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E-grāmata: Statistical Thermodynamics

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(Emeritus Professor, University of Sheffield), (Reader in Theoretical Chemistry, University of Sheffield)
  • Formāts: 128 pages
  • Sērija : Oxford Chemistry Primers
  • Izdošanas datums: 25-May-2017
  • Izdevniecība: Oxford University Press
  • Valoda: eng
  • ISBN-13: 9780191083563
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Statistical ThermodynamicsPalielināt
  • Formāts: 128 pages
  • Sērija : Oxford Chemistry Primers
  • Izdošanas datums: 25-May-2017
  • Izdevniecība: Oxford University Press
  • Valoda: eng
  • ISBN-13: 9780191083563
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The renowned Oxford Chemistry Primers series, which provides focused introductions to a range of important topics in chemistry, has been refreshed and updated to suit the needs of today's students, lecturers, and postgraduate researchers. The rigorous, yet accessible, treatment of each subject area is ideal for those wanting a primer in a given topic to prepare them for more advanced study or research.

The learning features provided, including end of book problems and online multiple-choice questions, encourage active learning and promote understanding. Furthermore, frequent diagrams and margin notes help to enhance a student's understanding of these essential areas of chemistry.

Statistical Thermodynamics gives a concise and accessible account of this fundamental topic by emphasizing the underlying physical chemistry, and using this to introduce the mathematics in an approachable way. The material is presented in short, self-contained sections making it flexible to teach and learn from, and concludes with the application of the theory to real systems.

Online Resources: The online resources to accompany Statistical Thermodynamics feature:

For registered adopters of the text: Ā· Figures from the book available to download

For students: Ā· Worked solutions to the questions and problems at the end of the book. Ā· Multiple-choice questions for self-directed learning

Recenzijas

The approachability of the text and the angle adopted by the authors makes the book a useful reference for my course. * Dr Mark Miller, Durham University *

Preface to 1st edition v
Preface to 2nd edition vi
1 The Boltzmann law
1(7)
1.1 Introduction
1(1)
1.2 The Boltzmann factor
1(1)
1.3 The average basis of the behaviour of matter
2(1)
1.4 Plan of attack
2(1)
1.5 Distinct, independent particles
3(1)
1.6 Configurations: sharing out the energy
3(1)
1.7 Statistical weights
3(1)
1.8 Equal probability of microstates
4(1)
1.9 Conservation of number and energy
5(1)
1.10 The predominant configuration
5(1)
1.11 Maximization subject to constraints
6(1)
1.12 Summary
7(1)
2 Sum over states: the molecular partition function
8(4)
2.1 Introduction
8(1)
2.2 Occupation numbers, n of molecular energy states
8(1)
2.3 The molecular partition function, q
9(1)
2.4 Energy states and energy levels
10(1)
2.5 The partition function explored
10(1)
2.6 Summary
11(1)
3 Applications of the molecular partition function
12(4)
3.1 Introduction
12(1)
3.2 The molecular energy, E
12(1)
3.3 The internal energy, U
12(1)
3.4 The relationship of β to temperature
13(1)
3.5 The statistical entropy
13(2)
3.6 Summary
15(1)
4 From molecule to mole: the canonical partition function
16(4)
4.1 Introduction
16(1)
4.2 System energy states
16(2)
4.3 The molar energy
18(1)
4.4 Summary
18(2)
5 Distinguishable and indistinguishable particles
20(4)
5.1 Introduction
20(1)
5.2 Linking q to Q
20(1)
5.3 Distinguishable and indistinguishable particles
21(1)
5.4 The origin of 1/N!
21(1)
5.5 The number of states per particle
22(1)
5.6 What is indistinguishability?
23(1)
5.7 Summary
23(1)
6 Two-level systems: a case study
24(7)
6.1 Introduction
24(1)
6.2 The effect of increasing temperature
24(2)
6.3 The two-level molecular partition function
26(1)
6.4 The energy of a two-level system
26(1)
6.5 The two-level heat capacity, Cv
27(2)
6.6 The effect of degeneracy
29(1)
6.7 Summary
30(1)
7 Thermodynamic functions: towards a statistical toolkit
31(10)
7.1 Introduction
31(1)
7.2 State functions
31(1)
7.3 The internal energy, U
32(1)
7.4 The entropy, S
33(1)
7.5 The Helmholtz energy, A: the Massieu bridge
34(1)
7.6 The internal energy, U, revisited
35(1)
7.7 The equation of state and the pressure, p
35(1)
7.8 The heat capacity, Cv
36(1)
7.9 The entropy, S, revisited
36(1)
7.10 The enthalpy, H
37(1)
7.11 The Gibbs free energy, G
37(2)
7.12 A full set of toolkit equations
39(1)
7.13 Summary
39(2)
8 The ideal monatomic gas: the translational partition function
41(8)
8.1 Introduction
41(1)
8.2 The translational partition function, qtrs
41(2)
8.3 The ideal monatomic gas: thermodynamic functions
43(2)
8.4 The entropy of the ideal monatomic gas
45(1)
8.5 Using the Sackur-Tetrode equation
46(2)
8.6 Summary
48(1)
9 The ideal diatomic gas: internal degrees of freedom
49(6)
9.1 Introduction
49(1)
9.2 Internal modes: separability of energies
49(1)
9.3 Weak coupling: factorizing the energy modes
50(2)
9.4 Factorizing translational energy modes
52(1)
9.5 Factorizing internal energy modes
52(1)
9.6 The canonical partition function, Q
53(1)
9.7 Summary
54(1)
10 The ideal diatomic gas: the rotational partition function
55(8)
10.1 Introduction
55(1)
10.2 The rigid rotor
55(1)
10.3 The continuum approximation: test of validity
56(1)
10.4 Accessible states and symmetry
57(1)
10.5 Origin of the symmetry factor
58(2)
10.6 The canonical partition function for rotation
60(1)
10.7 Rotational energy, heat capacity, and entropy
60(1)
10.8 Extension to polyatomic molecules
61(1)
10.9 Summary
61(2)
11 Ortho and para spin states: a case study
63(4)
11.1 Introduction
63(1)
11.2 Nuclear spin wavefunctions
63(1)
11.3 ortho- and para-hydrogen
64(1)
11.4 A special case: nuclei with zero spin
65(1)
11.5 Concluding remarks
66(1)
11.6 Summary
66(1)
12 The ideal diatomic gas: the vibrational partition function
67(8)
12.1 Introduction
67(1)
12.2 The diatomic SHO model
67(1)
12.3 The vibrational partition function, qvib
68(1)
12.4 High temperature limiting behaviour of qvib
69(1)
12.5 The canonical partition function, Qvib
69(1)
12.6 Vibrational energy Uvib
70(1)
12.7 The zero-point energy
70(1)
12.8 Vibrational heat capacity, Cvib
71(1)
12.9 The vibrational entropy, Svib
71(1)
12.10 From torsional oscillation to internal rotation
72(2)
12.11 Summary
74(1)
13 The electronic partition function
75(5)
13.1 Introduction
75(1)
13.2 The characteristic electronic temperature, θel
75(1)
13.3 Degeneracy
76(1)
13.4 The electronic partition function
77(1)
13.5 The singular case of NO
78(1)
13.6 Summary
79(1)
14 Heat capacity and Third Law entropy: two case studies
80(7)
14.1 Introduction
80(1)
14.2 The heat capacity Cv,m as a function of temperature
80(1)
14.3 The maximum in Crot,m
81(1)
14.4 Calorimetric and spectroscopic entropy
82(2)
14.5 Residual entropy
84(2)
14.6 Summary
86(1)
15 Calculating equilibrium constants
87(17)
15.1 Introduction
87(1)
15.2 The molar Gibbs free energy
87(2)
15.3 The equilibrium constant
89(1)
15.4 Interpreting the equilibrium constant
89(1)
15.5 Aspects of the equilibrium constant
90(3)
15.6 Calculating equilibrium constants
93(9)
15.7 Concluding remarks
102(1)
15.8 Summary
103(1)
Questions and problems 104(6)
Additional mathematical aspects 110(9)
Index 119
Andrew Maczek, until his retirement, was a Senior Lecturer in Physical Chemistry at the University of Sheffield, where his research focused on the thermophysical behaviour of fluids. He obtained his first degree in Chemistry at the University of Oxford, where he stayed on to obtain his DPhil in Inorganic Chemistry with Courtney Philips. During a postdoctoral period at the University of Leeds he came under the influence of Peter Gray and happily converted to become a physical chemist. The first edition of this Primer was written during the years while he was actively engaged in academic pursuits at Sheffield.

Anthony Meijer is a reader in Theoretical Chemistry at the University of Sheffield, where he and his research group work on the theoretical study of chemical reactions using both electronic structure and quantum dynamics methods for a wide variety of systems from the formation of molecules in the interstellar medium to the vibrational control of electronically excited states. He obtained an MSc in Chemistry from the University of Utrecht before obtaining a PhD with Ad van der Avoird at the University of Nijmegen. He has been at Sheffield for the past 13 years.
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