140a Final Exam, Fall 2006., κ T 1 V P. (? = P or V ), γ C P C V H = U + PV, F = U TS G = U + PV TS. T v. v 2 v 1. exp( 2πkT.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "140a Final Exam, Fall 2006., κ T 1 V P. (? = P or V ), γ C P C V H = U + PV, F = U TS G = U + PV TS. T v. v 2 v 1. exp( 2πkT."

Transcription

1 40a Final Exam, Fall 2006 Data: P Pa, R = J/kmol K = N A k, N A = particles/kilomole, T C = T K du = TdS PdV + i µ i dn i, U = TS PV + i µ i N i Defs: 2 β ( ) V V T ( ) /dq C? dt P? /dq/t ext S 2 S =, κ T V ( V P 2 ) T /dq R /T, κ S V (? = P or V ), γ C P C V = (f + 2)/f. ( ) V, P S c = C/n, v = V/n, s = S/n, P β κ K T κ T V av V. Ideal gas: PV = nrt = NkT, C P = C V + nr. PV γ = const.. η W / Q 2 T /T 2, ω Q / W. H = U + PV, F = U TS G = U + PV TS. W mech (U T 0 S + P 0 V ), (U T 0 S + P 0 V ) 0. F( v) = dp dt = s 2 s v 2 v = Free particles: Φ = 4 l T v. ( m ) 3/2 exp( 2πkT 2 m v2 /kt), N V v, P = N 3 V mv2. p(x) = σ 2 2π e (x x) /2σ 2, (x x) n p(x) = { π 2 n/2 σ n Γ( ( + n)) for n even 2 0 for n odd

2 0 dt t z e at = Γ(z)a z, 0 x4 e x dx (e x ) = 2 4π4 /5. where Γ(z + ) = zγ(z) and Γ() = (so Γ(n) = (n )! for integer n) and Γ(/2) = π. (p + q) N = i= N N =0 ( N N ) p N q N N. N = Np, N 2 = N2 p 2 + Npq. n! ( n ) n 2πn for n. e n p N i n i p({n i }) = N! N i!, where p i =. g(ɛ)dɛ 4πV 2 (2π h) 3 m3/2 ɛ /2 dɛ ω({n i }) B.E. = i S = k ln Ω k lnω max. ω({n i }) M.B. = i= (for free particle in box) n i= g N i i N i!. (N i + g i )! N i!(g i )! bosons ω({n i }) F.D. = i g i! N i!(g i N i )! fermions. N i g i = where α µ/kt and β /kt. { 0 MB e α βɛ where a = i + a bosons fermions k k lnω(ni i g ie α+βɛ i = kn MB ) + kαn + kβu k i g i ln( e α+βɛ i ) BE k. i g i ln( + e α+βɛ i ) FD Z(T, V ) i g i e βɛ i, ( ) µ MB = kt ln(n/z), U MB = NkT 2 T lnz V F MB = NkT ( + ln(z/n)). Z V ( ) 3/2 2πmkT ideal monatomic gas h 2 2

3 Z d SHO = n=0 e (n+ 2 )hν/kt = e hν/2kt e hν/kt. U SHO = kt 2 T lnz = N(ν)dν = with x m hν m /kt θ D /T. g(ν)dν e hν/kt = C V = 9Nkx 3 m [ 2 hν + hν { 9Nν 3 m e hν/kt ν 2 dν e hν/kt ]. ν ν m 0 ν > ν m. xm 0 x 4 e x (e x ) 2dx, 3

4 . An ideal gas of N particles has energy U = 2fNkT, for some constant f. The gas is initially in a box of volume V, at temperature T. A valve opens, and the gas undergoes free expansion, to fill a larger volume V 2 > V. No work is done in this process, and no heat is added or removed. What is the change in entropy of this process? For full credit, an explanation of what you re doing, and why, must accompany the calculation. [5 points]. 2. The particles of a monatomic ideal gas initially have v rms,i = 400m/s. The gas then undergoes an adiabatic process, in which the volume increases by a factor of eight, V f /V i = 8. What is the final v rms,f of the particles, after the process? [5 points] 3. An certain gas starts off at temperature T 0, with an entropy S 0. It then undergoes a total process, consisting of the following four steps. First, the system moves along an isotherm, to a state with entropy 2S 0. Next, it moves along an adiabat, to a state with temperature 6T 0. Next, the system then moves along an isotherm, to a state with entropy S 0. Finally, it moves on an adiabat, to a state with temperature T 0. (a) What is the net heat added to the system, for the total process (consisting of the above four steps)? Write it as negative, if appropriate. You don t need to write the separate contributions of each step, if you don t need that to write the net answer. (Just be sure to explain what you re doing, and why!) [5 points] (b) What is the net change in the internal energy of the gas, after the total process? (Same comments as the last part.) [5 points] (c) What is the net work done by the gas, after the total process? (Same comments.) [5 points] 4. The number of states available to a system of N particles, with total energy U, in volume V, is generally written as Ω(N, U, V ). Suppose that a certain system has Ω(N, U, V ) = Ω(N, UV b ), i.e. it only depends on U and V via the variable UV b, where b is some constant. The function Ω(N, UV b ) is a rapidly increasing function of both N and UV b. (a) The system initially has volume V i = 2m 3, and total energy U i = 00J. It then undergoes an adiabatic expansion to volume V f = 4m 3. What is the final total energy U f? (Write your answer in terms of the constant b). [5 points] (b) Derive a general expression for the pressure of the gas, as a function of U and V (and the constant b). Hint: the key to correctly solving this problem is to use the first law 4

5 of thermodynamics to write the pressure as a certain partial derivative, with something held fixed. Part (a) is also a hint. [5 points] 5. Container # has has n = kilomoles of monatomic ideal gas (γ = 5/3) and is points] at temperature T = 300K. Container #2 has n = 2 kilomoles of diatomic ideal gas (γ = 7/5), and is at temperature T 2 = 600K. The sizes of the containers are unchanging, and the walls do not allow any particle leakage. The two containers are placed in thermal contact for a little while, but are separated before they reach thermal equilibrium. After their separation, container # has temperature T = 400K. (a) What is the temperature T 2 of container #2 after the separation? [5 points] (b) What is the entropy change of the total system (both containers together)? [5 6. A certain particle has energy given by ɛ = c p, where p is the 3d momentum vector and c = the speed of light (this is the relativistic energy of a massless particle). (a) Compute the partition function of such a particle, in a box of volume V. Use the method where the sum over all states is replaced with an integral over the phase space, n d 3 rd 3 p/h 3. For full credit, evaluate the integral (using info in the formulae sheet). [5 points] (b) Compute C V for a gas of N such particles (take the gas to be sufficiently dilute that MB statistics apply). [5 points] (c) Compute the Helmholtz free energy, and use it to find the equation of state of the gas of N such particles. [5 points] 7. At low temperatures, the heat capacity of a certain sample of a solid material is given by C V = bt 3, for some constant b. A cyclic refrigerator cools the sample, from temperature T i = 2K to temperature T f = K. In this process, the refrigerator removes heat Q s = 5J from the sample. The refrigerator also emits some heat Q L into the outside lab, which is at temperature T L = 300K. (a) Using the information given above, find the numerical value of the constant b, in appropriate units. [5 points] (b) What is the change in entropy of the sample, the lab, and the refrigerator itself, in the cooling process? Write your answers as numbers (to the extent possible), in the appropriate units. [9 points (3 points each)] 5

6 (c) According to the laws of thermodynamics, what is the minimum energy which must go into running the refrigerator, for this cooling process? Also, what is the value of Q L in this case? Write your answers as numbers, in appropriate units. [5 points] 8. A certain thermodynamic system has nondegenerate energy levels, with energies 0, ɛ, 3ɛ, 6ɛ, 0ɛ, 5ɛ,.... Suppose that there are four particles, with total energy U = 0ɛ. Identify the possible distribution of particles, and evaluate their ω({n i }) and Ω. Also, compute the average occupation number N 0 of the ground state. (a) When the particles are distinguishable. [5 points] (b) When the particles are gaseous identical bosons. [3 points] (c) When the particles are gaseous identical fermions. [3 points] 9. Consider a modified version of the d simple harmonic oscillator, for which the energy levels are ɛ n = (2n )hν, for n = 0,, 2,.... These energy levels are each nondegenerate. (a) Compute the partition function for such a modified d harmonic oscillator. (For full credit, fully evaluate the mathematical expression for the function.) [5 points] (b) Consider a system of N distinguishable such d harmonic oscillators. Find the specific heat C V of this system, as a function of temperature. [5 points] 6

140a Final Exam, Fall 2007., κ T 1 V P. (? = P or V ), γ C P C V H = U + PV, F = U TS G = U + PV TS. T v. v 2 v 1. exp( 2πkT.

140a Final Exam, Fall 2007., κ T 1 V P. (? = P or V ), γ C P C V H = U + PV, F = U TS G = U + PV TS. T v. v 2 v 1. exp( 2πkT. 4a Final Exam, Fall 27 Data: P 5 Pa, R = 8.34 3 J/kmol K = N A k, N A = 6.2 26 particles/kilomole, T C = T K 273.5. du = TdS PdV + i µ i dn i, U = TS PV + i µ i N i Defs: 2 β ( ) V V T ( ) /dq C? dt P?

More information

UNIVERSITY OF SOUTHAMPTON

UNIVERSITY 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 information

Thermal and Statistical Physics Department Exam Last updated November 4, L π

Thermal 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 information

Chapter 7: Quantum Statistics

Chapter 7: Quantum Statistics Part II: Applications SDSMT, Physics 2014 Fall 1 Introduction Photons, E.M. Radiation 2 Blackbody Radiation The Ultraviolet Catastrophe 3 Thermal Quantities of Photon System Total Energy Entropy 4 Radiation

More information

Thermal & Statistical Physics Study Questions for the Spring 2018 Department Exam December 6, 2017

Thermal & 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 information

Physics 408 Final Exam

Physics 408 Final Exam Physics 408 Final Exam Name You are graded on your work (with partial credit where it is deserved) so please do not just write down answers with no explanation (or skip important steps)! Please give clear,

More information

Chemistry. Lecture 10 Maxwell Relations. NC State University

Chemistry. Lecture 10 Maxwell Relations. NC State University Chemistry Lecture 10 Maxwell Relations NC State University Thermodynamic state functions expressed in differential form We have seen that the internal energy is conserved and depends on mechanical (dw)

More information

Data Provided: A formula sheet and table of physical constants are attached to this paper.

Data Provided: A formula sheet and table of physical constants are attached to this paper. Data Provided: A formula sheet and table of physical constants are attached to this paper. DEPARTMENT OF PHYSICS AND ASTRONOMY Spring Semester (2016-2017) From Thermodynamics to Atomic and Nuclear Physics

More information

INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI Department of Physics MID SEMESTER EXAMINATION Statistical Mechanics: PH704 Solution

INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI Department of Physics MID SEMESTER EXAMINATION Statistical Mechanics: PH704 Solution INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI Department of Physics MID SEMESTER EXAMINATION Statistical Mechanics: PH74 Solution. There are two possible point defects in the crystal structure, Schottky and

More information

Chapter 3 - First Law of Thermodynamics

Chapter 3 - First Law of Thermodynamics Chapter 3 - dynamics The ideal gas law is a combination of three intuitive relationships between pressure, volume, temp and moles. David J. Starling Penn State Hazleton Fall 2013 When a gas expands, it

More information

Physics 360 Review 3

Physics 360 Review 3 Physics 360 Review 3 The test will be similar to the second test in that calculators will not be allowed and that the Unit #2 material will be divided into three different parts. There will be one problem

More information

Final Exam, Chemistry 481, 77 December 2016

Final Exam, Chemistry 481, 77 December 2016 1 Final Exam, Chemistry 481, 77 December 216 Show all work for full credit Useful constants: h = 6.626 1 34 J s; c (speed of light) = 2.998 1 8 m s 1 k B = 1.387 1 23 J K 1 ; R (molar gas constant) = 8.314

More information

Ch. 19: The Kinetic Theory of Gases

Ch. 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 information

Version 001 HW 15 Thermodynamics C&J sizemore (21301jtsizemore) 1

Version 001 HW 15 Thermodynamics C&J sizemore (21301jtsizemore) 1 Version 001 HW 15 Thermodynamics C&J sizemore 21301jtsizemore 1 This print-out should have 38 questions. Multiple-choice questions may continue on the next column or page find all choices before answering.

More information

Dr. Gundersen Phy 206 Test 2 March 6, 2013

Dr. 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 information

Multivariable Calculus

Multivariable Calculus Multivariable Calculus In thermodynamics, we will frequently deal with functions of more than one variable e.g., P PT, V, n, U UT, V, n, U UT, P, n U = energy n = # moles etensive variable: depends on

More information

Lecture 8. The Second Law of Thermodynamics; Energy Exchange

Lecture 8. The Second Law of Thermodynamics; Energy Exchange Lecture 8 The Second Law of Thermodynamics; Energy Exchange The second law of thermodynamics Statistics of energy exchange General definition of temperature Why heat flows from hot to cold Reading for

More information

Part II: Statistical Physics

Part II: Statistical Physics Chapter 6: Boltzmann Statistics SDSMT, Physics Fall Semester: Oct. - Dec., 2014 1 Introduction: Very brief 2 Boltzmann Factor Isolated System and System of Interest Boltzmann Factor The Partition Function

More information

Lecture Notes 2014March 13 on Thermodynamics A. First Law: based upon conservation of energy

Lecture Notes 2014March 13 on Thermodynamics A. First Law: based upon conservation of energy Dr. W. Pezzaglia Physics 8C, Spring 2014 Page 1 Lecture Notes 2014March 13 on Thermodynamics A. First Law: based upon conservation of energy 1. Work 1 Dr. W. Pezzaglia Physics 8C, Spring 2014 Page 2 (c)

More information

Set 3: Thermal Physics

Set 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 information

Chapter 2 Carnot Principle

Chapter 2 Carnot Principle Chapter 2 Carnot Principle 2.1 Temperature 2.1.1 Isothermal Process When two bodies are placed in thermal contact, the hotter body gives off heat to the colder body. As long as the temperatures are different,

More information

Enthalpy and Adiabatic Changes

Enthalpy and Adiabatic Changes Enthalpy and Adiabatic Changes Chapter 2 of Atkins: The First Law: Concepts Sections 2.5-2.6 of Atkins (7th & 8th editions) Enthalpy Definition of Enthalpy Measurement of Enthalpy Variation of Enthalpy

More information

8.21 The Physics of Energy Fall 2009

8.21 The Physics of Energy Fall 2009 MIT OpenCourseWare http://ocw.mit.edu 8.21 The Physics of Energy Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.21 Lecture 9 Heat Engines

More information

Lecture 8. The Second Law of Thermodynamics; Energy Exchange

Lecture 8. The Second Law of Thermodynamics; Energy Exchange Lecture 8 The Second Law of Thermodynamics; Energy Exchange The second law of thermodynamics Statistics of energy exchange General definition of temperature Why heat flows from hot to cold Reading for

More information

Problem: Calculate the entropy change that results from mixing 54.0 g of water at 280 K with 27.0 g of water at 360 K in a vessel whose walls are

Problem: Calculate the entropy change that results from mixing 54.0 g of water at 280 K with 27.0 g of water at 360 K in a vessel whose walls are Problem: Calculate the entropy change that results from mixing 54.0 g of water at 280 K with 27.0 g of water at 360 K in a vessel whose walls are perfectly insulated from the surroundings. Is this a spontaneous

More information

Specific Heat of Diatomic Gases and. The Adiabatic Process

Specific Heat of Diatomic Gases and. The Adiabatic Process Specific Heat of Diatomic Gases and Solids The Adiabatic Process Ron Reifenberger Birck Nanotechnology Center Purdue University February 22, 2012 Lecture 7 1 Specific Heat for Solids and Diatomic i Gasses

More information

Physics 4C Chapter 19: The Kinetic Theory of Gases

Physics 4C Chapter 19: The Kinetic Theory of Gases Physics 4C Chapter 19: The Kinetic Theory of Gases Whether you think you can or think you can t, you re usually right. Henry Ford The only thing in life that is achieved without effort is failure. Source

More information

1 mol ideal gas, PV=RT, show the entropy can be written as! S = C v. lnt + RlnV + cons tant

1 mol ideal gas, PV=RT, show the entropy can be written as! S = C v. lnt + RlnV + cons tant 1 mol ideal gas, PV=RT, show the entropy can be written as! S = C v lnt + RlnV + cons tant (1) p, V, T change Reversible isothermal process (const. T) TdS=du-!W"!S = # "Q r = Q r T T Q r = $W = # pdv =

More information

Internal Degrees of Freedom

Internal Degrees of Freedom Physics 301 16-Oct-2002 15-1 Internal Degrees of Freedom There are several corrections we might make to our treatment of the ideal gas If we go to high occupancies our treatment using the Maxwell-Boltzmann

More information

University of Illinois at Chicago Department of Physics SOLUTIONS. Thermodynamics and Statistical Mechanics Qualifying Examination

University of Illinois at Chicago Department of Physics SOLUTIONS. Thermodynamics and Statistical Mechanics Qualifying Examination University of Illinois at Chicago Department of Physics SOLUTIONS Thermodynamics and Statistical Mechanics Qualifying Eamination January 7, 2 9: AM to 2: Noon Full credit can be achieved from completely

More information

Module 5 : Electrochemistry Lecture 21 : Review Of Thermodynamics

Module 5 : Electrochemistry Lecture 21 : Review Of Thermodynamics Module 5 : Electrochemistry Lecture 21 : Review Of Thermodynamics Objectives In this Lecture you will learn the following The need for studying thermodynamics to understand chemical and biological processes.

More information

Some properties of the Helmholtz free energy

Some properties of the Helmholtz free energy Some properties of the Helmholtz free energy Energy slope is T U(S, ) From the properties of U vs S, it is clear that the Helmholtz free energy is always algebraically less than the internal energy U.

More information

Thermodynamics Boltzmann (Gibbs) Distribution Maxwell-Boltzmann Distribution Second Law Entropy

Thermodynamics Boltzmann (Gibbs) Distribution Maxwell-Boltzmann Distribution Second Law Entropy Thermodynamics Boltzmann (Gibbs) Distribution Maxwell-Boltzmann Distribution Second Law Entropy Lana Sheridan De Anza College May 8, 2017 Last time modeling an ideal gas at the microscopic level pressure,

More information

Chapter 3. Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc.

Chapter 3. Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc. Chapter 3 Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc. Concepts Energy functions F and G Chemical potential, µ Partial Molar properties

More information

Statistical Mechanics Notes. Ryan D. Reece

Statistical 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 information

Physics 607 Final Exam

Physics 607 Final Exam Physics 607 Final Exam Please show all significant steps clearly in all problems. 1. Let E,S,V,T, and P be the internal energy, entropy, volume, temperature, and pressure of a system in thermodynamic equilibrium

More information

Classical Physics I. PHY131 Lecture 36 Entropy and the Second Law of Thermodynamics. Lecture 36 1

Classical Physics I. PHY131 Lecture 36 Entropy and the Second Law of Thermodynamics. Lecture 36 1 Classical Physics I PHY131 Lecture 36 Entropy and the Second Law of Thermodynamics Lecture 36 1 Recap: (Ir)reversible( Processes Reversible processes are processes that occur under quasi-equilibrium conditions:

More information

MCQs THERMODYNAMICS. Physics Without Fear.

MCQs THERMODYNAMICS. Physics Without Fear. MCQs THERMODYNAMICS Physics Without Fear Thermodynamics: At a glance Zeroth law of thermodynamics: Two systems A and B each in thermal equilibrium with a third system C are in thermal equilibrium with

More information

Entropy in Macroscopic Systems

Entropy in Macroscopic Systems Lecture 15 Heat Engines Review & Examples p p b b Hot reservoir at T h p a a c adiabats Heat leak Heat pump Q h Q c W d V 1 V 2 V Cold reservoir at T c Lecture 15, p 1 Review Entropy in Macroscopic Systems

More information

+ 1. which gives the expected number of Fermions in energy state ɛ. The expected number of Fermions in energy range ɛ to ɛ + dɛ is then dn = n s g s

+ 1. which gives the expected number of Fermions in energy state ɛ. The expected number of Fermions in energy range ɛ to ɛ + dɛ is then dn = n s g s Chapter 8 Fermi Systems 8.1 The Perfect Fermi Gas In this chapter, we study a gas of non-interacting, elementary Fermi particles. Since the particles are non-interacting, the potential energy is zero,

More information

UNIVERSITY OF SOUTHAMPTON

UNIVERSITY OF SOUTHAMPTON UNIVERSIY OF SOUHAMPON PHYS1013W1 SEMESER 2 EXAMINAION 2013-2014 Energy and Matter Duration: 120 MINS (2 hours) his paper contains 9 questions. Answers to Section A and Section B must be in separate answer

More information

Chapter 3. Entropy, temperature, and the microcanonical partition function: how to calculate results with statistical mechanics.

Chapter 3. Entropy, temperature, and the microcanonical partition function: how to calculate results with statistical mechanics. Chapter 3. Entropy, temperature, and the microcanonical partition function: how to calculate results with statistical mechanics. The goal of equilibrium statistical mechanics is to calculate the density

More information

The Second Law of Thermodynamics (Chapter 4)

The Second Law of Thermodynamics (Chapter 4) The Second Law of Thermodynamics (Chapter 4) First Law: Energy of universe is constant: ΔE system = - ΔE surroundings Second Law: New variable, S, entropy. Changes in S, ΔS, tell us which processes made

More information

Lecture 6 Free Energy

Lecture 6 Free Energy Lecture 6 Free Energy James Chou BCMP21 Spring 28 A quick review of the last lecture I. Principle of Maximum Entropy Equilibrium = A system reaching a state of maximum entropy. Equilibrium = All microstates

More information

Unit 05 Kinetic Theory of Gases

Unit 05 Kinetic Theory of Gases Unit 05 Kinetic Theory of Gases Unit Concepts: A) A bit more about temperature B) Ideal Gas Law C) Molar specific heats D) Using them all Unit 05 Kinetic Theory, Slide 1 Temperature and Velocity Recall:

More information

Adiabats and entropy (Hiroshi Matsuoka) In this section, we will define the absolute temperature scale and entropy.

Adiabats and entropy (Hiroshi Matsuoka) In this section, we will define the absolute temperature scale and entropy. 1184 Adiabats and entropy (Hiroshi Matsuoka In this section, we will define the absolute temperature scale and entropy Quasi-static adiabatic processes and adiabats Suppose that we have two equilibrium

More information

Physics 123 Unit #2 Review

Physics 123 Unit #2 Review Physics 123 Unit #2 Review I. Definitions & Facts thermal equilibrium ideal gas thermal energy internal energy heat flow heat capacity specific heat heat of fusion heat of vaporization phase change expansion

More information

ChE 503 A. Z. Panagiotopoulos 1

ChE 503 A. Z. Panagiotopoulos 1 ChE 503 A. Z. Panagiotopoulos 1 STATISTICAL MECHANICAL ENSEMLES 1 MICROSCOPIC AND MACROSCOPIC ARIALES The central question in Statistical Mechanics can be phrased as follows: If particles (atoms, molecules,

More information

Physics 53. Thermal Physics 1. Statistics are like a bikini. What they reveal is suggestive; what they conceal is vital.

Physics 53. Thermal Physics 1. Statistics are like a bikini. What they reveal is suggestive; what they conceal is vital. Physics 53 Thermal Physics 1 Statistics are like a bikini. What they reveal is suggestive; what they conceal is vital. Arthur Koestler Overview In the following sections we will treat macroscopic systems

More information

Preliminary Examination - Day 2 May 16, 2014

Preliminary Examination - Day 2 May 16, 2014 UNL - Department of Physics and Astronomy Preliminary Examination - Day May 6, 04 This test covers the topics of Thermodynamics and Statistical Mechanics (Topic ) and Mechanics (Topic ) Each topic has

More information

4. All questions are NOT ofequal value. Marks available for each question are shown in the examination paper.

4. All questions are NOT ofequal value. Marks available for each question are shown in the examination paper. THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF PHYSICS \1111~11\llllllllllllftllll~flrllllllllll\11111111111111111 >014407892 PHYS2060 THER1\1AL PHYSICS FINAL EXAMINATION SESSION 2 - NOVEMBER 2010 I. Time

More information

Crystals. Peter Košovan. Dept. of Physical and Macromolecular Chemistry

Crystals. Peter Košovan. Dept. of Physical and Macromolecular Chemistry Crystals Peter Košovan peter.kosovan@natur.cuni.cz Dept. of Physical and Macromolecular Chemistry Lecture 1, Statistical Thermodynamics, MC26P15, 5.1.216 If you find a mistake, kindly report it to the

More information

Honors Physics. Notes Nov 16, 20 Heat. Persans 1

Honors Physics. Notes Nov 16, 20 Heat. Persans 1 Honors Physics Notes Nov 16, 20 Heat Persans 1 Properties of solids Persans 2 Persans 3 Vibrations of atoms in crystalline solids Assuming only nearest neighbor interactions (+Hooke's law) F = C( u! u

More information

Statistical thermodynamics L1-L3. Lectures 11, 12, 13 of CY101

Statistical thermodynamics L1-L3. Lectures 11, 12, 13 of CY101 Statistical thermodynamics L1-L3 Lectures 11, 12, 13 of CY101 Need for statistical thermodynamics Microscopic and macroscopic world Distribution of energy - population Principle of equal a priori probabilities

More information

The goal of equilibrium statistical mechanics is to calculate the diagonal elements of ˆρ eq so we can evaluate average observables < A >= Tr{Â ˆρ eq

The goal of equilibrium statistical mechanics is to calculate the diagonal elements of ˆρ eq so we can evaluate average observables < A >= Tr{Â ˆρ eq Chapter. The microcanonical ensemble The goal of equilibrium statistical mechanics is to calculate the diagonal elements of ˆρ eq so we can evaluate average observables < A >= Tr{Â ˆρ eq } = A that give

More information

Chapter 12. The Laws of Thermodynamics. First Law of Thermodynamics

Chapter 12. The Laws of Thermodynamics. First Law of Thermodynamics Chapter 12 The Laws of Thermodynamics First Law of Thermodynamics The First Law of Thermodynamics tells us that the internal energy of a system can be increased by Adding energy to the system Doing work

More information

Superposition & Interference

Superposition & Interference Lecture 29, Dec. 10 To do : Chapter 21 Understand beats as the superposition of two waves of unequal frequency. Prep for exam. Room 2103 Chamberlain Hall Sections: 602, 604, 605, 606, 610, 611, 612, 614

More information

I.G Approach to Equilibrium and Thermodynamic Potentials

I.G Approach to Equilibrium and Thermodynamic Potentials I.G Approach to Equilibrium and Thermodynamic otentials Evolution of non-equilibrium systems towards equilibrium is governed by the second law of thermodynamics. For eample, in the previous section we

More information

[S R (U 0 ɛ 1 ) S R (U 0 ɛ 2 ]. (0.1) k B

[S R (U 0 ɛ 1 ) S R (U 0 ɛ 2 ]. (0.1) k B Canonical ensemble (Two derivations) Determine the probability that a system S in contact with a reservoir 1 R to be in one particular microstate s with energy ɛ s. (If there is degeneracy we are picking

More information

Process Nature of Process

Process Nature of Process AP Physics Free Response Practice Thermodynamics 1983B. The pv-diagram above represents the states of an ideal gas during one cycle of operation of a reversible heat engine. The cycle consists of the following

More information

Thermodynamics is the Science of Energy and Entropy

Thermodynamics is the Science of Energy and Entropy Definition of Thermodynamics: Thermodynamics is the Science of Energy and Entropy - Some definitions. - The zeroth law. - Properties of pure substances. - Ideal gas law. - Entropy and the second law. Some

More information

Exam 1 (Chaps. 1-6 of the notes)

Exam 1 (Chaps. 1-6 of the notes) 10/12/06 ATS 541 - Atmospheric Thermodynamics and Cloud Physics 1 Exam 1 (Chaps. 1-6 of the notes) ATS 541 students: Answer all questions ATS 441 students: You may delete problem 3 or problem 5 1. [10

More information

Chemistry 1A, Spring 2007 Midterm Exam 3 April 9, 2007 (90 min, closed book)

Chemistry 1A, Spring 2007 Midterm Exam 3 April 9, 2007 (90 min, closed book) Chemistry 1A, Spring 2007 Midterm Exam 3 April 9, 2007 (90 min, closed book) Name: KEY SID: TA Name: 1.) Write your name on every page of this exam. 2.) This exam has 34 multiple choice questions. Fill

More information

On my honor as a Texas A&M University student, I will neither give nor receive unauthorized help on this exam.

On my honor as a Texas A&M University student, I will neither give nor receive unauthorized help on this exam. Physics 201, Exam 4 Name (printed) On my honor as a Texas A&M University student, I will neither give nor receive unauthorized help on this exam. Name (signed) The multiple-choice problems carry no partial

More information

U(T), H(T), and Heat Capacities (C )

U(T), H(T), and Heat Capacities (C ) Chapter 3 U(T), H(T), and Heat Capacities (C ) Thermodynamics is a collection of useful relations between quantities, every one of which is independently measurable. What do such relations tell one about

More information

You MUST sign the honor pledge:

You MUST sign the honor pledge: CHEM 3411 MWF 9:00AM Fall 2010 Physical Chemistry I Exam #2, Version B (Dated: October 15, 2010) Name: GT-ID: NOTE: Partial Credit will be awarded! However, full credit will be awarded only if the correct

More information

Thermodynamic system is classified into the following three systems. (ii) Closed System It exchanges only energy (not matter) with surroundings.

Thermodynamic system is classified into the following three systems. (ii) Closed System It exchanges only energy (not matter) with surroundings. 1 P a g e The branch of physics which deals with the study of transformation of heat energy into other forms of energy and vice-versa. A thermodynamical system is said to be in thermal equilibrium when

More information

A thermodynamic system is taken from an initial state X along the path XYZX as shown in the PV-diagram.

A thermodynamic system is taken from an initial state X along the path XYZX as shown in the PV-diagram. AP Physics Multiple Choice Practice Thermodynamics 1. The maximum efficiency of a heat engine that operates between temperatures of 1500 K in the firing chamber and 600 K in the exhaust chamber is most

More information

Thermodynamics General

Thermodynamics General Thermodynamics General Lecture 5 Second Law and Entropy (Read pages 587-6; 68-63 Physics for Scientists and Engineers (Third Edition) by Serway) Review: The first law of thermodynamics tells us the energy

More information

Alternate Midterm Examination Physics 100 Feb. 20, 2014

Alternate Midterm Examination Physics 100 Feb. 20, 2014 Alternate Midterm Examination Physics 100 Feb. 20, 2014 Name/Student #: Instructions: Formulas at the back (you can rip that sheet o ). Questions are on both sides. Calculator permitted. Put your name

More information

Chapter 5. Simple Mixtures Fall Semester Physical Chemistry 1 (CHM2201)

Chapter 5. Simple Mixtures Fall Semester Physical Chemistry 1 (CHM2201) Chapter 5. Simple Mixtures 2011 Fall Semester Physical Chemistry 1 (CHM2201) Contents The thermodynamic description of mixtures 5.1 Partial molar quantities 5.2 The thermodynamic of Mixing 5.3 The chemical

More information

dv = adx, where a is the active area of the piston. In equilibrium, the external force F is related to pressure P as

dv = adx, where a is the active area of the piston. In equilibrium, the external force F is related to pressure P as Chapter 3 Work, heat and the first law of thermodynamics 3.1 Mechanical work Mechanical work is defined as an energy transfer to the system through the change of an external parameter. Work is the only

More information

(b) [ 3 points] What will be the change in Gibbs free energy function G in terms of RT, where R is the gas constant?

(b) [ 3 points] What will be the change in Gibbs free energy function G in terms of RT, where R is the gas constant? DAY TWO In this exam you will have to answer four questions in Thermal Physics and four in Quantum Mechanics. Read the instructions carefully since in some cases, but not all, you will have a choice of

More information

Physics Nov Cooling by Expansion

Physics Nov Cooling by Expansion Physics 301 19-Nov-2004 25-1 Cooling by Expansion Now we re going to change the subject and consider the techniques used to get really cold temperatures. Of course, the best way to learn about these techniques

More information

Reading Assignment #13 :Ch.23: (23-3,5,6,7,8), Ch24: (24-1,2,4,5,6) )] = 450J. ) ( 3x10 5 Pa) ( 1x10 3 m 3

Reading Assignment #13 :Ch.23: (23-3,5,6,7,8), Ch24: (24-1,2,4,5,6) )] = 450J. ) ( 3x10 5 Pa) ( 1x10 3 m 3 Ph70A Spring 004 Prof. Pui Lam SOLUTION Reading Assignment #3 :h.3: (3-3,5,6,7,8), h4: (4-,,4,5,6) Homework #3: First Law and Second of Thermodynamics Due: Monday 5/3/004.. A monatomic ideal gas is allowed

More information

Chapter 12. The Laws of Thermodynamics

Chapter 12. The Laws of Thermodynamics Chapter 12 The Laws of Thermodynamics First Law of Thermodynamics The First Law of Thermodynamics tells us that the internal energy of a system can be increased by Adding energy to the system Doing work

More information

Chapter 20 The Second Law of Thermodynamics

Chapter 20 The Second Law of Thermodynamics Chapter 20 The Second Law of Thermodynamics When we previously studied the first law of thermodynamics, we observed how conservation of energy provided us with a relationship between U, Q, and W, namely

More information

PH575 Spring Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5

PH575 Spring Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5 PH575 Spring 2009 Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5 PH575 Spring 2009 POP QUIZ Phonons are: A. Fermions B. Bosons C. Lattice vibrations D. Light/matter interactions PH575 Spring 2009 POP QUIZ

More information

2. Thermodynamics. Introduction. Understanding Molecular Simulation

2. Thermodynamics. Introduction. Understanding Molecular Simulation 2. Thermodynamics Introduction Molecular Simulations Molecular dynamics: solve equations of motion r 1 r 2 r n Monte Carlo: importance sampling r 1 r 2 r n How do we know our simulation is correct? Molecular

More information

12 The Laws of Thermodynamics

12 The Laws of Thermodynamics June 14, 1998 12 The Laws of Thermodynamics Using Thermal Energy to do Work Understanding the laws of thermodynamics allows us to use thermal energy in a practical way. The first law of thermodynamics

More information

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 8 Introduction to Vapour Power Cycle Today, we will continue

More information

Physics 112 The Classical Ideal Gas

Physics 112 The Classical Ideal Gas Physics 112 The Classical Ideal Gas Peter Young (Dated: February 6, 2012) We will obtain the equation of state and other properties, such as energy and entropy, of the classical ideal gas. We will start

More information

Thermodynamics and Phase Transitions in Minerals

Thermodynamics and Phase Transitions in Minerals Studiengang Geowissenschaften M.Sc. Wintersemester 2004/05 Thermodynamics and Phase Transitions in Minerals Victor Vinograd & Andrew Putnis Basic thermodynamic concepts One of the central themes in Mineralogy

More information

Pressure Volume Temperature Relationship of Pure Fluids

Pressure Volume Temperature Relationship of Pure Fluids Pressure Volume Temperature Relationship of Pure Fluids Volumetric data of substances are needed to calculate the thermodynamic properties such as internal energy and work, from which the heat requirements

More information

You MUST sign the honor pledge:

You MUST sign the honor pledge: Chemistry 3411 MWF 9:00AM Spring 2009 Physical Chemistry I Final Exam, Version A (Dated: April 30, 2009 Name: GT-ID: NOTE: Partial Credit will be awarded! However, full credit will be awarded only if the

More information

PHYSICS DEPARTMENT, PRINCETON UNIVERSITY PHYSICS 301 FINAL EXAMINATION. January 13, 2005, 7:30 10:30pm, Jadwin A10 SOLUTIONS

PHYSICS DEPARTMENT, PRINCETON UNIVERSITY PHYSICS 301 FINAL EXAMINATION. January 13, 2005, 7:30 10:30pm, Jadwin A10 SOLUTIONS PHYSICS DEPARTMENT, PRINCETON UNIVERSITY PHYSICS 301 FINAL EXAMINATION January 13, 2005, 7:30 10:30pm, Jadwin A10 SOLUTIONS This exam contains five problems. Work any three of the five problems. All problems

More information

Copyright 2008, University of Chicago, Department of Physics. Experiment I. RATIO OF SPECIFIC HEATS OF GASES; γ C p

Copyright 2008, University of Chicago, Department of Physics. Experiment I. RATIO OF SPECIFIC HEATS OF GASES; γ C p Experiment I RATIO OF SPECIFIC HEATS OF GASES; γ C p / C v 1. Recommended Reading M. W. Zemansky, Heat and Thermodynamics, Fifth Edition, McGraw Hill, 1968, p. 122-132, 161-2. 2. Introduction You have

More information

U = 4.18 J if we heat 1.0 g of water through 1 C. U = 4.18 J if we cool 1.0 g of water through 1 C.

U = 4.18 J if we heat 1.0 g of water through 1 C. U = 4.18 J if we cool 1.0 g of water through 1 C. CHAPER LECURE NOES he First Law of hermodynamics: he simplest statement of the First Law is as follows: U = q + w. Here U is the internal energy of the system, q is the heat and w is the work. CONVENIONS

More information

PHY 206 SPRING Problem #1 NAME: SIGNATURE: UM ID: Problem #2. Problem #3. Total. Prof. Massimiliano Galeazzi. Midterm #2 March 8, 2006

PHY 206 SPRING Problem #1 NAME: SIGNATURE: UM ID: Problem #2. Problem #3. Total. Prof. Massimiliano Galeazzi. Midterm #2 March 8, 2006 PHY 06 SPRING 006 Prof. Massimiliano Galeazzi Midterm # March 8, 006 NAME: Problem # SIGNAURE: UM ID: Problem # Problem # otal Some useful relations: st lat of thermodynamic: U Q - W Heat in an isobaric

More information

Physics 2101, Final Exam, Form A

Physics 2101, Final Exam, Form A Physics 2101, Final Exam, Form A December 11, 2007 Name: SOLUTIONS Section: (Circle one) 1 (Rupnik, MWF 7:40am) 2 (Rupnik, MWF 9:40am) 3 (González, MWF 2:40pm) 4 (Pearson, TTh 9:10am) 5 (Pearson, TTh 12:10pm)

More information

Chapter 19: The Kinetic Theory of Gases Questions and Example Problems

Chapter 19: The Kinetic Theory of Gases Questions and Example Problems Chapter 9: The Kinetic Theory of Gases Questions and Example Problems N M V f N M Vo sam n pv nrt Nk T W nrt ln B A molar nmv RT k T rms B p v K k T λ rms avg B V M m πd N/V Q nc T Q nc T C C + R E nc

More information

Atkins / Paula Physical Chemistry, 8th Edition. Chapter 3. The Second Law

Atkins / Paula Physical Chemistry, 8th Edition. Chapter 3. The Second Law Atkins / Paula Physical Chemistry, 8th Edition Chapter 3. The Second Law The direction of spontaneous change 3.1 The dispersal of energy 3.2 Entropy 3.3 Entropy changes accompanying specific processes

More information

CONTENTS 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. 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 information

Distinguish between. and non-thermal energy sources.

Distinguish between. and non-thermal energy sources. Distinguish between System & Surroundings We also distinguish between thermal We also distinguish between thermal and non-thermal energy sources. P Work The gas in the cylinder is the system How much work

More information

Definite Integral and the Gibbs Paradox

Definite Integral and the Gibbs Paradox Acta Polytechnica Hungarica ol. 8, No. 4, 0 Definite Integral and the Gibbs Paradox TianZhi Shi College of Physics, Electronics and Electrical Engineering, HuaiYin Normal University, HuaiAn, JiangSu, China,

More information

Speed Distribution at CONSTANT Temperature is given by the Maxwell Boltzmann Speed Distribution

Speed 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 information

UNIVERSITY 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:- 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 information

Dept. of Materials Science & Engineering. Problem Set 2 Solutions

Dept. of Materials Science & Engineering. Problem Set 2 Solutions Problem Set 2 Solutions 1. Using dv and ds as a function of T and P that we derived in class, fully derive the rest of toolbox 3 (i.e., du, dh, df, and dg). See DeHoff pages 73 74, equations 4.41 4.43.

More information

Lecture 30. Chapter 21 Examine two wave superposition (-ωt and +ωt) Examine two wave superposition (-ω 1 t and -ω 2 t)

Lecture 30. Chapter 21 Examine two wave superposition (-ωt and +ωt) Examine two wave superposition (-ω 1 t and -ω 2 t) To do : Lecture 30 Chapter 21 Examine two wave superposition (-ωt and +ωt) Examine two wave superposition (-ω 1 t and -ω 2 t) Review for final (Location: CHEM 1351, 7:45 am ) Tomorrow: Review session,

More information

S = k log W 11/8/2016 CHEM Thermodynamics. Change in Entropy, S. Entropy, S. Entropy, S S = S 2 -S 1. Entropy is the measure of dispersal.

S = k log W 11/8/2016 CHEM Thermodynamics. Change in Entropy, S. Entropy, S. Entropy, S S = S 2 -S 1. Entropy is the measure of dispersal. Entropy is the measure of dispersal. The natural spontaneous direction of any process is toward greater dispersal of matter and of energy. Dispersal of matter: Thermodynamics We analyze the constraints

More information