Particle in 3-d hei = h 1 2 mv2 x mv2 y mv2 zi = 3 2 kt
17 5. A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. The average total energy of the oscillator is GRE0177 (A) 1 2 kt (B) kt (C) 3 2 kt (D) 3kT (E) 6kT
18 5. A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. The average total energy of the oscillator is GRE0177 (A) 1 2 kt (B) kt (C) 3 2 kt (D) 3kT (E) 6kT
19 48. A gaseous mixture of O 2 (molecular mass 32 u) and N 2 (molecular mass 28 u) is maintained at constant temperature. What is the ratio u u rms ( N ) rms( O 2 2) of the root-mean-square speeds of the molecules? GRE0177 (A) 7 8 (B) (C) (D) FH 8 I K 7 2 FH (E) ln 8I K 7
20 48. A gaseous mixture of O 2 (molecular mass 32 u) and N 2 (molecular mass 28 u) is maintained at constant temperature. What is the ratio u u rms ( N ) rms( O 2 2) of the root-mean-square speeds of the molecules? GRE0177 (A) 7 8 (B) (C) (D) FH 8 I K 7 2 FH (E) ln 8I K 7
21 Avagadro number N = (1 mole) Avagadro number of H atoms weigh 1 gram Avagadro number of He atoms weigh 4 grams Molar mass of H = 1gm = mass of H atom times N Molar mass of He = 4 gm = mass of He atom times N We define kn = R R =8.31 JK 1 /mole One degree of freedom hei = 1 2 kt N degrees of freedom hei = 1 2 NkT = 1 2 RT
22 9. The root-mean-square speed of molecules in an ideal gas of molar mass M at temperature T is (A) 0 GREPracticeBook (B) (C) (D) (E) RT M RT M 3RT M 3RT M
23 9. The root-mean-square speed of molecules in an ideal gas of molar mass M at temperature T is (A) 0 GREPracticeBook (B) (C) (D) (E) RT M RT M 3RT M 3RT M
24 Blackbody radiation is made of photons p y P e E kt p x p =0 Wien displacement constant W = mk W peak = T peak Wien displacement law: Double T double peak E halve wavelength
25 GRE The distribution of relative intensity I ( l ) of blackbody radiation from a solid object versus the wavelength l is shown in the figure above. If the Wien displacement law constant is m K, what is the approximate temperature of the object? (A) 10 K (B) 50 K (C) 250 K (D) 1,500 K (E) 6,250 K
26 GRE The distribution of relative intensity I ( l ) of blackbody radiation from a solid object versus the wavelength l is shown in the figure above. If the Wien displacement law constant is m K, what is the approximate temperature of the object? (A) 10 K (B) 50 K (C) 250 K (D) 1,500 K (E) 6,250 K
27 Approximations e E kt E = kt E For x 1 e x 1 x +... Low energy e E kt 1 E kt
28 GRE0177 C 3kN hv A kt hv / kt F I = H K hv / kt - 2 (e e 1) Einstein s formula for the molar heat capacity C of solids is given above. At high temperatures, C approaches which of the following? (A) 0 (B) 3kN A F H (C) 3kN hv A (D) 3kN A (E) Nhv A hv kt I K
29 GRE0177 C 3kN hv A kt hv / kt F I = H K hv / kt - 2 (e e 1) Einstein s formula for the molar heat capacity C of solids is given above. At high temperatures, C approaches which of the following? (A) 0 (B) 3kN A F H (C) 3kN hv A (D) 3kN A (E) Nhv A hv kt I K
30 The partition function
31 The average energy is hei = P i P i E i P i P i with P i / e E i kt To compute this, we define the Partition Function Z = X i e E i kt We write 1 kt = This gives Z = X i e = X i e E i E i = P i e E i E i Pi e E i = hei
32 98. Suppose that a system in quantum state i has energy E i. In thermal equilibrium, the expression GRE0177  i  i Ee i e - E - E i i / kt / kt represents which of the following? (A) The average energy of the system (B) The partition function (C) Unity (D) The probability to find the system with energy E i (E) The entropy of the system
33 98. Suppose that a system in quantum state i has energy E i. In thermal equilibrium, the expression GRE0177  i  i Ee i e - E - E i i / kt / kt represents which of the following? (A) The average energy of the system (B) The partition function (C) Unity (D) The probability to find the system with energy E i (E) The entropy of the system
34 49. In a Maxwell-Boltzmann system with two states of energies and 2, respectively, and a degeneracy of 2 for each state, the partition function is GRE0177 (A) e- /kt (B) 2e-2 /kt (C) 2e-3 /kt (D) e - /kt + e-2 /kt (E) 2[e - /kt + e -2 /kt ]
35 49. In a Maxwell-Boltzmann system with two states of energies and 2, respectively, and a degeneracy of 2 for each state, the partition function is GRE0177 (A) e- /kt (B) 2e-2 /kt (C) 2e-3 /kt (D) e - /kt + e-2 /kt (E) 2[e - /kt + e -2 /kt ]
36 An unusual situation
37 76. The mean kinetic energy of the conduction electrons in metals is ordinarily much higher than kt because (A) electrons have many more degrees of freedom than atoms do (B) the electrons and the lattice are not in thermal equilibrium (C) the electrons form a degenerate Fermi gas (D) electrons in metals are highly relativistic (E) electrons interact strongly with phonons GRE0177
38 76. The mean kinetic energy of the conduction electrons in metals is ordinarily much higher than kt because (A) electrons have many more degrees of freedom than atoms do (B) the electrons and the lattice are not in thermal equilibrium (C) the electrons form a degenerate Fermi gas (D) electrons in metals are highly relativistic (E) electrons interact strongly with phonons p y GRE0177 E kt p x p =0
39 Deriving hei = 1 2 kt
40 First consider the 1-dimensional problem v P e E kt E = 1 2 mv2 P (v) / e mv2 2kT Adding over all possibilities : Z 1 1 dv
41 First consider the 1-dimensional problem v hei = P i p i E i P i p i p / e E kt E = 1 2 mv2 p(v) / e mv2 2kT hei = R 1 1 dv( 1 2 mv2 ) e mv2 2kT R 1 1 mv2 dv e 2kT = 1 2 kt
42 Hot bath, temperature T K p / e E kt m E = 1 2 mv Kx2 p / e mv2 2kT e Kx 2 2kT Adding over all possibilities of velocity : Adding over all possibilities of position : Z 1 1 Z 1 1 dv dx
43 Hot bath, temperature T K p / e E kt m E = 1 2 mv Kx2 p / e mv2 2kT e Kx 2 2kT Adding over all probabilities Z Z dvdx e mv2 2kT e Kx 2 2kT = Z dv e mv2 2kT Z dx e Kx2 2kT
44 Hot bath, temperature T K m p / e mv2 2kT e Kx 2 2kT E = 1 2 mv Kx2 h 1 2 mv2 i = R dv dx ( 1 2 mv2 ) e mv R dv dx e mv 2 2kT 2 2kT e Kx2 2kT e Kx2 2kT = R dv ( 1 2 mv2 ) e mv R dv e mv 2 2kT 2 2kT R dx e Kx 2 2kT R dx e Kx 2 2kT = 1 2 kt
45 Hot bath, temperature T K m p / e mv2 2kT e Kx 2 2kT E = 1 2 mv Kx2 h 1 2 mv2 i + h 1 2 Kx2 i = 1 2 kt kt = kt
STSF2223 Quantum Mechanics I
STSF2223 Quantum Mechanics I What is quantum mechanics? Why study quantum mechanics? How does quantum mechanics get started? What is the relation between quantum physics with classical physics? Where is
More informationCh. 19: The Kinetic Theory of Gases
Ch. 19: The Kinetic Theory of Gases In this chapter we consider the physics of gases. If the atoms or molecules that make up a gas collide with the walls of their container, they exert a pressure p on
More informationPhysics 408 Final Exam
Physics 408 Final Exam Name You are graded on your work, with partial credit where it is deserved. Please give clear, well-organized solutions. 1. Consider the coexistence curve separating two different
More informationChapter 15 Thermal Properties of Matter
Chapter 15 Thermal Properties of Matter To understand the mole and Avogadro's number. To understand equations of state. To study the kinetic theory of ideal gas. To understand heat capacity. To learn and
More informationRate of Heating and Cooling
Rate of Heating and Cooling 35 T [ o C] Example: Heating and cooling of Water E 30 Cooling S 25 Heating exponential decay 20 0 100 200 300 400 t [sec] Newton s Law of Cooling T S > T E : System S cools
More informationThermal & Statistical Physics Study Questions for the Spring 2018 Department Exam December 6, 2017
Thermal & Statistical Physics Study Questions for the Spring 018 Department Exam December 6, 017 1. a. Define the chemical potential. Show that two systems are in diffusive equilibrium if 1. You may start
More informationThermal and Statistical Physics Department Exam Last updated November 4, L π
Thermal and Statistical Physics Department Exam Last updated November 4, 013 1. a. Define the chemical potential µ. Show that two systems are in diffusive equilibrium if µ 1 =µ. You may start with F =
More informationThermodynamics & Statistical Mechanics SCQF Level 9, U03272, PHY-3-ThermStat. Thursday 24th April, a.m p.m.
College of Science and Engineering School of Physics H T O F E E U D N I I N V E B R U S I R T Y H G Thermodynamics & Statistical Mechanics SCQF Level 9, U03272, PHY-3-ThermStat Thursday 24th April, 2008
More informationPV = n R T = N k T. Measured from Vacuum = 0 Gauge Pressure = Vacuum - Atmospheric Atmospheric = 14.7 lbs/sq in = 10 5 N/m
PV = n R T = N k T P is the Absolute pressure Measured from Vacuum = 0 Gauge Pressure = Vacuum - Atmospheric Atmospheric = 14.7 lbs/sq in = 10 5 N/m V is the volume of the system in m 3 often the system
More informationLecture 25 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas
Lecture 5 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas law. redict the molar specific heats of gases and solids. Understand how heat is transferred via molecular collisions
More informationProblem #1 30 points Problem #2 30 points Problem #3 30 points Problem #4 30 points Problem #5 30 points
Name ME 5 Exam # November 5, 7 Prof. Lucht ME 55. POINT DISTRIBUTION Problem # 3 points Problem # 3 points Problem #3 3 points Problem #4 3 points Problem #5 3 points. EXAM INSTRUCTIONS You must do four
More informationPart II Statistical Physics
Part II Statistical Physics Theorems Based on lectures by H. S. Reall Notes taken by Dexter Chua Lent 2017 These notes are not endorsed by the lecturers, and I have modified them (often significantly)
More informationChapter 18 Thermal Properties of Matter
Chapter 18 Thermal Properties of Matter In this section we define the thermodynamic state variables and their relationship to each other, called the equation of state. The system of interest (most of the
More informationADIABATIC PROCESS Q = 0
THE KINETIC THEORY OF GASES Mono-atomic Fig.1 1 3 Average kinetic energy of a single particle Fig.2 INTERNAL ENERGY U and EQUATION OF STATE For a mono-atomic gas, we will assume that the total energy
More informationSpeed Distribution at CONSTANT Temperature is given by the Maxwell Boltzmann Speed Distribution
Temperature ~ Average KE of each particle Particles have different speeds Gas Particles are in constant RANDOM motion Average KE of each particle is: 3/2 kt Pressure is due to momentum transfer Speed Distribution
More informationChapter 17 Temperature & Kinetic Theory of Gases 1. Thermal Equilibrium and Temperature
Chapter 17 Temperature & Kinetic Theory of Gases 1. Thermal Equilibrium and Temperature Any physical property that changes with temperature is called a thermometric property and can be used to measure
More informationPhysics 607 Final Exam
Physics 67 Final Exam Please be well-organized, and show all significant steps clearly in all problems. You are graded on your work, so please do not just write down answers with no explanation! Do all
More informationPhysics 4230 Final Examination 10 May 2007
Physics 43 Final Examination May 7 In each problem, be sure to give the reasoning for your answer and define any variables you create. If you use a general formula, state that formula clearly before manipulating
More informationThermodynamics and Statistical Physics Exam
Thermodynamics and Statistical Physics Exam You may use your textbook (Thermal Physics by Schroeder) and a calculator. 1. Short questions. No calculation needed. (a) Two rooms A and B in a building are
More informationEinstein s Approach to Planck s Law
Supplement -A Einstein s Approach to Planck s Law In 97 Albert Einstein wrote a remarkable paper in which he used classical statistical mechanics and elements of the old Bohr theory to derive the Planck
More informationThermal Properties of Matter (Microscopic models)
Chapter 18 Thermal Properties of Matter (Microscopic models) PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 6_18_2012
More informationElements of Statistical Mechanics
Dr. Y. Aparna, Associate Prof., Dept. of Physics, JNTU College of ngineering, JNTU - H, lements of Statistical Mechanics Question: Discuss about principles of Maxwell-Boltzmann Statistics? Answer: Maxwell
More informationPlease read the following instructions:
MIDTERM #1 PHYS 33 (MODERN PHYSICS II) DATE/TIME: February 16, 17 (8:3 a.m. - 9:45 a.m.) PLACE: RB 11 Only non-programmable calculators are allowed. Name: ID: Please read the following instructions: This
More informationPhysics 404: Final Exam Name (print): "I pledge on my honor that I have not given or received any unauthorized assistance on this examination.
Physics 404: Final Exam Name (print): "I pledge on my honor that I have not given or received any unauthorized assistance on this examination." May 20, 2008 Sign Honor Pledge: Don't get bogged down on
More informationPhysics 333, Thermal and Statistical Physics: Homework #2 Solutions Manual
Physics 333, Thermal and Statistical Physics: Homework #2 Solutions Manual 1. n 5 = 0 n 5 = 1 n 5 = 2 n 5 = 3 n 5 = 4 n 5 = 5 d n 5,0,0,0,0 4 0 0 0 0 1 5 4,1,0,0,0 12 4 0 0 4 0 20 3,2,0,0,0 12 0 4 4 0
More informationPHYS3113, 3d year Statistical Mechanics Tutorial problems. Tutorial 1, Microcanonical, Canonical and Grand Canonical Distributions
1 PHYS3113, 3d year Statistical Mechanics Tutorial problems Tutorial 1, Microcanonical, Canonical and Grand Canonical Distributions Problem 1 The macrostate probability in an ensemble of N spins 1/2 is
More information5. Systems in contact with a thermal bath
5. Systems in contact with a thermal bath So far, isolated systems (micro-canonical methods) 5.1 Constant number of particles:kittel&kroemer Chap. 3 Boltzmann factor Partition function (canonical methods)
More informationto satisfy the large number approximations, W W sys can be small.
Chapter 12. The canonical ensemble To discuss systems at constant T, we need to embed them with a diathermal wall in a heat bath. Note that only the system and bath need to be large for W tot and W bath
More informationThe Equipartition Theorem
Chapter 8 The Equipartition Theorem Topics Equipartition and kinetic energy. The one-dimensional harmonic oscillator. Degrees of freedom and the equipartition theorem. Rotating particles in thermal equilibrium.
More informationImperial College London BSc/MSci EXAMINATION May 2008 THERMODYNAMICS & STATISTICAL PHYSICS
Imperial College London BSc/MSci EXAMINATION May 2008 This paper is also taken for the relevant Examination for the Associateship THERMODYNAMICS & STATISTICAL PHYSICS For Second-Year Physics Students Wednesday,
More informationPhysics 576 Stellar Astrophysics Prof. James Buckley. Lecture 14 Relativistic Quantum Mechanics and Quantum Statistics
Physics 576 Stellar Astrophysics Prof. James Buckley Lecture 14 Relativistic Quantum Mechanics and Quantum Statistics Reading/Homework Assignment Read chapter 3 in Rose. Midterm Exam, April 5 (take home)
More information18.13 Review & Summary
5/2/10 10:04 PM Print this page 18.13 Review & Summary Temperature; Thermometers Temperature is an SI base quantity related to our sense of hot and cold. It is measured with a thermometer, which contains
More informationIntroduction Statistical Thermodynamics. Monday, January 6, 14
Introduction Statistical Thermodynamics 1 Molecular Simulations Molecular dynamics: solve equations of motion Monte Carlo: importance sampling r 1 r 2 r n MD MC r 1 r 2 2 r n 2 3 3 4 4 Questions How can
More information(Heat capacity c is also called specific heat) this means that the heat capacity number c for water is 1 calorie/gram-k.
Lecture 23: Ideal Gas Law and The First Law of Thermodynamics 1 (REVIEW) Chapter 17: Heat Transfer Origin of the calorie unit A few hundred years ago when people were investigating heat and temperature
More informationfiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Kinetic Theory, Thermodynamics OBJECTIVE QUESTIONS IIT-JAM-2005
Institute for NE/JRF, GAE, II JAM, JES, IFR and GRE in HYSIAL SIENES Kinetic heory, hermodynamics OBJEIE QUESIONS II-JAM-005 5 Q. he molar specific heat of a gas as given from the kinetic theory is R.
More informationPHYS 352 Homework 2 Solutions
PHYS 352 Homework 2 Solutions Aaron Mowitz (, 2, and 3) and Nachi Stern (4 and 5) Problem The purpose of doing a Legendre transform is to change a function of one or more variables into a function of variables
More informationThermodynamics. Fill in the blank (1pt)
Fill in the blank (1pt) Thermodynamics 1. The Newton temperature scale is made up of different points 2. When Antonine Lavoisier began his study of combustion, he noticed that metals would in weight upon
More informationChapter 1. From Classical to Quantum Mechanics
Chapter 1. From Classical to Quantum Mechanics Classical Mechanics (Newton): It describes the motion of a classical particle (discrete object). dp F ma, p = m = dt dx m dt F: force (N) a: acceleration
More informationAlso: Question: what is the nature of radiation emitted by an object in equilibrium
They already knew: Total power/surface area Also: But what is B ν (T)? Question: what is the nature of radiation emitted by an object in equilibrium Body in thermodynamic equilibrium: i.e. in chemical,
More informationThermodynamics & Statistical Mechanics
hysics GRE: hermodynamics & Statistical Mechanics G. J. Loges University of Rochester Dept. of hysics & Astronomy xkcd.com/66/ c Gregory Loges, 206 Contents Ensembles 2 Laws of hermodynamics 3 hermodynamic
More informationThis is a statistical treatment of the large ensemble of molecules that make up a gas. We had expressed the ideal gas law as: pv = nrt (1)
1. Kinetic Theory of Gases This is a statistical treatment of the large ensemble of molecules that make up a gas. We had expressed the ideal gas law as: pv = nrt (1) where n is the number of moles. We
More informationε tran ε tran = nrt = 2 3 N ε tran = 2 3 nn A ε tran nn A nr ε tran = 2 N A i.e. T = R ε tran = 2
F1 (a) Since the ideal gas equation of state is PV = nrt, we can equate the right-hand sides of both these equations (i.e. with PV = 2 3 N ε tran )and write: nrt = 2 3 N ε tran = 2 3 nn A ε tran i.e. T
More information(# = %(& )(* +,(- Closed system, well-defined energy (or e.g. E± E/2): Microcanonical ensemble
Recall from before: Internal energy (or Entropy): &, *, - (# = %(& )(* +,(- Closed system, well-defined energy (or e.g. E± E/2): Microcanonical ensemble & = /01Ω maximized Ω: fundamental statistical quantity
More informationUNIVERSITY OF SOUTHAMPTON
UNIVERSITY OF SOUTHAMPTON PHYS1013W1 SEMESTER 2 EXAMINATION 2014-2015 ENERGY AND MATTER Duration: 120 MINS (2 hours) This paper contains 8 questions. Answers to Section A and Section B must be in separate
More informationThe goal of thermodynamics is to understand how heat can be converted to work. Not all the heat energy can be converted to mechanical energy
Thermodynamics The goal of thermodynamics is to understand how heat can be converted to work Main lesson: Not all the heat energy can be converted to mechanical energy This is because heat energy comes
More informationThermodynamics, Gibbs Method and Statistical Physics of Electron Gases
Bahram M. Askerov Sophia R. Figarova Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases With im Figures Springer Contents 1 Basic Concepts of Thermodynamics and Statistical Physics...
More informationPlease read the following instructions:
MIDTERM #1 PHYS 33 (MODERN PHYSICS II) DATE/TIME: February 16, 17 (8:3 a.m. - 9:45 a.m.) PLACE: RB 11 Only non-programmable calculators are allowed. Name: ID: Please read the following instructions: This
More informationLecture 11: Models of the chemical potential
Lecture 11: 10.15.05 Models of the chemical potential Today: LAST TIME... 2 MORE ON THE RELATIONSHIP BETWEEN CHEMICAL POTENTIAL AND GIBBS FREE ENERGY... 3 Chemical potentials in multicomponent systems
More informationUNIVERSITY COLLEGE LONDON. University of London EXAMINATION FOR INTERNAL STUDENTS. For The Following Qualifications:-
UNIVERSITY COLLEGE LONDON University of London EXAMINATION FOR INTERNAL STUDENTS For The Following Qualifications:- B. Sc. M. Sci. Physics 2B28: Statistical Thermodynamics and Condensed Matter Physics
More informationPreliminary Examination - Day 2 August 16, 2013
UNL - Department of Physics and Astronomy Preliminary Examination - Day August 16, 13 This test covers the topics of Quantum Mechanics (Topic 1) and Thermodynamics and Statistical Mechanics (Topic ). Each
More information19-9 Adiabatic Expansion of an Ideal Gas
19-9 Adiabatic Expansion of an Ideal Gas Learning Objectives 19.44 On a p-v diagram, sketch an adiabatic expansion (or contraction) and identify that there is no heat exchange Q with the environment. 19.45
More informationPhysics Oct A Quantum Harmonic Oscillator
Physics 301 5-Oct-2005 9-1 A Quantum Harmonic Oscillator The quantum harmonic oscillator (the only kind there is, really) has energy levels given by E n = (n + 1/2) hω, where n 0 is an integer and the
More information2. Fingerprints of Matter: Spectra
2. Fingerprints of Matter: Spectra 2.1 Measuring spectra: prism and diffraction grating Light from the sun: white light, broad spectrum (wide distribution) of wave lengths. 19th century: light assumed
More informationPhysics 2203, Fall 2011 Modern Physics
Physics 2203, Fall 2011 Modern Physics. Friday, Nov. 2 nd, 2012. Energy levels in Nitrogen molecule Sta@s@cal Physics: Quantum sta@s@cs: Ch. 15 in our book. Notes from Ch. 10 in Serway Announcements Second
More informationSpeed Distribution at CONSTANT Temperature is given by the Maxwell Boltzmann Speed Distribution
Temperature ~ Average KE of each particle Particles have different speeds Gas Particles are in constant RANDOM motion Average KE of each particle is: 3/2 kt Pressure is due to momentum transfer Speed Distribution
More informationQUANTUM MECHANICS AND MOLECULAR SPECTROSCOPY
QUANTUM MECHANICS AND MOLECULAR SPECTROSCOPY CHEM 330 B. O. Owaga Classical physics Classical physics is based on three assumptions i. Predicts precise trajectory for particles with precisely specified
More informationDownloaded from
Chapter 13 (Kinetic Theory) Q1. A cubic vessel (with face horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of500 ms in vertical direction.
More informationPhysics 207 Lecture 25. Lecture 25, Nov. 26 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas
Lecture 25, Nov. 26 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas law. redict the molar specific heats of gases and solids. Understand how heat is transferred via molecular
More informationKINETICE THEROY OF GASES
INTRODUCTION: Kinetic theory of gases relates the macroscopic properties of gases (like pressure, temperature, volume... etc) to the microscopic properties of the gas molecules (like speed, momentum, kinetic
More informationChapter 14 Kinetic Theory
Chapter 14 Kinetic Theory Kinetic Theory of Gases A remarkable triumph of molecular theory was showing that the macroscopic properties of an ideal gas are related to the molecular properties. This is the
More informationLecture 15: Electron Degeneracy Pressure
Lecture 15: Electron Degeneracy Pressure As the core contracts during shell H-burning we reach densities where the equation of state becomes significantly modified from that of the ideal gas law. The reason
More informationUNIVERSITY OF SOUTHAMPTON
UNIVERSITY OF SOUTHAMPTON PHYS2024W1 SEMESTER 2 EXAMINATION 2011/12 Quantum Physics of Matter Duration: 120 MINS VERY IMPORTANT NOTE Section A answers MUST BE in a separate blue answer book. If any blue
More informationTurning up the heat: thermal expansion
Lecture 3 Turning up the heat: Kinetic molecular theory & thermal expansion Gas in an oven: at the hot of materials science Here, the size of helium atoms relative to their spacing is shown to scale under
More informationChapter 10. Thermal Physics
Chapter 10 Thermal Physics Thermal Physics Thermal physics is the study of Temperature Heat How these affect matter Thermal Physics, cont Descriptions require definitions of temperature, heat and internal
More informationSolid Thermodynamics (1)
Solid Thermodynamics (1) Class notes based on MIT OCW by KAN K.A.Nelson and MB M.Bawendi Statistical Mechanics 2 1. Mathematics 1.1. Permutation: - Distinguishable balls (numbers on the surface of the
More informationSet 3: Thermal Physics
Set 3: Thermal Physics Equilibrium Thermal physics describes the equilibrium distribution of particles for a medium at temperature T Expect that the typical energy of a particle by equipartition is E kt,
More informationLecture 18 Molecular Motion and Kinetic Energy
Physical Principles in Biology Biology 3550 Fall 2017 Lecture 18 Molecular Motion and Kinetic Energy Monday, 2 October c David P. Goldenberg University of Utah goldenberg@biology.utah.edu Fick s First
More informationContents. 1 Introduction and guide for this text 1. 2 Equilibrium and entropy 6. 3 Energy and how the microscopic world works 21
Preface Reference tables Table A Counting and combinatorics formulae Table B Useful integrals, expansions, and approximations Table C Extensive thermodynamic potentials Table D Intensive per-particle thermodynamic
More informationComputer simulations as concrete models for student reasoning
Computer simulations as concrete models for student reasoning Jan Tobochnik Department of Physics Kalamazoo College Kalamazoo MI 49006 In many thermal physics courses, students become preoccupied with
More informationLecture 24. Ideal Gas Law and Kinetic Theory
Lecture 4 Ideal Gas Law and Kinetic Theory Today s Topics: Ideal Gas Law Kinetic Theory of Gases Phase equilibria and phase diagrams Ideal Gas Law An ideal gas is an idealized model for real gases that
More informationIdeal Gas Behavior. NC State University
Chemistry 331 Lecture 6 Ideal Gas Behavior NC State University Macroscopic variables P, T Pressure is a force per unit area (P= F/A) The force arises from the change in momentum as particles hit an object
More informationKinetic theory of the ideal gas
Appendix H Kinetic theory of the ideal gas This Appendix contains sketchy notes, summarizing the main results of elementary kinetic theory. The students who are not familiar with these topics should refer
More informationCONTENTS 1. In this course we will cover more foundational topics such as: These topics may be taught as an independent study sometime next year.
CONTENTS 1 0.1 Introduction 0.1.1 Prerequisites Knowledge of di erential equations is required. Some knowledge of probabilities, linear algebra, classical and quantum mechanics is a plus. 0.1.2 Units We
More informationUGC ACADEMY LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM PH 05 PHYSICAL SCIENCE TEST SERIES # 1. Quantum, Statistical & Thermal Physics
UGC ACADEMY LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM BOOKLET CODE SUBJECT CODE PH 05 PHYSICAL SCIENCE TEST SERIES # Quantum, Statistical & Thermal Physics Timing: 3: H M.M: 00 Instructions. This test
More informationMinimum Bias Events at ATLAS
Camille Bélanger-Champagne Lehman McGill College University City University of New York Thermodynamics Charged Particle and Correlations Statistical Mechanics in Minimum Bias Events at ATLAS Statistical
More informationPhysics 607 Final Exam
Physics 607 Final Exam Please be well-organized, and show all significant steps clearly in all problems. You are graded on your work, so please do not just write down answers with no explanation! Do all
More informationTemperature, Thermal Expansion and the Gas Laws
Temperature, Thermal Expansion and the Gas Laws z x Physics 053 Lecture Notes Temperature,Thermal Expansion and the Gas Laws Temperature and Thermometers Thermal Equilibrium Thermal Expansion The Ideal
More informationLecture 7: Kinetic Theory of Gases, Part 2. ! = mn v x
Lecture 7: Kinetic Theory of Gases, Part 2 Last lecture, we began to explore the behavior of an ideal gas in terms of the molecules in it We found that the pressure of the gas was: P = N 2 mv x,i! = mn
More informationStatistical Mechanics Notes. Ryan D. Reece
Statistical Mechanics Notes Ryan D. Reece August 11, 2006 Contents 1 Thermodynamics 3 1.1 State Variables.......................... 3 1.2 Inexact Differentials....................... 5 1.3 Work and Heat..........................
More information2.57/2.570 Midterm Exam No. 1 April 4, :00 am -12:30 pm
Name:.57/.570 Midterm Exam No. April 4, 0 :00 am -:30 pm Instructions: ().57 students: try all problems ().570 students: Problem plus one of two long problems. You can also do both long problems, and one
More informationCHAPTER 21 THE KINETIC THEORY OF GASES-PART? Wen-Bin Jian ( 簡紋濱 ) Department of Electrophysics National Chiao Tung University
CHAPTER 1 THE KINETIC THEORY OF GASES-PART? Wen-Bin Jian ( 簡紋濱 ) Department of Electrophysics National Chiao Tung University 1. Molecular Model of an Ideal Gas. Molar Specific Heat of an Ideal Gas. Adiabatic
More informationUNIVERSITY COLLEGE LONDON. University of London EXAMINATION FOR INTERNAL STUDENTS. For The Following Qualifications:-
UNIVERSITY COLLEGE LONDON University of London EXAMINATION FOR INTERNAL STUDENTS For The Following Qualifications:- B.Sc. M.Sci. Statistical Thermodynamics COURSE CODE : PHAS2228 UNIT VALUE : 0.50 DATE
More informationFinal Review Prof. WAN, Xin
General Physics I Final Review Prof. WAN, Xin xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ About the Final Exam Total 6 questions. 40% mechanics, 30% wave and relativity, 30% thermal physics. Pick
More informationThe answer (except for Z = 19) can be seen in Figure 1. All credit to McGraw- Hill for the image.
Problem 9.3 Which configuration has a greater number of unpaired spins? Which one has a lower energy? [Kr]4d 9 5s or [Kr]4d. What is the element and how does Hund s rule apply?. Solution The element is
More informationPHYSICS - CLUTCH CH 19: KINETIC THEORY OF IDEAL GASSES.
!! www.clutchprep.com CONCEPT: ATOMIC VIEW OF AN IDEAL GAS Remember! A gas is a type of fluid whose volume can change to fill a container - What makes a gas ideal? An IDEAL GAS is a gas whose particles
More informationChapter 10. Thermal Physics. Thermodynamic Quantities: Volume V and Mass Density ρ Pressure P Temperature T: Zeroth Law of Thermodynamics
Chapter 10 Thermal Physics Thermodynamic Quantities: Volume V and Mass Density ρ Pressure P Temperature T: Zeroth Law of Thermodynamics Temperature Scales Thermal Expansion of Solids and Liquids Ideal
More informationPotential Descending Principle, Dynamic Law of Physical Motion and Statistical Theory of Heat
Potential Descending Principle, Dynamic Law of Physical Motion and Statistical Theory of Heat Tian Ma and Shouhong Wang Supported in part by NSF, ONR and Chinese NSF http://www.indiana.edu/ fluid Outline
More informationPart I: Basic Concepts of Thermodynamics
Part I: Basic Concepts of Thermodynamics Lecture 3: Heat and Work Kinetic Theory of Gases Ideal Gases 3-1 HEAT AND WORK Here we look in some detail at how heat and work are exchanged between a system and
More informationLesson 12. Luis Anchordoqui. Physics 168. Tuesday, November 28, 17
Lesson 12 Physics 168 1 Temperature and Kinetic Theory of Gases 2 Atomic Theory of Matter On microscopic scale, arrangements of molecules in solids, liquids, and gases are quite different 3 Temperature
More informationPhysics 132- Fundamentals of Physics for Biologists II
Physics 132- Fundamentals of Physics for Biologists II Statistical Physics and Thermodynamics It s all about energy Classifying Energy Kinetic Energy Potential Energy Macroscopic Energy Moving baseball
More informationDr. Gundersen Phy 206 Test 2 March 6, 2013
Signature: Idnumber: Name: You must do all four questions. There are a total of 100 points. Each problem is worth 25 points and you have to do ALL problems. A formula sheet is provided on the LAST page
More informationPhysics 160 Thermodynamics and Statistical Physics: Lecture 2. Dr. Rengachary Parthasarathy Jan 28, 2013
Physics 160 Thermodynamics and Statistical Physics: Lecture 2 Dr. Rengachary Parthasarathy Jan 28, 2013 Chapter 1: Energy in Thermal Physics Due Date Section 1.1 1.1 2/3 Section 1.2: 1.12, 1.14, 1.16,
More informationIntroduction. Chapter The Purpose of Statistical Mechanics
Chapter 1 Introduction 1.1 The Purpose of Statistical Mechanics Statistical Mechanics is the mechanics developed to treat a collection of a large number of atoms or particles. Such a collection is, for
More informationa. 4.2x10-4 m 3 b. 5.5x10-4 m 3 c. 1.2x10-4 m 3 d. 1.4x10-5 m 3 e. 8.8x10-5 m 3
The following two problems refer to this situation: #1 A cylindrical chamber containing an ideal diatomic gas is sealed by a movable piston with cross-sectional area A = 0.0015 m 2. The volume of the chamber
More informationDr. Kasra Etemadi September 21, 2011
Dr. Kasra Etemadi September, 0 - Velocity Distribution -Reaction Rate and Equilibrium (Saha Equation 3-E3 4- Boltzmann Distribution 5- Radiation (Planck s Function 6- E4 z r dxdydz y x Applets f( x r
More informationTemperature and Heat. Ken Intriligator s week 4 lectures, Oct 21, 2013
Temperature and Heat Ken Intriligator s week 4 lectures, Oct 21, 2013 This week s subjects: Temperature and Heat chapter of text. All sections. Thermal properties of Matter chapter. Omit the section there
More information5. Systems in contact with a thermal bath
5. Systems in contact with a thermal bath So far, isolated systems (micro-canonical methods) 5.1 Constant number of particles:kittel&kroemer Chap. 3 Boltzmann factor Partition function (canonical methods)
More informationPart II: Statistical Physics
Chapter 6: Boltzmann Statistics SDSMT, Physics Fall Semester: Oct. - Dec., 2013 1 Introduction: Very brief 2 Boltzmann Factor Isolated System and System of Interest Boltzmann Factor The Partition Function
More informationLecture 24. Ideal Gas Law and Kinetic Theory
Lecture 4 Ideal Gas Law and Kinetic Theory Today s Topics: Ideal Gas Law Kinetic Theory of Gases Phase equilibria and phase diagrams Ideal Gas Law An ideal gas is an idealized model for real gases that
More informationKinetic Theory 1 / Probabilities
Kinetic Theory 1 / Probabilities 1. Motivations: statistical mechanics and fluctuations 2. Probabilities 3. Central limit theorem 1 Reading check Main concept introduced in first half of this chapter A)Temperature
More information