1 mol ideal gas, PV=RT, show the entropy can be written as! S = C v. lnt + RlnV + cons tant
|
|
|
- Magdalene Davidson
- 6 years ago
- Views:
Transcription
1 1 mol ideal gas, PV=RT, show the entropy can be written as! S = C v lnt + RlnV + cons tant
2 (1) p, V, T change Reversible isothermal process (const. T) TdS=du-!W"!S = # "Q r = Q r T T Q r = $W = # pdv = # nrt dv V!S = nr 1 V dv # = nrln V 2 V 1 = nrln P 1 P 2
3 Reversible isochoric process (const. V) HEATING TdS=du-!W" TdS = du = C v dt T 2!S = " C vdt = C v ln( T 2 ) T T 1 T 1 C v = T (!S!T ) v
4 Reversible isobaric process (const. P) TdS=du-!W" HEATING TdS = d(u + pv ) = dh = C p dt T 2!S = " C p dt = C p ln( T 2 ) T T 1 T 1 C p = T (!S!T ) p
5 A( 1mol, g, V1, T1)!B(1 mol, g,v2,t2)" P (P1,V1,T1) const. V (Px,V1,T2) const. T (P2,V2,T2) T 2!S 1 = " C vdt = C v ln( T 2 ) T T 1 T 1!S 2 = Rln V 2 V 1 = Rln P 1 P 2 V!S = C V,m ln T 2 T 1 + Rln V 2 V 1
6 A( 1mol, g, V1, T1)!B(1 mol, g,v2,t2)" TdS = du + pdv du = C v dt P = RT V TdS = C v dt + RT V dv ds = C v T dt + R V dv!s = C v ln T 2 T 1 + Rln V 2 V 1
7 P A( 1mol, g, P1, T1)!B(1 mol, g,p2,t2)" const. P (P1,V1,T1) (P1,Vx,T2) const. T T 2!S 1 = " C p dt = C p ln( T 2 ) T T 1 T 1 (P2,V2,T2) V!S 2 = Rln V 2 V 1 = Rln P 1 P 2!S = C p,m ln T 2 T 1 or!s = C p,m ln T 2 T 1 + Rln V 2 V 1 " Rln P 2 P 1
8 A( 1mol, g, V1, T1)!B(1 mol, g,v2,t2)" TdS = du + pdv du = dh! pdv! Vdp TdS = dh! VdP dh = C p dt V = RT P TdS = C p dt! RT P dp ds = C p T dt! R p dp "S = C p ln T 2 T 1! Rln P 2 P 1
9 A( 1mol, g, P1,V1)!B(1 mol, g,p2, V2)" Proof "!S = C p ln V 2 V 1 + C V ln p 2 p 1 We already have!!s = C p ln T 2 T 1 " Rln P 2 P 1 Ideal gas! T 2 T 1 = P 2 V 2 P 1 V 1!S = C p ln P 2 V 2 P 1 V 1 " Rln P 2 P 1 = C p ln V 2 V 1 + (C p " R)ln P 2 P 1 = C p ln V 2 V 1 + C V ln P 2 P 1
10 !S = C p ln V 2 V 1 + C V ln p 2 p 1 can be used to determine isentropic relationships between properties in states 1 and 2!!S = C p ln V 2 V 1 + C V ln p 2 p 1 = 0 C p C v ln V 2 V 1 + ln p 2 p 1 = 0 define C p C v =! ln[ p 2 p 1 ( V 2 V 1 )! ] = 0 Isentropic compression process on a T-S diagram! P 2 V 2! = P 1 V 1! What we have for adiabatic process (isentropic process)!
11 (2) mixing of different perfect gas at constant temperature and constant pressure mixing at constant T, p n 1 n 2 n 1 +n 2 T, p, V 1 T, p,v 2 T, p, V 1 +V 2 Two steps (1) n 1 T, p, V 1 n 1 T, p 1, V 1 +V 2 (2) n 2 T, p,v 2 n 2 T, p 2, V 1 +V 2 V 2!S = nrt " 1 dv = nrtln V 2 V V 1 V 1
12 (2) mixing of different perfect gas at constant temperature and constant pressure mixing at constant T, p n 1 n 2 n 1 +n 2 T, p, V 1 T, p,v 2 T, p, V 1 +V 2 at constant T, p! mix S = (n 1 Rlny 1 n 2 Rlny 2 ) y 1 1 y 2 1 so! mix S
13 ! mix S = (n 1 Rlny 1 n 2 Rlny 2 ) y 1 1 y 2 1 so! mix S
14
15 2. The phase transition (1) The phase transition at transition temperature At constant T, p, the two phase in the system are in equilibrium, the process is reversible, and W" so Q p!h! fus H m! vap H m S m (s) S m (l) S m (g)
16
17 (2) irreversible phase transition eg.!s!s!s!s
18 Supercooled Water " Supercooling was discovered already in 1724 by Fahrenheit, but even today the phenomenon remains a subject for intense discussions.! Supercooled water freezes at different temperatures in the presence of a surface with a positive or negative charge Science 2010, 327, 672. Supercool: Water Doesn't Have to Freeze Until -48 C (-55 F) Nature, 2011, 479, 506
19
20
21 For example H 2 O l, 90,100kPa)!S =? Irreversible H 2 O g, 90, 100kPa)!S 1!S 3!S 2 H 2 O l, 100, 100kPa) H 2 O g, 100, 100kPa) Reversible!S!S!S!S
22 Absolute Entropies "
23 "S m =S m (298.15K) S m (0K)= J/K mol.!
24
25 2.2 The third law The third law Nernst heat theorem (1905): The entropy change accompanying any physical or chemical transformation approaches zero as the temperature approaches zero:!s!0,!t!0 More general and useful formulation! Planck (1911): The entropy of all perfect crystalline substance is zero at 0 K. S * (perfect crystalline 0 K) -
26 Lowest Achieved Temperature! Achieved by MIT researchers in 2003! 0.45 nk =4.5 x K! You can approach 0K, but can not reach the limit.!
27 2.2.3 The entropy change of chemical reaction For reaction aa b B #yy zz! r S! m( T) $! S! m B,%,T )! r S! m (298.15K) $! S! m B, %,298.15K )! r S! m (T) = ys! m (Y, %,T ) z S! m (Z, %,T ) a S! m (A, %,T ) b S! m (B, %,T )
28 Standard entropy S o (at K and 1 bar)!
29
30 2.3 Helmholtz and Gibbs energies- Criteria for Spontaneous Change The 2 nd Law gave the Clausius inequality TdS &Q du = &Q +&W &W=-pdV 1 st Law TdS du+pdv Combined statement of 1 st and 2 nd Law "
31 Use the general criterion to under specific conditions " TdS du+pdv
32 TdS du+pdv
33 TdS du+pdv
34 TdS du+pdv
35
36 TdS du+pdv For constant V and constant T=T surr, equilibrium is achieved! when the Helmholtz free energy is minimized!
37 TdS du+pdv For constant P=P ext and constant T=T surr, equilibrium is achieved when the Gibbs free energy is minimized!
38
39 2.3.3 Calculation of!a and!g (1) change p,v at constant temperature du = TdS - pdv A =U-TS da = - SdT - pdv at constant T, reversible da T pdv V 2!A T = "# pdv V 1 closed system, change p,v at constant T, W! 0 reversible process For perfect gas
40 du = TdS - pdv H =U+PV G=H-TS dg = - SdT + Vdp at constant T, reversible dg T Vdp closed system, change p,v at constant T, reversible process For an perfect gas
41 (2) phase transition (i) reversible phase transition G =H - (TS)!G =!H-!(TS) =!H- T!S reversible phase transition at constant T and p!h =T!S!G=!H- T!S = 0
42 (i) reversible phase transition A = U - (TS)!A =!U -!(TS) =!U - T!S reversible vaporization or sublimation at constant T and p, and vapor is an perfect gas!u =!H-!(pV) =!H- p!v =!H- nrt!a =!U -!(TS) =!H - nrt - T!S = - nrt (ii) irreversible phase transition
43 2.3.4 Fundamental relations of thermodynamic functions U, H, S, A, G, p, V and T H = U + pv
44 1. Fundamental equations of thermodynamic For a reversible change If &W r " 0 then &W r pdv &Q r TdS du=&q r +&W r H =U+pV A =U-TS G =H-TS du = TdS - pdv dh = TdS + Vdp da = - SdT - pdv dg = - SdT + Vdp closed system of constant composition reversible process volume work only. Fundamental equation of thermodynamic
45 dz = M dx + N dy du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = SdT + Vdp
46 2. Maxwell s relation dz = M dx + N dy du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = SdT + Vdp
47 Quotient Rule for Derivatives! Product Rule! [ f (x) g(x) ]' = [ f (x) 1 g(x) ]' = f (x)[ 1 g(x) ]'+ f (x)' 1 g(x) =! f (x)g'(x) g 2 (x) = + f (x)' 1 g(x) f (x)'g(x)! f (x)g'(x) g 2 (x)
48 3. Gibbs - helmholtz equation dg = SdT + Vdp " # $!(G / T )!T % & ' = ( H V T 2
49 3. Gibbs - helmholtz equation " # $!(A / T )!T % & ' = V T " # $! A!T % & ' " ( A!T # $!T V T 2 =!TS! A T 2 % & ' V da = SdT pdv =! U T 2 " # $!(A / T )!T % & ' = ( U V T 2
50 2.4 Chemical potential Chemical potential Consider a system that consists of a single homogeneous phase whose composition can be varied G f (T p n A n B ) Total differential
51
52 Chemical potential is an intensive state function. µ B of pure substance G * (T p n B ) = n B G * m,b (T p )
53 Heterogeneous system du = " T! ds! #" p! dv! + " µ! dn! B B!! "! B
54 2.4.2 Equilibrium criterion of substance (1) Condition of phase equilibrium dn B B(') B(% ) T p µ B! = µ B " Condition of phase equilibrium µ B! > µ B " '!% spontaneous
55 (2) Condition of chemical reaction equilibrium Chemical reaction Homogeneous system d" $v B µ B 0 d" 0 spontaneous $v B µ B 0 equilibrium For example aa bb yy zz aµ A +bµ B yµ Y +zµ Z
56 A potential of chemical reaction aa bb yy zz A= (aµ A +bµ B ) -( yµ Y +zµ Z ) A 0 at equilibrium A 0 right spontaneous A 0 left spontaneous
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
Lecture 4 Clausius Inequality
Lecture 4 Clausius Inequality Entropy distinguishes between irreversible and reversible processes. irrev S > 0 rev In a spontaneous process, there should be a net increase in the entropy of the system
Thermodynamic Variables and Relations
MME 231: Lecture 10 Thermodynamic Variables and Relations A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Thermodynamic relations derived from the Laws of Thermodynamics Definitions
Lecture 4 Clausius Inequality
Lecture 4 Clausius Inequality We know: Heat flows from higher temperature to lower temperature. T A V A U A + U B = constant V A, V B constant S = S A + S B T B V B Diathermic The wall insulating, impermeable
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.
ESCI 341 Atmospheric Thermodynamics Lesson 12 The Energy Minimum Principle
ESCI 341 Atmospheric Thermodynamics Lesson 12 The Energy Minimum Principle References: Thermodynamics and an Introduction to Thermostatistics, Callen Physical Chemistry, Levine THE ENTROPY MAXIMUM PRINCIPLE
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)
Concentrating on the system
Concentrating on the system Entropy is the basic concept for discussing the direction of natural change, but to use it we have to analyze changes in both the system and its surroundings. We have seen that
where R = universal gas constant R = PV/nT R = atm L mol R = atm dm 3 mol 1 K 1 R = J mol 1 K 1 (SI unit)
Ideal Gas Law PV = nrt where R = universal gas constant R = PV/nT R = 0.0821 atm L mol 1 K 1 R = 0.0821 atm dm 3 mol 1 K 1 R = 8.314 J mol 1 K 1 (SI unit) Standard molar volume = 22.4 L mol 1 at 0 C and
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
Practice Examinations Chem 393 Fall 2005 Time 1 hr 15 min for each set.
Practice Examinations Chem 393 Fall 2005 Time 1 hr 15 min for each set. The symbols used here are as discussed in the class. Use scratch paper as needed. Do not give more than one answer for any question.
CHAPTER 3 LECTURE NOTES 3.1. The Carnot Cycle Consider the following reversible cyclic process involving one mole of an ideal gas:
CHATER 3 LECTURE NOTES 3.1. The Carnot Cycle Consider the following reversible cyclic process involving one mole of an ideal gas: Fig. 3. (a) Isothermal expansion from ( 1, 1,T h ) to (,,T h ), (b) Adiabatic
even at constant T and P, many reversible and irreversible changes of thermodynamic state may
Chapter 5 Spontaneity and Equilibrium: Free Energy 5.1 Spontaneity and Equilibrium Let us consider that a system is at a constant temperature, T and a constant pressure (P). Note, even at constant T and
Physical Chemistry Physical chemistry is the branch of chemistry that establishes and develops the principles of Chemistry in terms of the underlying concepts of Physics Physical Chemistry Main book: Atkins
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
Last Name or Student ID
10/06/08, Chem433 Exam # 1 Last Name or Student ID 1. (3 pts) 2. (3 pts) 3. (3 pts) 4. (2 pts) 5. (2 pts) 6. (2 pts) 7. (2 pts) 8. (2 pts) 9. (6 pts) 10. (5 pts) 11. (6 pts) 12. (12 pts) 13. (22 pts) 14.
Summarizing, Key Point: An irreversible process is either spontaneous (ΔS universe > 0) or does not occur (ΔS universe < 0)
Summarizing, Key Point: An irreversible process is either spontaneous (ΔS universe > 0) or does not occur (ΔS universe < 0) Key Point: ΔS universe allows us to distinguish between reversible and irreversible
Lecture 3 Clausius Inequality
Lecture 3 Clausius Inequality Rudolf Julius Emanuel Clausius 2 January 1822 24 August 1888 Defined Entropy Greek, en+tropein content transformative or transformation content The energy of the universe
NENG 301 Week 8 Unary Heterogeneous Systems (DeHoff, Chap. 7, Chap )
NENG 301 Week 8 Unary Heterogeneous Systems (DeHoff, Chap. 7, Chap. 5.3-5.4) Learning objectives for Chapter 7 At the end of this chapter you will be able to: Understand the general features of a unary
MS212 Thermodynamics of Materials ( 소재열역학의이해 ) Lecture Note: Chapter 7
2017 Spring Semester MS212 Thermodynamics of Materials ( 소재열역학의이해 ) Lecture Note: Chapter 7 Byungha Shin ( 신병하 ) Dept. of MSE, KAIST Largely based on lecture notes of Prof. Hyuck-Mo Lee and Prof. WooChul
MME 2010 METALLURGICAL THERMODYNAMICS II. Fundamentals of Thermodynamics for Systems of Constant Composition
MME 2010 METALLURGICAL THERMODYNAMICS II Fundamentals of Thermodynamics for Systems of Constant Composition Thermodynamics addresses two types of problems: 1- Computation of energy difference between two
CHAPTER 6 CHEMICAL EQUILIBRIUM
CHAPTER 6 CHEMICAL EQUILIBRIUM Spontaneous process involving a reactive mixture of gases Two new state functions A: criterion for determining if a reaction mixture will evolve towards the reactants or
Solutions to Problem Set 6
Solutions to Problem Set 6 1. non- ideal gas, 1 mol 20.0 L 300 K 40.0 L 300 K isothermal, reversible Equation of state: (a)b is a constant independent of T Given du = ( U/ T) V dt + ( U/ V) T dv U = U(T,V)
Outline Review Example Problem 1 Example Problem 2. Thermodynamics. Review and Example Problems. X Bai. SDSMT, Physics. Fall 2013
Review and Example Problems SDSMT, Physics Fall 013 1 Review Example Problem 1 Exponents of phase transformation 3 Example Problem Application of Thermodynamic Identity : contents 1 Basic Concepts: Temperature,
10, Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Subect Chemistry Paper No and Title Module No and Title Module Tag 0, Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics) 0, Free energy
CHEMICAL THERMODYNAMICS
DEPARTMENT OF APPLIED CHEMISTRY LECTURE NOTES 6151- ENGINEERING CHEMISTRY-II UNIT II CHEMICAL THERMODYNAMICS Unit syllabus: Terminology of thermodynamics - Second law: Entropy - entropy change for an ideal
Thermodynamics II. Week 9
hermodynamics II Week 9 Example Oxygen gas in a piston cylinder at 300K, 00 kpa with volume o. m 3 is compressed in a reversible adiabatic process to a final temperature of 700K. Find the final pressure
Effect of adding an ideal inert gas, M
Effect of adding an ideal inert gas, M Add gas M If there is no change in volume, then the partial pressures of each of the ideal gas components remains unchanged by the addition of M. If the reaction
University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014
Lecture 11 07/18/14 University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014 A. he Helmholt Free Energy and Reversible Work he entropy change S provides an absolutely general
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
I affirm that I have never given nor received aid on this examination. I understand that cheating in the exam will result in a grade F for the class.
Chem340 Physical Chemistry for Biochemists Exam Mar 16, 011 Your Name _ I affirm that I have never given nor received aid on this examination. I understand that cheating in the exam will result in a grade
...Thermodynamics. Entropy: The state function for the Second Law. Entropy ds = d Q. Central Equation du = TdS PdV
...Thermodynamics Entropy: The state function for the Second Law Entropy ds = d Q T Central Equation du = TdS PdV Ideal gas entropy s = c v ln T /T 0 + R ln v/v 0 Boltzmann entropy S = klogw Statistical
Chapter 3. The Second Law Fall Semester Physical Chemistry 1 (CHM2201)
Chapter 3. The Second Law 2011 Fall Semester Physical Chemistry 1 (CHM2201) Contents The direction of spontaneous change 3.1 The dispersal of energy 3.2 The entropy 3.3 Entropy changes accompanying specific
Chem Lecture Notes 6 Fall 2013 Second law
Chem 340 - Lecture Notes 6 Fall 2013 Second law In the first law, we determined energies, enthalpies heat and work for any process from an initial to final state. We could know if the system did work or
Thermodynamics of solids 5. Unary systems. Kwangheon Park Kyung Hee University Department of Nuclear Engineering
Thermodynamics of solids 5. Unary systems Kwangheon ark Kyung Hee University Department of Nuclear Engineering 5.1. Unary heterogeneous system definition Unary system: one component system. Unary heterogeneous
Measure separately. Properties D, E, F. Properties A, B, C. Thermodynamic relations
1 Review of Fundamentals The following brief notes cover some of the more important points which students have met in previous courses on thermodynamics. A principal objective of thermodynamics is to provide
Lecture 4. The Second Law of Thermodynamics
Lecture 4. The Second Law of Thermodynamics LIMITATION OF THE FIRST LAW: -Does not address whether a particular process is spontaneous or not. -Deals only with changes in energy. Consider this examples:
Outline Review Example Problem 1. Thermodynamics. Review and Example Problems: Part-2. X Bai. SDSMT, Physics. Fall 2014
Review and Example Problems: Part- SDSMT, Physics Fall 014 1 Review Example Problem 1 Exponents of phase transformation : contents 1 Basic Concepts: Temperature, Work, Energy, Thermal systems, Ideal Gas,
Liquids and Solids. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Liquids and Solids Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Gases, Liquids and Solids Gases are compressible fluids. They have no proper volume and proper
SPONTANEOUS PROCESSES AND THERMODYNAMIC EQUILIBRIUM
13 CHAPER SPONANEOUS PROCESSES AND HERMODYNAMIC EQUILIBRIUM 13.1 he Nature of Spontaneous Processes 13.2 Entropy and Spontaneity: A Molecular Statistical Interpretation 13.3 Entropy and Heat: Macroscopic
The Standard Gibbs Energy Change, G
The Standard Gibbs Energy Change, G S univ = S surr + S sys S univ = H sys + S sys T S univ = H sys TS sys G sys = H sys TS sys Spontaneous reaction: S univ >0 G sys < 0 More observations on G and Gº I.
The Gibbs Phase Rule F = 2 + C - P
The Gibbs Phase Rule The phase rule allows one to determine the number of degrees of freedom (F) or variance of a chemical system. This is useful for interpreting phase diagrams. F = 2 + C - P Where F
Chapter 4: Partial differentiation
Chapter 4: Partial differentiation It is generally the case that derivatives are introduced in terms of functions of a single variable. For example, y = f (x), then dy dx = df dx = f. However, most of
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
Lecture. Polymer Thermodynamics 0331 L First and Second Law of Thermodynamics
1 Prof. Dr. rer. nat. habil. S. Enders Faculty III for Process Science Institute of Chemical Engineering Department of hermodynamics Lecture Polymer hermodynamics 0331 L 337 2.1. First Law of hermodynamics
Chemistry 163B Absolute Entropies and Entropy of Mixing
Chemistry 163B Absolute Entropies and Entropy of Mixing 1 APPENDIX A: H f, G f, BUT S (no Δ, no sub f ) Hº f Gº f Sº 2 Third Law of Thermodynamics The entropy of any perfect crystalline substance approaches
Chapter 7. Entropy. by Asst.Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn
Chapter 7 Entropy by Asst.Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn Reference: Cengel, Yunus A. and Michael A. Boles, Thermodynamics: An Engineering Approach, 5th ed.,
4) It is a state function because enthalpy(h), entropy(s) and temperature (T) are state functions.
Chemical Thermodynamics S.Y.BSc. Concept of Gibb s free energy and Helmholtz free energy a) Gibb s free energy: 1) It was introduced by J.Willard Gibb s to account for the work of expansion due to volume
OCN 623: Thermodynamic Laws & Gibbs Free Energy. or how to predict chemical reactions without doing experiments
OCN 623: Thermodynamic Laws & Gibbs Free Energy or how to predict chemical reactions without doing experiments Definitions Extensive properties Depend on the amount of material e.g. # of moles, mass or
1. (10) True or False: A material with an ideal thermal equation of state must have a constant c v.
AME 54531 Intermediate hermodynamics Examination : Prof. J. M. Powers 7 November 018 1. 10) rue or False: A material with an ideal thermal equation of state must have a constant c v. False. Forsuchamaterialc
Minimum Bias Events at ATLAS
Camille Bélanger-Champagne McGill University Lehman College City University of New York Thermodynamics Charged Particle and Statistical Correlations Mechanics in Minimum Bias Events at ATLAS Thermodynamics
The Story of Spontaneity and Energy Dispersal. You never get what you want: 100% return on investment
The Story of Spontaneity and Energy Dispersal You never get what you want: 100% return on investment Spontaneity Spontaneous process are those that occur naturally. Hot body cools A gas expands to fill
The Chemical Potential
CHEM 331 Physical Chemistry Fall 2017 The Chemical Potential Here we complete our pivot towards chemical thermodynamics with the introduction of the Chemical Potential ( ). This concept was first introduced
Unit 7 (B) Solid state Physics
Unit 7 (B) Solid state Physics hermal Properties of solids: Zeroth law of hermodynamics: If two bodies A and B are each separated in thermal equilibrium with the third body C, then A and B are also in
Thermodynamics! for Environmentology!
1 Thermodynamics! for Environmentology! Thermodynamics and kinetics of natural systems Susumu Fukatsu! Applied Quantum Physics Group! The University of Tokyo, Komaba Graduate School of Arts and Sciences
General Physical Chemistry I
General Physical Chemistry I Lecture 11 Aleksey Kocherzhenko March 12, 2015" Last time " W Entropy" Let be the number of microscopic configurations that correspond to the same macroscopic state" Ø Entropy
Lecture 3 Evaluation of Entropy
Lecture 3 Evaluation of Entropy If we wish to designate S by a proper name we can say of it that it is the transformation content of the body, in the same way that we say of the quantity U that it is the
Gibb s free energy change with temperature in a single component system
Gibb s free energy change with temperature in a single component system An isolated system always tries to maximize the entropy. That means the system is stable when it has maximum possible entropy. Instead
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
Thermodynamics Free E and Phase D. J.D. Price
Thermodynamics Free E and Phase D J.D. Price Force - the acceleration of matter (N, kg m/s 2 ) Pressure (P)( ) - a force applied over an area (N/m 2 ) Work (W) - force multiplied by distance (kg( m 2 /s
CHEMICAL ENGINEERING THERMODYNAMICS. Andrew S. Rosen
CHEMICAL ENGINEERING THERMODYNAMICS Andrew S. Rosen SYMBOL DICTIONARY 1 TABLE OF CONTENTS Symbol Dictionary... 3 1. Measured Thermodynamic Properties and Other Basic Concepts... 5 1.1 Preliminary Concepts
HOMOGENEOUS CLOSED SYSTEM
CHAE II A closed system is one that does not exchange matter with its surroundings, although it may exchange energy. W n in = 0 HOMOGENEOUS CLOSED SYSEM System n out = 0 Q dn i = 0 (2.1) i = 1, 2, 3,...
THE SECOND LAW Chapter 3 Outline. HW: Questions are below. Solutions are in separate file on the course web site. Sect. Title and Comments Required?
THE SECOND LAW Chapter 3 Outline HW: Questions are below. Solutions are in separate file on the course web site. Sect. Title and Comments Required? 1. The Dispersal of Energy YES 2. Entropy YES We won
Introduction. Statistical physics: microscopic foundation of thermodynamics degrees of freedom 2 3 state variables!
Introduction Thermodynamics: phenomenological description of equilibrium bulk properties of matter in terms of only a few state variables and thermodynamical laws. Statistical physics: microscopic foundation
Thermodynamics. Chem 36 Spring The study of energy changes which accompany physical and chemical processes
Thermodynamics Chem 36 Spring 2002 Thermodynamics The study of energy changes which accompany physical and chemical processes Why do we care? -will a reaction proceed spontaneously? -if so, to what extent?
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.
Exam Thermodynamics 12 April 2018
1 Exam Thermodynamics 12 April 2018 Please, hand in your answers to problems 1, 2, 3 and 4 on separate sheets. Put your name and student number on each sheet. The examination time is 12:30 until 15:30.
Thermodynamic condition for equilibrium between two phases a and b is G a = G b, so that during an equilibrium phase change, G ab = G a G b = 0.
CHAPTER 5 LECTURE NOTES Phases and Solutions Phase diagrams for two one component systems, CO 2 and H 2 O, are shown below. The main items to note are the following: The lines represent equilibria between
Identify the intensive quantities from the following: (a) enthalpy (b) volume (c) refractive index (d) none of these
Q 1. Q 2. Q 3. Q 4. Q 5. Q 6. Q 7. The incorrect option in the following table is: H S Nature of reaction (a) negative positive spontaneous at all temperatures (b) positive negative non-spontaneous regardless
Chap. 3 The Second Law. Spontaneous change
Chap. 3 The Second Law Spontaneous change Some things happen naturally; some things don t. the spontaneous direction of change, the direction of change that does not require work to be done to bring it
Chpt 19: Chemical. Thermodynamics. Thermodynamics
CEM 152 1 Reaction Spontaneity Can we learn anything about the probability of a reaction occurring based on reaction enthaplies? in general, a large, negative reaction enthalpy is indicative of a spontaneous
Entropy Changes & Processes
Entropy Changes & Processes Chapter 4 of Atkins: The Second Law: The Concepts Section 4.4-4.7 Third Law of Thermodynamics Nernst Heat Theorem Third- Law Entropies Reaching Very Low Temperatures Helmholtz
Homework Problem Set 8 Solutions
Chemistry 360 Dr. Jean M. Standard Homework roblem Set 8 Solutions. Starting from G = H S, derive the fundamental equation for G. o begin, we take the differential of G, dg = dh d( S) = dh ds Sd. Next,
Chem 75 Winter, 2017 Practice Exam 1
This was Exam 1 last year. It is presented here with, first, just the problems and then with the problems and their solutions. YOU WILL BENEFIT MOST if you attempt first just the problems as if you were
Chapter 7. Entropy: A Measure of Disorder
Chapter 7 Entropy: A Measure of Disorder Entropy and the Clausius Inequality The second law of thermodynamics leads to the definition of a new property called entropy, a quantitative measure of microscopic
THERMODYNAMICS. Extensive properties Intensive properties
Thermodynamics The branch of chemistry deals with the energy change associated with chemical reactions is called chemical thermodynamics. System and surrounding A system may be defined as the specified
Chap. 3. The Second Law. Law of Spontaneity, world gets more random
Chap. 3. The Second Law Law of Spontaneity, world gets more random Kelvin - No process can transform heat completely into work Chap. 3. The Second Law Law of Spontaneity, world gets more random Kelvin
Thermodynamics of phase transitions
Thermodynamics of phase transitions Katarzyna Sznajd-Weron Department of Theoretical of Physics Wroc law University of Science and Technology, Poland March 12, 2017 Katarzyna Sznajd-Weron (WUST) Thermodynamics
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
1. (10) Calorically perfect ideal air at 300 K, 100 kpa, 1000 m/s, is brought to rest isentropically. Determine its final temperature.
AME 5053 Intermediate Thermodynamics Examination Prof J M Powers 30 September 0 0 Calorically perfect ideal air at 300 K, 00 kpa, 000 m/s, is brought to rest isentropically Determine its final temperature
Classical Thermodynamics. Dr. Massimo Mella School of Chemistry Cardiff University
Classical Thermodynamics Dr. Massimo Mella School of Chemistry Cardiff University E-mail:MellaM@cardiff.ac.uk The background The field of Thermodynamics emerged as a consequence of the necessity to understand
Thermodynamic Third class Dr. Arkan J. Hadi
5.5 ENTROPY CHANGES OF AN IDEAL GAS For one mole or a unit mass of fluid undergoing a mechanically reversible process in a closed system, the first law, Eq. (2.8), becomes: Differentiation of the defining
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
Physical Biochemistry. Kwan Hee Lee, Ph.D. Handong Global University
Physical Biochemistry Kwan Hee Lee, Ph.D. Handong Global University Week 3 CHAPTER 2 The Second Law: Entropy of the Universe increases What is entropy Definition: measure of disorder The greater the disorder,
THERMODYNAMICS NOTES. These notes give a brief overview of engineering thermodynamics. They are based on the thermodynamics text by Black & Hartley.
THERMODYNAMICS NOTES These notes give a brief overview of engineering thermodynamics. They are based on the thermodynamics text by Black & Hartley. Topics covered include: concepts; properties; conservation
Thermodynamics (Lecture Notes) Heat and Thermodynamics (7 th Edition) by Mark W. Zemansky & Richard H. Dittman
Thermodynamics (Lecture Notes Heat and Thermodynamics (7 th Edition by Mark W. Zemansky & Richard H. Dittman 2 Chapter 1 Temperature and the Zeroth Law of Thermodynamics 1.1 Macroscopic Point of View If
Pressure Volume Work 2
ressure olume Work Multi-stage Expansion 1 3 w= 4 5 ( ) + 3( 3 ) + 4( 4 3) + ( ) 1 5 5 4 Reversible Expansion Make steps so small that hen d 0, d 0 δ w= d ( ) = + d d int d int w= dw= d path 1 int For
Part 1: (18 points) Define or explain three out of the 6 terms or phrases, below. Limit definitions to 200 words or less.
Chemistry 452/456 23 July 24 Midterm Examination Key rofessor G. Drobny Boltzmann s constant=k B =1.38x1-23 J/K=R/N A, where N A is Avagadro s number and R is the Universal Gas Constant. Universal gas
Introduction to Chemical Thermodynamics. D. E. Manolopoulos First Year (13 Lectures) Michaelmas Term
Introduction to Chemical Thermodynamics D. E. Manolopoulos First Year (13 Lectures) Michaelmas Term Lecture Synopsis 1. Introduction & Background. Le Chatelier s Principle. Equations of state. Systems
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)
Preliminary Examination - Day 2 August 15, 2014
UNL - Department of Physics and Astronomy Preliminary Examination - Day 2 August 15, 2014 This test covers the topics of Thermodynamics and Statistical Mechanics (Topic 1) and Mechanics (Topic 2). Each
NAME and Section No. b). A refrigerator is a Carnot cycle run backwards. That is, heat is now withdrawn from the cold reservoir at T cold
Chemistry 391 Fall 007 Exam II KEY 1. (30 Points) ***Do 5 out of 7***(If 6 or 7 are done only the first 5 will be graded)*** a). How does the efficiency of a reversible engine compare with that of an irreversible
The underlying prerequisite to the application of thermodynamic principles to natural systems is that the system under consideration should be at equilibrium. http://eps.mcgill.ca/~courses/c220/ Reversible
Legendre Transforms, Thermodynamic Potentials and Equilibrium
CHEM 331 Physical Chemistry Fall 2017 Legendre Transforms, Thermodynamic Potentials and Equilibrium We now pivot to the development of new Thermodynamic Potentials which will allow us to more naturally
CHAPTER 4 Physical Transformations of Pure Substances.
I. Generalities. CHAPTER 4 Physical Transformations of Pure Substances. A. Definitions: 1. A phase of a substance is a form of matter that is uniform throughout in chemical composition and physical state.
Chapter 19. Entropy, Free Energy, and Equilibrium
Chapter 19 Entropy, Free Energy, and Equilibrium Spontaneous Physical and Chemical Processes A waterfall runs downhill A lump of sugar dissolves in a cup of coffee At 1 atm, water freezes below 0 0 C and
Challa Vijaya Kumar University of Connecticut Module 4. Physical Chemistry 1 (Thermodynamics) Module 4. Open Source Textbook. Challa Vijaya Kumar
Challa Vijaya Kumar University of Connecticut Module 4 Physical Chemistry 1 (Thermodynamics) Module 4 Open Source Textbook Challa Vijaya Kumar Department of Chemistry University of Connecticut Storrs CT
5.60 Thermodynamics & Kinetics Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 5.60 Thermodynamics & Kinetics Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.60 Spring 2008 Lecture
Physical Chemistry I Exam points
Chemistry 360 Fall 2018 Dr. Jean M. tandard October 17, 2018 Name Physical Chemistry I Exam 2 100 points Note: You must show your work on problems in order to receive full credit for any answers. You must
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