I. Classical Thermodynamics Preliminaries 

The Ideal Gas Law 
46:05 
 
Intro 
0:00  
 
Course Overview 
0:16  
 
 Thermodynamics & Classical Thermodynamics 
0:17  
 
 Structure of the Course 
1:30  
 
The Ideal Gas Law 
3:06  
 
 Ideal Gas Law: PV=nRT 
3:07  
 
 Units of Pressure 
4:51  
 
 Manipulating Units 
5:52  
 
 Atmosphere : atm 
8:15  
 
 Millimeter of Mercury: mm Hg 
8:48  
 
 SI Unit of Volume 
9:32  
 
 SI Unit of Temperature 
10:32  
 
 Value of R (Gas Constant): Pv = nRT 
10:51  
 
Extensive and Intensive Variables (Properties) 
15:23  
 
 Intensive Property 
15:52  
 
 Extensive Property 
16:30  
 
 Example: Extensive and Intensive Variables 
18:20  
 
Ideal Gas Law 
19:24  
 
 Ideal Gas Law with Intensive Variables 
19:25  
 
Graphing Equations 
23:51  
 
 Hold T Constant & Graph P vs. V 
23:52  
 
 Hold P Constant & Graph V vs. T 
31:08  
 
 Hold V Constant & Graph P vs. T 
34:38  
 
 Isochores or Isometrics 
37:08  
 
 More on the V vs. T Graph 
39:46  
 
 More on the P vs. V Graph 
42:06  
 
 Ideal Gas Law at Low Pressure & High Temperature 
44:26  
 
 Ideal Gas Law at High Pressure & Low Temperature 
45:16  

Math Lesson 1: Partial Differentiation 
46:02 
 
Intro 
0:00  
 
Math Lesson 1: Partial Differentiation 
0:38  
 
 Overview 
0:39  
 
Example I 
3:00  
 
Example II 
6:33  
 
Example III 
9:52  
 
Example IV 
17:26  
 
Differential & Derivative 
21:44  
 
 What Does It Mean? 
21:45  
 
 Total Differential (or Total Derivative) 
30:16  
 
 Net Change in Pressure (P) 
33:58  
 
 General Equation for Total Differential 
38:12  
 
Example 5: Total Differential 
39:28  
II. Energy 

Energy & the First Law I 
1:06:45 
 
Intro 
0:00  
 
Properties of Thermodynamic State 
1:38  
 
 Big Picture: 3 Properties of Thermodynamic State 
1:39  
 
 Enthalpy & Free Energy 
3:30  
 
 Associated Law 
4:40  
 
Energy & the First Law of Thermodynamics 
7:13  
 
 System & Its Surrounding Separated by a Boundary 
7:14  
 
 In Other Cases the Boundary is Less Clear 
10:47  
 
State of a System 
12:37  
 
 State of a System 
12:38  
 
 Change in State 
14:00  
 
 Path for a Change in State 
14:57  
 
 Example: State of a System 
15:46  
 
Open, Close, and Isolated System 
18:26  
 
 Open System 
18:27  
 
 Closed System 
19:02  
 
 Isolated System 
19:22  
 
Important Questions 
20:38  
 
 Important Questions 
20:39  
 
Work & Heat 
22:50  
 
 Definition of Work 
23:33  
 
 Properties of Work 
25:34  
 
 Definition of Heat 
32:16  
 
 Properties of Heat 
34:49  
 
 Experiment #1 
42:23  
 
 Experiment #2 
47:00  
 
More on Work & Heat 
54:50  
 
 More on Work & Heat 
54:51  
 
Conventions for Heat & Work 
60:50  
 
 Convention for Heat 
62:40  
 
 Convention for Work 
64:24  
 
 Schematic Representation 
65:00  

Energy & the First Law II 
1:06:33 
 
Intro 
0:00  
 
The First Law of Thermodynamics 
0:53  
 
 The First Law of Thermodynamics 
0:54  
 
Example 1: What is the Change in Energy of the System & Surroundings? 
8:53  
 
Energy and The First Law II, cont. 
11:55  
 
 The Energy of a System Changes in Two Ways 
11:56  
 
 Systems Possess Energy, Not Heat or Work 
12:45  
 
 Scenario 1 
16:00  
 
 Scenario 2 
16:46  
 
 State Property, Path Properties, and Path Functions 
18:10  
 
PressureVolume Work 
22:36  
 
 When a System Changes 
22:37  
 
 Gas Expands 
24:06  
 
 Gas is Compressed 
25:13  
 
 Pressure Volume Diagram: Analyzing Expansion 
27:17  
 
 What if We do the Same Expansion in Two Stages? 
35:22  
 
 Multistage Expansion 
43:58  
 
 General Expression for the PressureVolume Work 
46:59  
 
 Upper Limit of Isothermal Expansion 
50:00  
 
 Expression for the Work Done in an Isothermal Expansion 
52:45  
 
Example 2: Find an Expression for the Maximum Work Done by an Ideal Gas upon Isothermal Expansion 
56:18  
 
Example 3: Calculate the External Pressure and Work Done 
58:50  

Energy & the First Law III 
1:02:17 
 
Intro 
0:00  
 
Compression 
0:20  
 
 Compression Overview 
0:34  
 
 Singlestage compression vs. 2stage Compression 
2:16  
 
 Multistage Compression 
8:40  
 
Example I: Compression 
14:47  
 
 Example 1: Singlestage Compression 
14:47  
 
 Example 1: 2stage Compression 
20:07  
 
 Example 1: Absolute Minimum 
26:37  
 
More on Compression 
32:55  
 
 Isothermal Expansion & Compression 
32:56  
 
 External & Internal Pressure of the System 
35:18  
 
Reversible & Irreversible Processes 
37:32  
 
 Process 1: Overview 
38:57  
 
 Process 2: Overview 
39:36  
 
 Process 1: Analysis 
40:42  
 
 Process 2: Analysis 
45:29  
 
 Reversible Process 
50:03  
 
 Isothermal Expansion and Compression 
54:31  
 
Example II: Reversible Isothermal Compression of a Van der Waals Gas 
58:10  
 
 Example 2: Reversible Isothermal Compression of a Van der Waals Gas 
58:11  

Changes in Energy & State: Constant Volume 
1:04:39 
 
Intro 
0:00  
 
Recall 
0:37  
 
 State Function & Path Function 
0:38  
 
First Law 
2:11  
 
 Exact & Inexact Differential 
2:12  
 
Where Does (∆U = Q  W) or dU = dQ  dU Come from? 
8:54  
 
 Cyclic Integrals of Path and State Functions 
8:55  
 
 Our Empirical Experience of the First Law 
12:31  
 
 ∆U = Q  W 
18:42  
 
Relations between Changes in Properties and Energy 
22:24  
 
 Relations between Changes in Properties and Energy 
22:25  
 
 Rate of Change of Energy per Unit Change in Temperature 
29:54  
 
 Rate of Change of Energy per Unit Change in Volume at Constant Temperature 
32:39  
 
 Total Differential Equation 
34:38  
 
Constant Volume 
41:08  
 
 If Volume Remains Constant, then dV = 0 
41:09  
 
 Constant Volume Heat Capacity 
45:22  
 
 Constant Volume Integrated 
48:14  
 
 Increase & Decrease in Energy of the System 
54:19  
 
Example 1: ∆U and Qv 
57:43  
 
Important Equations 
62:06  

Joule's Experiment 
16:50 
 
Intro 
0:00  
 
Joule's Experiment 
0:09  
 
 Joule's Experiment 
1:20  
 
Interpretation of the Result 
4:42  
 
 The Gas Expands Against No External Pressure 
4:43  
 
 Temperature of the Surrounding Does Not Change 
6:20  
 
 System & Surrounding 
7:04  
 
 Joule's Law 
10:44  
 
 More on Joule's Experiment 
11:08  
 
 Later Experiment 
12:38  
 
 Dealing with the 2nd Law & Its Mathematical Consequences 
13:52  

Changes in Energy & State: Constant Pressure 
43:40 
 
Intro 
0:00  
 
Changes in Energy & State: Constant Pressure 
0:20  
 
 Integrating with Constant Pressure 
0:35  
 
 Defining the New State Function 
6:24  
 
 Heat & Enthalpy of the System at Constant Pressure 
8:54  
 
 Finding ∆U 
12:10  
 
 dH 
15:28  
 
 Constant Pressure Heat Capacity 
18:08  
 
Important Equations 
25:44  
 
 Important Equations 
25:45  
 
 Important Equations at Constant Pressure 
27:32  
 
Example I: Change in Enthalpy (∆H) 
28:53  
 
Example II: Change in Internal Energy (∆U) 
34:19  

The Relationship Between Cp & Cv 
32:23 
 
Intro 
0:00  
 
The Relationship Between Cp & Cv 
0:21  
 
 For a Constant Volume Process No Work is Done 
0:22  
 
 For a Constant Pressure Process ∆V ≠ 0, so Work is Done 
1:16  
 
 The Relationship Between Cp & Cv: For an Ideal Gas 
3:26  
 
 The Relationship Between Cp & Cv: In Terms of Molar heat Capacities 
5:44  
 
 Heat Capacity Can Have an Infinite # of Values 
7:14  
 
 The Relationship Between Cp & Cv 
11:20  
 
When Cp is Greater than Cv 
17:13  
 
 2nd Term 
18:10  
 
 1st Term 
19:20  
 
Constant P Process: 3 Parts 
22:36  
 
 Part 1 
23:45  
 
 Part 2 
24:10  
 
 Part 3 
24:46  
 
Define : γ = (Cp/Cv) 
28:06  
 
 For Gases 
28:36  
 
 For Liquids 
29:04  
 
 For an Ideal Gas 
30:46  

The Joule Thompson Experiment 
39:15 
 
Intro 
0:00  
 
General Equations 
0:13  
 
 Recall 
0:14  
 
 How Does Enthalpy of a System Change Upon a Unit Change in Pressure? 
2:58  
 
 For Liquids & Solids 
12:11  
 
 For Ideal Gases 
14:08  
 
 For Real Gases 
16:58  
 
The Joule Thompson Experiment 
18:37  
 
 The Joule Thompson Experiment Setup 
18:38  
 
 The Flow in 2 Stages 
22:54  
 
 Work Equation for the Joule Thompson Experiment 
24:14  
 
 Insulated Pipe 
26:33  
 
 JouleThompson Coefficient 
29:50  
 
 Changing Temperature & Pressure in Such a Way that Enthalpy Remains Constant 
31:44  
 
Joule Thompson Inversion Temperature 
36:26  
 
 Positive & Negative JouleThompson Coefficient 
36:27  
 
 Joule Thompson Inversion Temperature 
37:22  
 
 Inversion Temperature of Hydrogen Gas 
37:59  

Adiabatic Changes of State 
35:52 
 
Intro 
0:00  
 
Adiabatic Changes of State 
0:10  
 
 Adiabatic Changes of State 
0:18  
 
 Work & Energy in an Adiabatic Process 
3:44  
 
 PressureVolume Work 
7:43  
 
Adiabatic Changes for an Ideal Gas 
9:23  
 
 Adiabatic Changes for an Ideal Gas 
9:24  
 
 Equation for a Fixed Change in Volume 
11:20  
 
 Maximum & Minimum Values of Temperature 
14:20  
 
Adiabatic Path 
18:08  
 
 Adiabatic Path Diagram 
18:09  
 
 Reversible Adiabatic Expansion 
21:54  
 
 Reversible Adiabatic Compression 
22:34  
 
 Fundamental Relationship Equation for an Ideal Gas Under Adiabatic Expansion 
25:00  
 
 More on the Equation 
28:20  
 
Important Equations 
32:16  
 
 Important Adiabatic Equation 
32:17  
 
 Reversible Adiabatic Change of State Equation 
33:02  
III. Energy Example Problems 

1st Law Example Problems I 
42:40 
 
Intro 
0:00  
 
Fundamental Equations 
0:56  
 
 Work 
2:40  
 
 Energy (1st Law) 
3:10  
 
 Definition of Enthalpy 
3:44  
 
 Heat capacity Definitions 
4:06  
 
 The Mathematics 
6:35  
 
Fundamental Concepts 
8:13  
 
 Isothermal 
8:20  
 
 Adiabatic 
8:54  
 
 Isobaric 
9:25  
 
 Isometric 
9:48  
 
 Ideal Gases 
10:14  
 
Example I 
12:08  
 
 Example I: Conventions 
12:44  
 
 Example I: Part A 
15:30  
 
 Example I: Part B 
18:24  
 
 Example I: Part C 
19:53  
 
Example II: What is the Heat Capacity of the System? 
21:49  
 
Example III: Find Q, W, ∆U & ∆H for this Change of State 
24:15  
 
Example IV: Find Q, W, ∆U & ∆H 
31:37  
 
Example V: Find Q, W, ∆U & ∆H 
38:20  

1st Law Example Problems II 
1:00:23 
 
Intro 
0:00  
 
Example I 
0:11  
 
 Example I: Finding ∆U 
1:49  
 
 Example I: Finding W 
6:22  
 
 Example I: Finding Q 
11:23  
 
 Example I: Finding ∆H 
16:09  
 
 Example I: Summary 
17:07  
 
Example II 
21:16  
 
 Example II: Finding W 
22:42  
 
 Example II: Finding ∆H 
27:48  
 
 Example II: Finding Q 
30:58  
 
 Example II: Finding ∆U 
31:30  
 
Example III 
33:33  
 
 Example III: Finding ∆U, Q & W 
33:34  
 
 Example III: Finding ∆H 
38:07  
 
Example IV 
41:50  
 
 Example IV: Finding ∆U 
41:51  
 
 Example IV: Finding ∆H 
45:42  
 
Example V 
49:31  
 
 Example V: Finding W 
49:32  
 
 Example V: Finding ∆U 
55:26  
 
 Example V: Finding Q 
56:26  
 
 Example V: Finding ∆H 
56:55  

1st Law Example Problems III 
44:34 
 
Intro 
0:00  
 
Example I 
0:15  
 
 Example I: Finding the Final Temperature 
3:40  
 
 Example I: Finding Q 
8:04  
 
 Example I: Finding ∆U 
8:25  
 
 Example I: Finding W 
9:08  
 
 Example I: Finding ∆H 
9:51  
 
Example II 
11:27  
 
 Example II: Finding the Final Temperature 
11:28  
 
 Example II: Finding ∆U 
21:25  
 
 Example II: Finding W & Q 
22:14  
 
 Example II: Finding ∆H 
23:03  
 
Example III 
24:38  
 
 Example III: Finding the Final Temperature 
24:39  
 
 Example III: Finding W, ∆U, and Q 
27:43  
 
 Example III: Finding ∆H 
28:04  
 
Example IV 
29:23  
 
 Example IV: Finding ∆U, W, and Q 
25:36  
 
 Example IV: Finding ∆H 
31:33  
 
Example V 
32:24  
 
 Example V: Finding the Final Temperature 
33:32  
 
 Example V: Finding ∆U 
39:31  
 
 Example V: Finding W 
40:17  
 
 Example V: First Way of Finding ∆H 
41:10  
 
 Example V: Second Way of Finding ∆H 
42:10  

Thermochemistry Example Problems 
59:07 
 
Intro 
0:00  
 
Example I: Find ∆H° for the Following Reaction 
0:42  
 
Example II: Calculate the ∆U° for the Reaction in Example I 
5:33  
 
Example III: Calculate the Heat of Formation of NH₃ at 298 K 
14:23  
 
Example IV 
32:15  
 
 Part A: Calculate the Heat of Vaporization of Water at 25°C 
33:49  
 
 Part B: Calculate the Work Done in Vaporizing 2 Mols of Water at 25°C Under a Constant Pressure of 1 atm 
35:26  
 
 Part C: Find ∆U for the Vaporization of Water at 25°C 
41:00  
 
 Part D: Find the Enthalpy of Vaporization of Water at 100°C 
43:12  
 
Example V 
49:24  
 
 Part A: Constant Temperature & Increasing Pressure 
50:25  
 
 Part B: Increasing temperature & Constant Pressure 
56:20  
IV. Entropy 

Entropy 
49:16 
 
Intro 
0:00  
 
Entropy, Part 1 
0:16  
 
 Coefficient of Thermal Expansion (Isobaric) 
0:38  
 
 Coefficient of Compressibility (Isothermal) 
1:25  
 
 Relative Increase & Relative Decrease 
2:16  
 
 More on α 
4:40  
 
 More on κ 
8:38  
 
Entropy, Part 2 
11:04  
 
 Definition of Entropy 
12:54  
 
 Differential Change in Entropy & the Reversible Path 
20:08  
 
 State Property of the System 
28:26  
 
 Entropy Changes Under Isothermal Conditions 
35:00  
 
 Recall: Heating Curve 
41:05  
 
 Some Phase Changes Take Place Under Constant Pressure 
44:07  
 
Example I: Finding ∆S for a Phase Change 
46:05  

Math Lesson II 
33:59 
 
Intro 
0:00  
 
Math Lesson II 
0:46  
 
 Let F(x,y) = x²y³ 
0:47  
 
 Total Differential 
3:34  
 
 Total Differential Expression 
6:06  
 
 Example 1 
9:24  
 
More on Math Expression 
13:26  
 
 Exact Total Differential Expression 
13:27  
 
 Exact Differentials 
19:50  
 
 Inexact Differentials 
20:20  
 
The Cyclic Rule 
21:06  
 
 The Cyclic Rule 
21:07  
 
 Example 2 
27:58  

Entropy As a Function of Temperature & Volume 
54:37 
 
Intro 
0:00  
 
Entropy As a Function of Temperature & Volume 
0:14  
 
 Fundamental Equation of Thermodynamics 
1:16  
 
 Things to Notice 
9:10  
 
 Entropy As a Function of Temperature & Volume 
14:47  
 
 Temperaturedependence of Entropy 
24:00  
 
Example I 
26:19  
 
Entropy As a Function of Temperature & Volume, Cont. 
31:55  
 
 Volumedependence of Entropy at Constant Temperature 
31:56  
 
 Differentiate with Respect to Temperature, Holding Volume Constant 
36:16  
 
 Recall the Cyclic Rule 
45:15  
 
Summary & Recap 
46:47  
 
 Fundamental Equation of Thermodynamics 
46:48  
 
 For Entropy as a Function of Temperature & Volume 
47:18  
 
 The Volumedependence of Entropy for Liquids & Solids 
52:52  

Entropy as a Function of Temperature & Pressure 
31:18 
 
Intro 
0:00  
 
Entropy as a Function of Temperature & Pressure 
0:17  
 
 Entropy as a Function of Temperature & Pressure 
0:18  
 
 Rewrite the Total Differential 
5:54  
 
 Temperaturedependence 
7:08  
 
 Pressuredependence 
9:04  
 
 Differentiate with Respect to Pressure & Holding Temperature Constant 
9:54  
 
 Differentiate with Respect to Temperature & Holding Pressure Constant 
11:28  
 
PressureDependence of Entropy for Liquids & Solids 
18:45  
 
 PressureDependence of Entropy for Liquids & Solids 
18:46  
 
Example I: ∆S of Transformation 
26:20  

Summary of Entropy So Far 
23:06 
 
Intro 
0:00  
 
Summary of Entropy So Far 
0:43  
 
 Defining dS 
1:04  
 
 Fundamental Equation of Thermodynamics 
3:51  
 
 Temperature & Volume 
6:04  
 
 Temperature & Pressure 
9:10  
 
 Two Important Equations for How Entropy Behaves 
13:38  
 
 State of a System & Heat Capacity 
15:34  
 
 Temperaturedependence of Entropy 
19:49  

Entropy Changes for an Ideal Gas 
25:42 
 
Intro 
0:00  
 
Entropy Changes for an Ideal Gas 
1:10  
 
 General Equation 
1:22  
 
 The Fundamental Theorem of Thermodynamics 
2:37  
 
 Recall the Basic Total Differential Expression for S = S (T,V) 
5:36  
 
 For a Finite Change in State 
7:58  
 
 If Cv is Constant Over the Particular Temperature Range 
9:05  
 
Change in Entropy of an Ideal Gas as a Function of Temperature & Pressure 
11:35  
 
 Change in Entropy of an Ideal Gas as a Function of Temperature & Pressure 
11:36  
 
 Recall the Basic Total Differential expression for S = S (T, P) 
15:13  
 
 For a Finite Change 
18:06  
 
Example 1: Calculate the ∆S of Transformation 
22:02  
V. Entropy Example Problems 

Entropy Example Problems I 
43:39 
 
Intro 
0:00  
 
Entropy Example Problems I 
0:24  
 
 Fundamental Equation of Thermodynamics 
1:10  
 
 Entropy as a Function of Temperature & Volume 
2:04  
 
 Entropy as a Function of Temperature & Pressure 
2:59  
 
 Entropy For Phase Changes 
4:47  
 
 Entropy For an Ideal Gas 
6:14  
 
 Third Law Entropies 
8:25  
 
 Statement of the Third Law 
9:17  
 
 Entropy of the Liquid State of a Substance Above Its Melting Point 
10:23  
 
 Entropy For the Gas Above Its Boiling Temperature 
13:02  
 
 Entropy Changes in Chemical Reactions 
15:26  
 
 Entropy Change at a Temperature Other than 25°C 
16:32  
 
Example I 
19:31  
 
 Part A: Calculate ∆S for the Transformation Under Constant Volume 
20:34  
 
 Part B: Calculate ∆S for the Transformation Under Constant Pressure 
25:04  
 
Example II: Calculate ∆S fir the Transformation Under Isobaric Conditions 
27:53  
 
Example III 
30:14  
 
 Part A: Calculate ∆S if 1 Mol of Aluminum is taken from 25°C to 255°C 
31:14  
 
 Part B: If S°₂₉₈ = 28.4 J/molK, Calculate S° for Aluminum at 498 K 
33:23  
 
Example IV: Calculate Entropy Change of Vaporization for CCl₄ 
34:19  
 
Example V 
35:41  
 
 Part A: Calculate ∆S of Transformation 
37:36  
 
 Part B: Calculate ∆S of Transformation 
39:10  

Entropy Example Problems II 
56:44 
 
Intro 
0:00  
 
Example I 
0:09  
 
 Example I: Calculate ∆U 
1:28  
 
 Example I: Calculate Q 
3:29  
 
 Example I: Calculate Cp 
4:54  
 
 Example I: Calculate ∆S 
6:14  
 
Example II 
7:13  
 
 Example II: Calculate W 
8:14  
 
 Example II: Calculate ∆U 
8:56  
 
 Example II: Calculate Q 
10:18  
 
 Example II: Calculate ∆H 
11:00  
 
 Example II: Calculate ∆S 
12:36  
 
Example III 
18:47  
 
 Example III: Calculate ∆H 
19:38  
 
 Example III: Calculate Q 
21:14  
 
 Example III: Calculate ∆U 
21:44  
 
 Example III: Calculate W 
23:59  
 
 Example III: Calculate ∆S 
24:55  
 
Example IV 
27:57  
 
 Example IV: Diagram 
29:32  
 
 Example IV: Calculate W 
32:27  
 
 Example IV: Calculate ∆U 
36:36  
 
 Example IV: Calculate Q 
38:32  
 
 Example IV: Calculate ∆H 
39:00  
 
 Example IV: Calculate ∆S 
40:27  
 
 Example IV: Summary 
43:41  
 
Example V 
48:25  
 
 Example V: Diagram 
49:05  
 
 Example V: Calculate W 
50:58  
 
 Example V: Calculate ∆U 
53:29  
 
 Example V: Calculate Q 
53:44  
 
 Example V: Calculate ∆H 
54:34  
 
 Example V: Calculate ∆S 
55:01  

Entropy Example Problems III 
57:06 
 
Intro 
0:00  
 
Example I: Isothermal Expansion 
0:09  
 
 Example I: Calculate W 
1:19  
 
 Example I: Calculate ∆U 
1:48  
 
 Example I: Calculate Q 
2:06  
 
 Example I: Calculate ∆H 
2:26  
 
 Example I: Calculate ∆S 
3:02  
 
Example II: Adiabatic and Reversible Expansion 
6:10  
 
 Example II: Calculate Q 
6:48  
 
 Example II: Basic Equation for the Reversible Adiabatic Expansion of an Ideal Gas 
8:12  
 
 Example II: Finding Volume 
12:40  
 
 Example II: Finding Temperature 
17:58  
 
 Example II: Calculate ∆U 
19:53  
 
 Example II: Calculate W 
20:59  
 
 Example II: Calculate ∆H 
21:42  
 
 Example II: Calculate ∆S 
23:42  
 
Example III: Calculate the Entropy of Water Vapor 
25:20  
 
Example IV: Calculate the Molar ∆S for the Transformation 
34:32  
 
Example V 
44:19  
 
 Part A: Calculate the Standard Entropy of Liquid Lead at 525°C 
46:17  
 
 Part B: Calculate ∆H for the Transformation of Solid Lead from 25°C to Liquid Lead at 525°C 
52:23  
VI. Entropy and Probability 

Entropy & Probability I 
54:35 
 
Intro 
0:00  
 
Entropy & Probability 
0:11  
 
 Structural Model 
3:05  
 
 Recall the Fundamental Equation of Thermodynamics 
9:11  
 
 Two Independent Ways of Affecting the Entropy of a System 
10:05  
 
 Boltzmann Definition 
12:10  
 
Omega 
16:24  
 
 Definition of Omega 
16:25  
 
Energy Distribution 
19:43  
 
 The Energy Distribution 
19:44  
 
 In How Many Ways can N Particles be Distributed According to the Energy Distribution 
23:05  
 
Example I: In How Many Ways can the Following Distribution be Achieved 
32:51  
 
Example II: In How Many Ways can the Following Distribution be Achieved 
33:51  
 
Example III: In How Many Ways can the Following Distribution be Achieved 
34:45  
 
Example IV: In How Many Ways can the Following Distribution be Achieved 
38:50  
 
Entropy & Probability, cont. 
40:57  
 
 More on Distribution 
40:58  
 
 Example I Summary 
41:43  
 
 Example II Summary 
42:12  
 
 Distribution that Maximizes Omega 
42:26  
 
 If Omega is Large, then S is Large 
44:22  
 
 Two Constraints for a System to Achieve the Highest Entropy Possible 
47:07  
 
 What Happened When the Energy of a System is Increased? 
49:00  

Entropy & Probability II 
35:05 
 
Intro 
0:00  
 
Volume Distribution 
0:08  
 
 Distributing 2 Balls in 3 Spaces 
1:43  
 
 Distributing 2 Balls in 4 Spaces 
3:44  
 
 Distributing 3 Balls in 10 Spaces 
5:30  
 
 Number of Ways to Distribute P Particles over N Spaces 
6:05  
 
 When N is Much Larger than the Number of Particles P 
7:56  
 
 Energy Distribution 
25:04  
 
 Volume Distribution 
25:58  
 
Entropy, Total Entropy, & Total Omega Equations 
27:34  
 
 Entropy, Total Entropy, & Total Omega Equations 
27:35  
VII. Spontaneity, Equilibrium, and the Fundamental Equations 

Spontaneity & Equilibrium I 
28:42 
 
Intro 
0:00  
 
Reversible & Irreversible 
0:24  
 
 Reversible vs. Irreversible 
0:58  
 
 Defining Equation for Equilibrium 
2:11  
 
 Defining Equation for Irreversibility (Spontaneity) 
3:11  
 
 TdS ≥ dQ 
5:15  
 
Transformation in an Isolated System 
11:22  
 
 Transformation in an Isolated System 
11:29  
 
Transformation at Constant Temperature 
14:50  
 
 Transformation at Constant Temperature 
14:51  
 
Helmholtz Free Energy 
17:26  
 
 Define: A = U  TS 
17:27  
 
 Spontaneous Isothermal Process & Helmholtz Energy 
20:20  
 
 Pressurevolume Work 
22:02  

Spontaneity & Equilibrium II 
34:38 
 
Intro 
0:00  
 
Transformation under Constant Temperature & Pressure 
0:08  
 
 Transformation under Constant Temperature & Pressure 
0:36  
 
 Define: G = U + PV  TS 
3:32  
 
 Gibbs Energy 
5:14  
 
 What Does This Say? 
6:44  
 
 Spontaneous Process & a Decrease in G 
14:12  
 
 Computing ∆G 
18:54  
 
Summary of Conditions 
21:32  
 
 Constraint & Condition for Spontaneity 
21:36  
 
 Constraint & Condition for Equilibrium 
24:54  
 
A Few Words About the Word Spontaneous 
26:24  
 
 Spontaneous Does Not Mean Fast 
26:25  
 
 Putting Hydrogen & Oxygen Together in a Flask 
26:59  
 
 Spontaneous Vs. Not Spontaneous 
28:14  
 
 Thermodynamically Favorable 
29:03  
 
 Example: Making a Process Thermodynamically Favorable 
29:34  
 
Driving Forces for Spontaneity 
31:35  
 
 Equation: ∆G = ∆H  T∆S 
31:36  
 
 Always Spontaneous Process 
32:39  
 
 Never Spontaneous Process 
33:06  
 
 A Process That is Endothermic Can Still be Spontaneous 
34:00  

The Fundamental Equations of Thermodynamics 
30:50 
 
Intro 
0:00  
 
The Fundamental Equations of Thermodynamics 
0:44  
 
 Mechanical Properties of a System 
0:45  
 
 Fundamental Properties of a System 
1:16  
 
 Composite Properties of a System 
1:44  
 
 General Condition of Equilibrium 
3:16  
 
 Composite Functions & Their Differentiations 
6:11  
 
 dH = TdS + VdP 
7:53  
 
 dA = SdT  PdV 
9:26  
 
 dG = SdT + VdP 
10:22  
 
Summary of Equations 
12:10  
 
 Equation #1 
14:33  
 
 Equation #2 
15:15  
 
 Equation #3 
15:58  
 
 Equation #4 
16:42  
 
Maxwell's Relations 
20:20  
 
 Maxwell's Relations 
20:21  
 
 Isothermal VolumeDependence of Entropy & Isothermal PressureDependence of Entropy 
26:21  

The General Thermodynamic Equations of State 
34:06 
 
Intro 
0:00  
 
The General Thermodynamic Equations of State 
0:10  
 
 Equations of State for Liquids & Solids 
0:52  
 
 More General Condition for Equilibrium 
4:02  
 
 General Conditions: Equation that Relates P to Functions of T & V 
6:20  
 
 The Second Fundamental Equation of Thermodynamics 
11:10  
 
 Equation 1 
17:34  
 
 Equation 2 
21:58  
 
 Recall the General Expression for Cp  Cv 
28:11  
 
 For the JouleThomson Coefficient 
30:44  
 
 JouleThomson Inversion Temperature 
32:12  

Properties of the Helmholtz & Gibbs Energies 
39:18 
 
Intro 
0:00  
 
Properties of the Helmholtz & Gibbs Energies 
0:10  
 
 Equating the Differential Coefficients 
1:34  
 
 An Increase in T; a Decrease in A 
3:25  
 
 An Increase in V; a Decrease in A 
6:04  
 
 We Do the Same Thing for G 
8:33  
 
 Increase in T; Decrease in G 
10:50  
 
 Increase in P; Decrease in G 
11:36  
 
 Gibbs Energy of a Pure Substance at a Constant Temperature from 1 atm to any Other Pressure. 
14:12  
 
 If the Substance is a Liquid or a Solid, then Volume can be Treated as a Constant 
18:57  
 
 For an Ideal Gas 
22:18  
 
 Special Note 
24:56  
 
Temperature Dependence of Gibbs Energy 
27:02  
 
 Temperature Dependence of Gibbs Energy #1 
27:52  
 
 Temperature Dependence of Gibbs Energy #2 
29:01  
 
 Temperature Dependence of Gibbs Energy #3 
29:50  
 
 Temperature Dependence of Gibbs Energy #4 
34:50  

The Entropy of the Universe & the Surroundings 
19:40 
 
Intro 
0:00  
 
Entropy of the Universe & the Surroundings 
0:08  
 
 Equation: ∆G = ∆H  T∆S 
0:20  
 
 Conditions of Constant Temperature & Pressure 
1:14  
 
 Reversible Process 
3:14  
 
 Spontaneous Process & the Entropy of the Universe 
5:20  
 
 Tips for Remembering Everything 
12:40  
 
 Verify Using Known Spontaneous Process 
14:51  
VIII. Free Energy Example Problems 

Free Energy Example Problems I 
54:16 
 
Intro 
0:00  
 
Example I 
0:11  
 
 Example I: Deriving a Function for Entropy (S) 
2:06  
 
 Example I: Deriving a Function for V 
5:55  
 
 Example I: Deriving a Function for H 
8:06  
 
 Example I: Deriving a Function for U 
12:06  
 
Example II 
15:18  
 
Example III 
21:52  
 
Example IV 
26:12  
 
 Example IV: Part A 
26:55  
 
 Example IV: Part B 
28:30  
 
 Example IV: Part C 
30:25  
 
Example V 
33:45  
 
Example VI 
40:46  
 
Example VII 
43:43  
 
 Example VII: Part A 
44:46  
 
 Example VII: Part B 
50:52  
 
 Example VII: Part C 
51:56  

Free Energy Example Problems II 
31:17 
 
Intro 
0:00  
 
Example I 
0:09  
 
Example II 
5:18  
 
Example III 
8:22  
 
Example IV 
12:32  
 
Example V 
17:14  
 
Example VI 
20:34  
 
 Example VI: Part A 
21:04  
 
 Example VI: Part B 
23:56  
 
 Example VI: Part C 
27:56  

Free Energy Example Problems III 
45:00 
 
Intro 
0:00  
 
Example I 
0:10  
 
Example II 
15:03  
 
Example III 
21:47  
 
Example IV 
28:37  
 
 Example IV: Part A 
29:33  
 
 Example IV: Part B 
36:09  
 
 Example IV: Part C 
40:34  

Three Miscellaneous Example Problems 
58:05 
 
Intro 
0:00  
 
Example I 
0:41  
 
 Part A: Calculating ∆H 
3:55  
 
 Part B: Calculating ∆S 
15:13  
 
Example II 
24:39  
 
 Part A: Final Temperature of the System 
26:25  
 
 Part B: Calculating ∆S 
36:57  
 
Example III 
46:49  
IX. Equation Review for Thermodynamics 

Looking Back Over Everything: All the Equations in One Place 
25:20 
 
Intro 
0:00  
 
Work, Heat, and Energy 
0:18  
 
 Definition of Work, Energy, Enthalpy, and Heat Capacities 
0:23  
 
 Heat Capacities for an Ideal Gas 
3:40  
 
 Path Property & State Property 
3:56  
 
 Energy Differential 
5:04  
 
 Enthalpy Differential 
5:40  
 
 Joule's Law & JouleThomson Coefficient 
6:23  
 
 Coefficient of Thermal Expansion & Coefficient of Compressibility 
7:01  
 
 Enthalpy of a Substance at Any Other Temperature 
7:29  
 
 Enthalpy of a Reaction at Any Other Temperature 
8:01  
 
Entropy 
8:53  
 
 Definition of Entropy 
8:54  
 
 Clausius Inequality 
9:11  
 
 Entropy Changes in Isothermal Systems 
9:44  
 
 The Fundamental Equation of Thermodynamics 
10:12  
 
 Expressing Entropy Changes in Terms of Properties of the System 
10:42  
 
 Entropy Changes in the Ideal Gas 
11:22  
 
 Third Law Entropies 
11:38  
 
 Entropy Changes in Chemical Reactions 
14:02  
 
 Statistical Definition of Entropy 
14:34  
 
 Omega for the Spatial & Energy Distribution 
14:47  
 
Spontaneity and Equilibrium 
15:43  
 
 Helmholtz Energy & Gibbs Energy 
15:44  
 
 Condition for Spontaneity & Equilibrium 
16:24  
 
 Condition for Spontaneity with Respect to Entropy 
17:58  
 
 The Fundamental Equations 
18:30  
 
 Maxwell's Relations 
19:04  
 
 The Thermodynamic Equations of State 
20:07  
 
 Energy & Enthalpy Differentials 
21:08  
 
 Joule's Law & JouleThomson Coefficient 
21:59  
 
 Relationship Between Constant Pressure & Constant Volume Heat Capacities 
23:14  
 
 One Final Equation  Just for Fun 
24:04  
X. Quantum Mechanics Preliminaries 

Complex Numbers 
34:25 
 
Intro 
0:00  
 
Complex Numbers 
0:11  
 
 Representing Complex Numbers in the 2Dimmensional Plane 
0:56  
 
 Addition of Complex Numbers 
2:35  
 
 Subtraction of Complex Numbers 
3:17  
 
 Multiplication of Complex Numbers 
3:47  
 
 Division of Complex Numbers 
6:04  
 
 r & θ 
8:04  
 
 Euler's Formula 
11:00  
 
 Polar Exponential Representation of the Complex Numbers 
11:22  
 
Example I 
14:25  
 
Example II 
15:21  
 
Example III 
16:58  
 
Example IV 
18:35  
 
Example V 
20:40  
 
Example VI 
21:32  
 
Example VII 
25:22  

Probability & Statistics 
59:57 
 
Intro 
0:00  
 
Probability & Statistics 
1:51  
 
 Normalization Condition 
1:52  
 
 Define the Mean or Average of x 
11:04  
 
Example I: Calculate the Mean of x 
14:57  
 
Example II: Calculate the Second Moment of the Data in Example I 
22:39  
 
Define the Second Central Moment or Variance 
25:26  
 
 Define the Second Central Moment or Variance 
25:27  
 
 1st Term 
32:16  
 
 2nd Term 
32:40  
 
 3rd Term 
34:07  
 
Continuous Distributions 
35:47  
 
 Continuous Distributions 
35:48  
 
Probability Density 
39:30  
 
 Probability Density 
39:31  
 
 Normalization Condition 
46:51  
 
Example III 
50:13  
 
 Part A  Show that P(x) is Normalized 
51:40  
 
 Part B  Calculate the Average Position of the Particle Along the Interval 
54:31  
 
Important Things to Remember 
58:24  

Schrӧdinger Equation & Operators 
42:05 
 
Intro 
0:00  
 
Schrӧdinger Equation & Operators 
0:16  
 
 Relation Between a Photon's Momentum & Its Wavelength 
0:17  
 
 Louis de Broglie: Wavelength for Matter 
0:39  
 
 Schrӧdinger Equation 
1:19  
 
 Definition of Ψ(x) 
3:31  
 
 Quantum Mechanics 
5:02  
 
 Operators 
7:51  
 
Example I 
10:10  
 
Example II 
11:53  
 
Example III 
14:24  
 
Example IV 
17:35  
 
Example V 
19:59  
 
Example VI 
22:39  
 
Operators Can Be Linear or Non Linear 
27:58  
 
 Operators Can Be Linear or Non Linear 
28:34  
 
Example VII 
32:47  
 
Example VIII 
36:55  
 
Example IX 
39:29  

Schrӧdinger Equation as an Eigenvalue Problem 
30:26 
 
Intro 
0:00  
 
Schrӧdinger Equation as an Eigenvalue Problem 
0:10  
 
 Operator: Multiplying the Original Function by Some Scalar 
0:11  
 
 Operator, Eigenfunction, & Eigenvalue 
4:42  
 
 Example: Eigenvalue Problem 
8:00  
 
 Schrӧdinger Equation as an Eigenvalue Problem 
9:24  
 
 Hamiltonian Operator 
15:09  
 
Quantum Mechanical Operators 
16:46  
 
 Kinetic Energy Operator 
19:16  
 
 Potential Energy Operator 
20:02  
 
 Total Energy Operator 
21:12  
 
 Classical Point of View 
21:48  
 
 Linear Momentum Operator 
24:02  
 
Example I 
26:01  

The Plausibility of the Schrӧdinger Equation 
21:34 
 
Intro 
0:00  
 
The Plausibility of the Schrӧdinger Equation 
1:16  
 
 The Plausibility of the Schrӧdinger Equation, Part 1 
1:17  
 
 The Plausibility of the Schrӧdinger Equation, Part 2 
8:24  
 
 The Plausibility of the Schrӧdinger Equation, Part 3 
13:45  
XI. The Particle in a Box 

The Particle in a Box Part I 
56:22 
 
Intro 
0:00  
 
Free Particle in a Box 
0:28  
 
 Definition of a Free Particle in a Box 
0:29  
 
 Amplitude of the Matter Wave 
6:22  
 
 Intensity of the Wave 
6:53  
 
 Probability Density 
9:39  
 
 Probability that the Particle is Located Between x & dx 
10:54  
 
 Probability that the Particle will be Found Between o & a 
12:35  
 
 Wave Function & the Particle 
14:59  
 
 Boundary Conditions 
19:22  
 
 What Happened When There is No Constraint on the Particle 
27:54  
 
 Diagrams 
34:12  
 
 More on Probability Density 
40:53  
 
The Correspondence Principle 
46:45  
 
 The Correspondence Principle 
46:46  
 
Normalizing the Wave Function 
47:46  
 
 Normalizing the Wave Function 
47:47  
 
 Normalized Wave Function & Normalization Constant 
52:24  

The Particle in a Box Part II 
45:24 
 
Intro 
0:00  
 
Free Particle in a Box 
0:08  
 
 Free Particle in a 1dimensional Box 
0:09  
 
 For a Particle in a Box 
3:57  
 
Calculating Average Values & Standard Deviations 
5:42  
 
 Average Value for the Position of a Particle 
6:32  
 
 Standard Deviations for the Position of a Particle 
10:51  
 
 Recall: Energy & Momentum are Represented by Operators 
13:33  
 
 Recall: Schrӧdinger Equation in Operator Form 
15:57  
 
 Average Value of a Physical Quantity that is Associated with an Operator 
18:16  
 
 Average Momentum of a Free Particle in a Box 
20:48  
 
The Uncertainty Principle 
24:42  
 
 Finding the Standard Deviation of the Momentum 
25:08  
 
 Expression for the Uncertainty Principle 
35:02  
 
 Summary of the Uncertainty Principle 
41:28  

The Particle in a Box Part III 
48:43 
 
Intro 
0:00  
 
2Dimension 
0:12  
 
 Dimension 2 
0:31  
 
 Boundary Conditions 
1:52  
 
 Partial Derivatives 
4:27  
 
Example I 
6:08  
 
The Particle in a Box, cont. 
11:28  
 
 Operator Notation 
12:04  
 
 Symbol for the Laplacian 
13:50  
 
 The Equation Becomes… 
14:30  
 
 Boundary Conditions 
14:54  
 
 Separation of Variables 
15:33  
 
 Solution to the 1dimensional Case 
16:31  
 
 Normalization Constant 
22:32  
 
3Dimension 
28:30  
 
 Particle in a 3dimensional Box 
28:31  
 
 In Del Notation 
32:22  
 
 The Solutions 
34:51  
 
 Expressing the State of the System for a Particle in a 3D Box 
39:10  
 
 Energy Level & Degeneracy 
43:35  
XII. Postulates and Principles of Quantum Mechanics 

The Postulates & Principles of Quantum Mechanics, Part I 
46:18 
 
Intro 
0:00  
 
Postulate I 
0:31  
 
 Probability That The Particle Will Be Found in a Differential Volume Element 
0:32  
 
Example I: Normalize This Wave Function 
11:30  
 
Postulate II 
18:20  
 
 Postulate II 
18:21  
 
 Quantum Mechanical Operators: Position 
20:48  
 
 Quantum Mechanical Operators: Kinetic Energy 
21:57  
 
 Quantum Mechanical Operators: Potential Energy 
22:42  
 
 Quantum Mechanical Operators: Total Energy 
22:57  
 
 Quantum Mechanical Operators: Momentum 
23:22  
 
 Quantum Mechanical Operators: Angular Momentum 
23:48  
 
 More On The Kinetic Energy Operator 
24:48  
 
Angular Momentum 
28:08  
 
 Angular Momentum Overview 
28:09  
 
 Angular Momentum Operator in Quantum Mechanic 
31:34  
 
 The Classical Mechanical Observable 
32:56  
 
 Quantum Mechanical Operator 
37:01  
 
 Getting the Quantum Mechanical Operator from the Classical Mechanical Observable 
40:16  
 
Postulate II, cont. 
43:40  
 
 Quantum Mechanical Operators are Both Linear & Hermetical 
43:41  

The Postulates & Principles of Quantum Mechanics, Part II 
39:28 
 
Intro 
0:00  
 
Postulate III 
0:09  
 
 Postulate III: Part I 
0:10  
 
 Postulate III: Part II 
5:56  
 
 Postulate III: Part III 
12:43  
 
 Postulate III: Part IV 
18:28  
 
Postulate IV 
23:57  
 
 Postulate IV 
23:58  
 
Postulate V 
27:02  
 
 Postulate V 
27:03  
 
Average Value 
36:38  
 
 Average Value 
36:39  

The Postulates & Principles of Quantum Mechanics, Part III 
35:32 
 
Intro 
0:00  
 
The Postulates & Principles of Quantum Mechanics, Part III 
0:10  
 
 Equations: Linear & Hermitian 
0:11  
 
 Introduction to Hermitian Property 
3:36  
 
 Eigenfunctions are Orthogonal 
9:55  
 
 The Sequence of Wave Functions for the Particle in a Box forms an Orthonormal Set 
14:34  
 
 Definition of Orthogonality 
16:42  
 
 Definition of Hermiticity 
17:26  
 
 Hermiticity: The Left Integral 
23:04  
 
 Hermiticity: The Right Integral 
28:47  
 
 Hermiticity: Summary 
34:06  

The Postulates & Principles of Quantum Mechanics, Part IV 
29:55 
 
Intro 
0:00  
 
The Postulates & Principles of Quantum Mechanics, Part IV 
0:09  
 
 Operators can be Applied Sequentially 
0:10  
 
 Sample Calculation 1 
2:41  
 
 Sample Calculation 2 
5:18  
 
 Commutator of Two Operators 
8:16  
 
 The Uncertainty Principle 
19:01  
 
 In the Case of Linear Momentum and Position Operator 
23:14  
 
 When the Commutator of Two Operators Equals to Zero 
26:31  
XIII. Postulates and Principles Example Problems, Including Particle in a Box 

Example Problems I 
54:25 
 
Intro 
0:00  
 
Example I: Three Dimensional Box & Eigenfunction of The Laplacian Operator 
0:37  
 
Example II: Positions of a Particle in a 1dimensional Box 
15:46  
 
Example III: Transition State & Frequency 
29:29  
 
Example IV: Finding a Particle in a 1dimensional Box 
35:03  
 
Example V: Degeneracy & Energy Levels of a Particle in a Box 
44:59  

Example Problems II 
46:58 
 
Intro 
0:00  
 
Review 
0:25  
 
 Wave Function 
0:26  
 
 Normalization Condition 
2:28  
 
 Observable in Classical Mechanics & Linear/Hermitian Operator in Quantum Mechanics 
3:36  
 
 Hermitian 
6:11  
 
 Eigenfunctions & Eigenvalue 
8:20  
 
 Normalized Wave Functions 
12:00  
 
 Average Value 
13:42  
 
 If Ψ is Written as a Linear Combination 
15:44  
 
 Commutator 
16:45  
 
Example I: Normalize The Wave Function 
19:18  
 
Example II: Probability of Finding of a Particle 
22:27  
 
Example III: Orthogonal 
26:00  
 
Example IV: Average Value of the Kinetic Energy Operator 
30:22  
 
Example V: Evaluate These Commutators 
39:02  

Example Problems III 
44:11 
 
Intro 
0:00  
 
Example I: Good Candidate for a Wave Function 
0:08  
 
Example II: Variance of the Energy 
7:00  
 
Example III: Evaluate the Angular Momentum Operators 
15:00  
 
Example IV: Real Eigenvalues Imposes the Hermitian Property on Operators 
28:44  
 
Example V: A Demonstration of Why the Eigenfunctions of Hermitian Operators are Orthogonal 
35:33  
XIV. The Harmonic Oscillator 

The Harmonic Oscillator I 
35:33 
 
Intro 
0:00  
 
The Harmonic Oscillator 
0:10  
 
 Harmonic Motion 
0:11  
 
 Classical Harmonic Oscillator 
4:38  
 
 Hooke's Law 
8:18  
 
 Classical Harmonic Oscillator, cont. 
10:33  
 
 General Solution for the Differential Equation 
15:16  
 
 Initial Position & Velocity 
16:05  
 
 Period & Amplitude 
20:42  
 
 Potential Energy of the Harmonic Oscillator 
23:20  
 
 Kinetic Energy of the Harmonic Oscillator 
26:37  
 
 Total Energy of the Harmonic Oscillator 
27:23  
 
 Conservative System 
34:37  

The Harmonic Oscillator II 
43:04 
 
Intro 
0:00  
 
The Harmonic Oscillator II 
0:08  
 
 Diatomic Molecule 
0:10  
 
 Notion of Reduced Mass 
5:27  
 
 Harmonic Oscillator Potential & The Intermolecular Potential of a Vibrating Molecule 
7:33  
 
 The Schrӧdinger Equation for the 1dimensional Quantum Mechanic Oscillator 
14:14  
 
 Quantized Values for the Energy Level 
15:46  
 
 Ground State & the ZeroPoint Energy 
21:50  
 
 Vibrational Energy Levels 
25:18  
 
 Transition from One Energy Level to the Next 
26:42  
 
 Fundamental Vibrational Frequency for Diatomic Molecule 
34:57  
 
 Example: Calculate k 
38:01  

The Harmonic Oscillator III 
26:30 
 
Intro 
0:00  
 
The Harmonic Oscillator III 
0:09  
 
 The Wave Functions Corresponding to the Energies 
0:10  
 
 Normalization Constant 
2:34  
 
 Hermite Polynomials 
3:22  
 
 First Few Hermite Polynomials 
4:56  
 
 First Few WaveFunctions 
6:37  
 
 Plotting the Probability Density of the WaveFunctions 
8:37  
 
 Probability Density for Large Values of r 
14:24  
 
 Recall: Odd Function & Even Function 
19:05  
 
 More on the Hermite Polynomials 
20:07  
 
 Recall: If f(x) is Odd 
20:36  
 
 Average Value of x 
22:31  
 
 Average Value of Momentum 
23:56  
XV. The Rigid Rotator 

The Rigid Rotator I 
41:10 
 
Intro 
0:00  
 
Possible Confusion from the Previous Discussion 
0:07  
 
 Possible Confusion from the Previous Discussion 
0:08  
 
Rotation of a Single Mass Around a Fixed Center 
8:17  
 
 Rotation of a Single Mass Around a Fixed Center 
8:18  
 
 Angular Velocity 
12:07  
 
 Rotational Inertia 
13:24  
 
 Rotational Frequency 
15:24  
 
 Kinetic Energy for a Linear System 
16:38  
 
 Kinetic Energy for a Rotational System 
17:42  
 
Rotating Diatomic Molecule 
19:40  
 
 Rotating Diatomic Molecule: Part 1 
19:41  
 
 Rotating Diatomic Molecule: Part 2 
24:56  
 
 Rotating Diatomic Molecule: Part 3 
30:04  
 
Hamiltonian of the Rigid Rotor 
36:48  
 
 Hamiltonian of the Rigid Rotor 
36:49  

The Rigid Rotator II 
30:32 
 
Intro 
0:00  
 
The Rigid Rotator II 
0:08  
 
 Cartesian Coordinates 
0:09  
 
 Spherical Coordinates 
1:55  
 
 r 
6:15  
 
 θ 
6:28  
 
 φ 
7:00  
 
 Moving a Distance 'r' 
8:17  
 
 Moving a Distance 'r' in the Spherical Coordinates 
11:49  
 
 For a Rigid Rotator, r is Constant 
13:57  
 
 Hamiltonian Operator 
15:09  
 
 Square of the Angular Momentum Operator 
17:34  
 
 Orientation of the Rotation in Space 
19:44  
 
 Wave Functions for the Rigid Rotator 
20:40  
 
 The Schrӧdinger Equation for the Quantum Mechanic Rigid Rotator 
21:24  
 
 Energy Levels for the Rigid Rotator 
26:58  

The Rigid Rotator III 
35:19 
 
Intro 
0:00  
 
The Rigid Rotator III 
0:11  
 
 When a Rotator is Subjected to Electromagnetic Radiation 
1:24  
 
 Selection Rule 
2:13  
 
 Frequencies at Which Absorption Transitions Occur 
6:24  
 
 Energy Absorption & Transition 
10:54  
 
 Energy of the Individual Levels Overview 
20:58  
 
 Energy of the Individual Levels: Diagram 
23:45  
 
 Frequency Required to Go from J to J + 1 
25:53  
 
 Using Separation Between Lines on the Spectrum to Calculate Bond Length 
28:02  
 
Example I: Calculating Rotational Inertia & Bond Length 
29:18  
 
 Example I: Calculating Rotational Inertia 
29:19  
 
 Example I: Calculating Bond Length 
32:56  
XVI. Oscillator and Rotator Example Problems 

Example Problems I 
33:48 
 
Intro 
0:00  
 
Equations Review 
0:11  
 
 Energy of the Harmonic Oscillator 
0:12  
 
 Selection Rule 
3:02  
 
 Observed Frequency of Radiation 
3:27  
 
 Harmonic Oscillator Wave Functions 
5:52  
 
 Rigid Rotator 
7:26  
 
 Selection Rule for Rigid Rotator 
9:15  
 
 Frequency of Absorption 
9:35  
 
 Wave Numbers 
10:58  
 
Example I: Calculate the Reduced Mass of the Hydrogen Atom 
11:44  
 
Example II: Calculate the Fundamental Vibration Frequency & the ZeroPoint Energy of This Molecule 
13:37  
 
Example III: Show That the Product of Two Even Functions is even 
19:35  
 
Example IV: Harmonic Oscillator 
24:56  

Example Problems II 
46:43 
 
Intro 
0:00  
 
Example I: Harmonic Oscillator 
0:12  
 
Example II: Harmonic Oscillator 
23:26  
 
Example III: Calculate the RMS Displacement of the Molecules 
38:12  
XVII. The Hydrogen Atom 

The Hydrogen Atom I 
40:00 
 
Intro 
0:00  
 
The Hydrogen Atom I 
1:31  
 
 Review of the Rigid Rotator 
1:32  
 
 Hydrogen Atom & the Coulomb Potential 
2:50  
 
 Using the Spherical Coordinates 
6:33  
 
 Applying This Last Expression to Equation 1 
10:19  
 
 Angular Component & Radial Component 
13:26  
 
 Angular Equation 
15:56  
 
 Solution for F(φ) 
19:32  
 
 Determine The Normalization Constant 
20:33  
 
 Differential Equation for T(a) 
24:44  
 
 Legendre Equation 
27:20  
 
 Legendre Polynomials 
31:20  
 
 The Legendre Polynomials are Mutually Orthogonal 
35:40  
 
 Limits 
37:17  
 
 Coefficients 
38:28  

The Hydrogen Atom II 
35:58 
 
Intro 
0:00  
 
Associated Legendre Functions 
0:07  
 
 Associated Legendre Functions 
0:08  
 
 First Few Associated Legendre Functions 
6:39  
 
 s, p, & d Orbital 
13:24  
 
 The Normalization Condition 
15:44  
 
Spherical Harmonics 
20:03  
 
 Equations We Have Found 
20:04  
 
 Wave Functions for the Angular Component & Rigid Rotator 
24:36  
 
 Spherical Harmonics Examples 
25:40  
 
Angular Momentum 
30:09  
 
 Angular Momentum 
30:10  
 
 Square of the Angular Momentum 
35:38  
 
 Energies of the Rigid Rotator 
38:21  

The Hydrogen Atom III 
36:18 
 
Intro 
0:00  
 
The Hydrogen Atom III 
0:34  
 
 Angular Momentum is a Vector Quantity 
0:35  
 
 The Operators Corresponding to the Three Components of Angular Momentum Operator: In Cartesian Coordinates 
1:30  
 
 The Operators Corresponding to the Three Components of Angular Momentum Operator: In Spherical Coordinates 
3:27  
 
 Z Component of the Angular Momentum Operator & the Spherical Harmonic 
5:28  
 
 Magnitude of the Angular Momentum Vector 
20:10  
 
 Classical Interpretation of Angular Momentum 
25:22  
 
 Projection of the Angular Momentum Vector onto the xyplane 
33:24  

The Hydrogen Atom IV 
33:55 
 
Intro 
0:00  
 
The Hydrogen Atom IV 
0:09  
 
 The Equation to Find R( r ) 
0:10  
 
 Relation Between n & l 
3:50  
 
 The Solutions for the Radial Functions 
5:08  
 
 Associated Laguerre Polynomials 
7:58  
 
 1st Few Associated Laguerre Polynomials 
8:55  
 
 Complete Wave Function for the Atomic Orbitals of the Hydrogen Atom 
12:24  
 
 The Normalization Condition 
15:06  
 
 In Cartesian Coordinates 
18:10  
 
 Working in Polar Coordinates 
20:48  
 
 Principal Quantum Number 
21:58  
 
 Angular Momentum Quantum Number 
22:35  
 
 Magnetic Quantum Number 
25:55  
 
 Zeeman Effect 
30:45  

The Hydrogen Atom V: Where We Are 
51:53 
 
Intro 
0:00  
 
The Hydrogen Atom V: Where We Are 
0:13  
 
 Review 
0:14  
 
 Let's Write Out ψ₂₁₁ 
7:32  
 
 Angular Momentum of the Electron 
14:52  
 
 Representation of the Wave Function 
19:36  
 
 Radial Component 
28:02  
 
 Example: 1s Orbital 
28:34  
 
 Probability for Radial Function 
33:46  
 
 1s Orbital: Plotting Probability Densities vs. r 
35:47  
 
 2s Orbital: Plotting Probability Densities vs. r 
37:46  
 
 3s Orbital: Plotting Probability Densities vs. r 
38:49  
 
 4s Orbital: Plotting Probability Densities vs. r 
39:34  
 
 2p Orbital: Plotting Probability Densities vs. r 
40:12  
 
 3p Orbital: Plotting Probability Densities vs. r 
41:02  
 
 4p Orbital: Plotting Probability Densities vs. r 
41:51  
 
 3d Orbital: Plotting Probability Densities vs. r 
43:18  
 
 4d Orbital: Plotting Probability Densities vs. r 
43:48  
 
Example I: Probability of Finding an Electron in the 2s Orbital of the Hydrogen 
45:40  

The Hydrogen Atom VI 
51:53 
 
Intro 
0:00  
 
The Hydrogen Atom VI 
0:07  
 
 Last Lesson Review 
0:08  
 
 Spherical Component 
1:09  
 
 Normalization Condition 
2:02  
 
Complete 1s Orbital Wave Function 
4:08  
 
 1s Orbital Wave Function 
4:09  
 
 Normalization Condition 
6:28  
 
 Spherically Symmetric 
16:00  
 
 Average Value 
17:52  
 
Example I: Calculate the Region of Highest Probability for Finding the Electron 
21:19  
 
2s Orbital Wave Function 
25:32  
 
 2s Orbital Wave Function 
25:33  
 
 Average Value 
28:56  
 
 General Formula 
32:24  

The Hydrogen Atom VII 
34:29 
 
Intro 
0:00  
 
The Hydrogen Atom VII 
0:12  
 
 p Orbitals 
1:30  
 
 Not Spherically Symmetric 
5:10  
 
 Recall That the Spherical Harmonics are Eigenfunctions of the Hamiltonian Operator 
6:50  
 
 Any Linear Combination of These Orbitals Also Has The Same Energy 
9:16  
 
 Functions of Real Variables 
15:53  
 
 Solving for Px 
16:50  
 
 Real Spherical Harmonics 
21:56  
 
 Number of Nodes 
32:56  
XVIII. Hydrogen Atom Example Problems 

Hydrogen Atom Example Problems I 
43:49 
 
Intro 
0:00  
 
Example I: Angular Momentum & Spherical Harmonics 
0:20  
 
Example II: Pairwise Orthogonal Legendre Polynomials 
16:40  
 
Example III: General Normalization Condition for the Legendre Polynomials 
25:06  
 
Example IV: Associated Legendre Functions 
32:13  

The Hydrogen Atom Example Problems II 
1:01:57 
 
Intro 
0:00  
 
Example I: Normalization & Pairwise Orthogonal 
0:13  
 
 Part 1: Normalized 
0:43  
 
 Part 2: Pairwise Orthogonal 
16:53  
 
Example II: Show Explicitly That the Following Statement is True for Any Integer n 
27:10  
 
Example III: Spherical Harmonics 
29:26  
 
Angular Momentum Cones 
56:37  
 
 Angular Momentum Cones 
56:38  
 
 Physical Interpretation of Orbital Angular Momentum in Quantum mechanics 
60:16  

The Hydrogen Atom Example Problems III 
48:33 
 
Intro 
0:00  
 
Example I: Show That ψ₂₁₁ is Normalized 
0:07  
 
Example II: Show That ψ₂₁₁ is Orthogonal to ψ₃₁₀ 
11:48  
 
Example III: Probability That a 1s Electron Will Be Found Within 1 Bohr Radius of The Nucleus 
18:35  
 
Example IV: Radius of a Sphere 
26:06  
 
Example V: Calculate <r> for the 2s Orbital of the Hydrogenlike Atom 
36:33  

The Hydrogen Atom Example Problems IV 
48:33 
 
Intro 
0:00  
 
Example I: Probability Density vs. Radius Plot 
0:11  
 
Example II: Hydrogen Atom & The Coulombic Potential 
14:16  
 
Example III: Find a Relation Among <K>, <V>, & <E> 
25:47  
 
Example IV: Quantum Mechanical Virial Theorem 
48:32  
 
Example V: Find the Variance for the 2s Orbital 
54:13  

The Hydrogen Atom Example Problems V 
48:33 
 
Intro 
0:00  
 
Example I: Derive a Formula for the Degeneracy of a Given Level n 
0:11  
 
Example II: Using Linear Combinations to Represent the Spherical Harmonics as Functions of the Real Variables θ & φ 
8:30  
 
Example III: Using Linear Combinations to Represent the Spherical Harmonics as Functions of the Real Variables θ & φ 
23:01  
 
Example IV: Orbital Functions 
31:51  
XIX. Spin Quantum Number and Atomic Term Symbols 

Spin Quantum Number: Term Symbols I 
59:18 
 
Intro 
0:00  
 
Quantum Numbers Specify an Orbital 
0:24  
 
 n 
1:10  
 
 l 
1:20  
 
 m 
1:35  
 
 4th Quantum Number: s 
2:02  
 
Spin Orbitals 
7:03  
 
 Spin Orbitals 
7:04  
 
 Multielectron Atoms 
11:08  
 
Term Symbols 
18:08  
 
 RussellSaunders Coupling & The Atomic Term Symbol 
18:09  
 
Example: Configuration for C 
27:50  
 
 Configuration for C: 1s²2s²2p² 
27:51  
 
 Drawing Every Possible Arrangement 
31:15  
 
 Term Symbols 
45:24  
 
 Microstate 
50:54  

Spin Quantum Number: Term Symbols II 
34:54 
 
Intro 
0:00  
 
Microstates 
0:25  
 
 We Started With 21 Possible Microstates 
0:26  
 
 ³P State 
2:05  
 
 Microstates in ³P Level 
5:10  
 
 ¹D State 
13:16  
 
 ³P State 
16:10  
 
 ²P₂ State 
17:34  
 
 ³P₁ State 
18:34  
 
 ³P₀ State 
19:12  
 
 9 Microstates in ³P are Subdivided 
19:40  
 
 ¹S State 
21:44  
 
 Quicker Way to Find the Different Values of J for a Given Basic Term Symbol 
22:22  
 
 Ground State 
26:27  
 
Hund's Empirical Rules for Specifying the Term Symbol for the Ground Electronic State 
27:29  
 
 Hund's Empirical Rules: 1 
28:24  
 
 Hund's Empirical Rules: 2 
29:22  
 
 Hund's Empirical Rules: 3  Part A 
30:22  
 
 Hund's Empirical Rules: 3  Part B 
31:18  
 
 Example: 1s²2s²2p² 
31:54  

Spin Quantum Number: Term Symbols III 
38:03 
 
Intro 
0:00  
 
Spin Quantum Number: Term Symbols III 
0:14  
 
 Deriving the Term Symbols for the p² Configuration 
0:15  
 
 Table: MS vs. ML 
3:57  
 
 ¹D State 
16:21  
 
 ³P State 
21:13  
 
 ¹S State 
24:48  
 
 J Value 
25:32  
 
 Degeneracy of the Level 
27:28  
 
 When Given r Electrons to Assign to n Equivalent Spin Orbitals 
30:18  
 
 p² Configuration 
32:51  
 
 Complementary Configurations 
35:12  

Term Symbols & Atomic Spectra 
57:49 
 
Intro 
0:00  
 
Lyman Series 
0:09  
 
 Spectroscopic Term Symbols 
0:10  
 
 Lyman Series 
3:04  
 
Hydrogen Levels 
8:21  
 
 Hydrogen Levels 
8:22  
 
Term Symbols & Atomic Spectra 
14:17  
 
 SpinOrbit Coupling 
14:18  
 
 Selection Rules for Atomic Spectra 
21:31  
 
 Selection Rules for Possible Transitions 
23:56  
 
 Wave Numbers for The Transitions 
28:04  
 
Example I: Calculate the Frequencies of the Allowed Transitions from (4d) ²D →(2p) ²P 
32:23  
 
Helium Levels 
49:50  
 
 Energy Levels for Helium 
49:51  
 
Transitions & Spin Multiplicity 
52:27  
 
 Transitions & Spin Multiplicity 
52:28  
XX. Term Symbols Example Problems 

Example Problems I 
1:01:20 
 
Intro 
0:00  
 
Example I: What are the Term Symbols for the np¹ Configuration? 
0:10  
 
Example II: What are the Term Symbols for the np² Configuration? 
20:38  
 
Example III: What are the Term Symbols for the np³ Configuration? 
40:46  

Example Problems II 
56:34 
 
Intro 
0:00  
 
Example I: Find the Term Symbols for the nd² Configuration 
0:11  
 
Example II: Find the Term Symbols for the 1s¹2p¹ Configuration 
27:02  
 
Example III: Calculate the Separation Between the Doublets in the Lyman Series for Atomic Hydrogen 
41:41  
 
Example IV: Calculate the Frequencies of the Lines for the (4d) ²D → (3p) ²P Transition 
48:53  
XXI. Equation Review for Quantum Mechanics 

Quantum Mechanics: All the Equations in One Place 
18:24 
 
Intro 
0:00  
 
Quantum Mechanics Equations 
0:37  
 
 De Broglie Relation 
0:38  
 
 Statistical Relations 
1:00  
 
 The Schrӧdinger Equation 
1:50  
 
 The Particle in a 1Dimensional Box of Length a 
3:09  
 
 The Particle in a 2Dimensional Box of Area a x b 
3:48  
 
 The Particle in a 3Dimensional Box of Area a x b x c 
4:22  
 
 The Schrӧdinger Equation Postulates 
4:51  
 
 The Normalization Condition 
5:40  
 
 The Probability Density 
6:51  
 
 Linear 
7:47  
 
 Hermitian 
8:31  
 
 Eigenvalues & Eigenfunctions 
8:55  
 
 The Average Value 
9:29  
 
 Eigenfunctions of Quantum Mechanics Operators are Orthogonal 
10:53  
 
 Commutator of Two Operators 
10:56  
 
 The Uncertainty Principle 
11:41  
 
 The Harmonic Oscillator 
13:18  
 
 The Rigid Rotator 
13:52  
 
 Energy of the Hydrogen Atom 
14:30  
 
 Wavefunctions, Radial Component, and Associated Laguerre Polynomial 
14:44  
 
 Angular Component or Spherical Harmonic 
15:16  
 
 Associated Legendre Function 
15:31  
 
 Principal Quantum Number 
15:43  
 
 Angular Momentum Quantum Number 
15:50  
 
 Magnetic Quantum Number 
16:21  
 
 zcomponent of the Angular Momentum of the Electron 
16:53  
 
 Atomic Spectroscopy: Term Symbols 
17:14  
 
 Atomic Spectroscopy: Selection Rules 
18:03  
XXII. Molecular Spectroscopy 

Spectroscopic Overview: Which Equation Do I Use & Why 
50:02 
 
Intro 
0:00  
 
Spectroscopic Overview: Which Equation Do I Use & Why 
1:02  
 
 Lesson Overview 
1:03  
 
 Rotational & Vibrational Spectroscopy 
4:01  
 
 Frequency of Absorption/Emission 
6:04  
 
 Wavenumbers in Spectroscopy 
8:10  
 
 Starting State vs. Excited State 
10:10  
 
 Total Energy of a Molecule (Leaving out the Electronic Energy) 
14:02  
 
 Energy of Rotation: Rigid Rotor 
15:55  
 
 Energy of Vibration: Harmonic Oscillator 
19:08  
 
 Equation of the Spectral Lines 
23:22  
 
Harmonic OscillatorRigid Rotor Approximation (Making Corrections) 
28:37  
 
 Harmonic OscillatorRigid Rotor Approximation (Making Corrections) 
28:38  
 
 VibrationRotation Interaction 
33:46  
 
 Centrifugal Distortion 
36:27  
 
 Anharmonicity 
38:28  
 
 Correcting for All Three Simultaneously 
41:03  
 
 Spectroscopic Parameters 
44:26  
 
Summary 
47:32  
 
 Harmonic OscillatorRigid Rotor Approximation 
47:33  
 
 VibrationRotation Interaction 
48:14  
 
 Centrifugal Distortion 
48:20  
 
 Anharmonicity 
48:28  
 
 Correcting for All Three Simultaneously 
48:44  

VibrationRotation 
59:47 
 
Intro 
0:00  
 
VibrationRotation 
0:37  
 
 What is Molecular Spectroscopy? 
0:38  
 
 Microwave, Infrared Radiation, Visible & Ultraviolet 
1:53  
 
 Equation for the Frequency of the Absorbed Radiation 
4:54  
 
 Wavenumbers 
6:15  
 
 Diatomic Molecules: Energy of the Harmonic Oscillator 
8:32  
 
 Selection Rules for Vibrational Transitions 
10:35  
 
 Energy of the Rigid Rotator 
16:29  
 
 Angular Momentum of the Rotator 
21:38  
 
 Rotational Term F(J) 
26:30  
 
 Selection Rules for Rotational Transition 
29:30  
 
 Vibration Level & Rotational States 
33:20  
 
 Selection Rules for VibrationRotation 
37:42  
 
 Frequency of Absorption 
39:32  
 
 Diagram: Energy Transition 
45:55  
 
 VibrationRotation Spectrum: HCl 
51:27  
 
 VibrationRotation Spectrum: Carbon Monoxide 
54:30  

VibrationRotation Interaction 
46:22 
 
Intro 
0:00  
 
VibrationRotation Interaction 
0:13  
 
 VibrationRotation Spectrum: HCl 
0:14  
 
 Bond Length & Vibrational State 
4:23  
 
 Vibration Rotation Interaction 
10:18  
 
 Case 1 
12:06  
 
 Case 2 
17:17  
 
Example I: HCl VibrationRotation Spectrum 
22:58  
 
 Rotational Constant for the 0 & 1 Vibrational State 
26:30  
 
 Equilibrium Bond Length for the 1 Vibrational State 
39:42  
 
 Equilibrium Bond Length for the 0 Vibrational State 
42:13  
 
 Bₑ & αₑ 
44:54  

The NonRigid Rotator 
29:24 
 
Intro 
0:00  
 
The NonRigid Rotator 
0:09  
 
 Pure Rotational Spectrum 
0:54  
 
 The Selection Rules for Rotation 
3:09  
 
 Spacing in the Spectrum 
5:04  
 
 Centrifugal Distortion Constant 
9:00  
 
 Fundamental Vibration Frequency 
11:46  
 
 Observed Frequencies of Absorption 
14:14  
 
 Difference between the Rigid Rotator & the Adjusted Rigid Rotator 
16:51  
 
 Adjusted Rigid Rotator 
21:31  
 
 Observed Frequencies of Absorption 
26:26  

The Anharmonic Oscillator 
30:53 
 
Intro 
0:00  
 
The Anharmonic Oscillator 
0:09  
 
 VibrationRotation Interaction & Centrifugal Distortion 
0:10  
 
 Making Corrections to the Harmonic Oscillator 
4:50  
 
 Selection Rule for the Harmonic Oscillator 
7:50  
 
 Overtones 
8:40  
 
 True Oscillator 
11:46  
 
 Harmonic Oscillator Energies 
13:16  
 
 Anharmonic Oscillator Energies 
13:33  
 
 Observed Frequencies of the Overtones 
15:09  
 
 True Potential 
17:22  
 
 HCl Vibrational Frequencies: Fundamental & First Few Overtones 
21:10  
 
Example I: Vibrational States & Overtones of the Vibrational Spectrum 
22:42  
 
 Example I: Part A  First 4 Vibrational States 
23:44  
 
 Example I: Part B  Fundamental & First 3 Overtones 
25:31  
 
Important Equations 
27:45  
 
 Energy of the Q State 
29:14  
 
 The Difference in Energy between 2 Successive States 
29:23  
 
 Difference in Energy between 2 Spectral Lines 
29:40  

Electronic Transitions 
1:01:33 
 
Intro 
0:00  
 
Electronic Transitions 
0:16  
 
 Electronic State & Transition 
0:17  
 
 Total Energy of the Diatomic Molecule 
3:34  
 
 Vibronic Transitions 
4:30  
 
 Selection Rule for Vibronic Transitions 
9:11  
 
 More on Vibronic Transitions 
10:08  
 
 Frequencies in the Spectrum 
16:46  
 
 Difference of the Minima of the 2 Potential Curves 
24:48  
 
 Anharmonic Zeropoint Vibrational Energies of the 2 States 
26:24  
 
 Frequency of the 0 → 0 Vibronic Transition 
27:54  
 
 Making the Equation More Compact 
29:34  
 
 Spectroscopic Parameters 
32:11  
 
 FranckCondon Principle 
34:32  
 
Example I: Find the Values of the Spectroscopic Parameters for the Upper Excited State 
47:27  
 
Table of Electronic States and Parameters 
56:41  
XXIII. Molecular Spectroscopy Example Problems 

Example Problems I 
33:47 
 
Intro 
0:00  
 
Example I: Calculate the Bond Length 
0:10  
 
Example II: Calculate the Rotational Constant 
7:39  
 
Example III: Calculate the Number of Rotations 
10:54  
 
Example IV: What is the Force Constant & Period of Vibration? 
16:31  
 
Example V: Part A  Calculate the Fundamental Vibration Frequency 
21:42  
 
Example V: Part B  Calculate the Energies of the First Three Vibrational Levels 
24:12  
 
Example VI: Calculate the Frequencies of the First 2 Lines of the R & P Branches of the VibRot Spectrum of HBr 
26:28  

Example Problems II 
1:01:05 
 
Intro 
0:00  
 
Example I: Calculate the Frequencies of the Transitions 
0:09  
 
Example II: Specify Which Transitions are Allowed & Calculate the Frequencies of These Transitions 
22:07  
 
Example III: Calculate the Vibrational State & Equilibrium Bond Length 
34:31  
 
Example IV: Frequencies of the Overtones 
49:28  
 
Example V: VibRot Interaction, Centrifugal Distortion, & Anharmonicity 
54:47  

Example Problems III 
33:31 
 
Intro 
0:00  
 
Example I: Part A  Derive an Expression for ∆G( r ) 
0:10  
 
Example I: Part B  Maximum Vibrational Quantum Number 
6:10  
 
Example II: Part A  Derive an Expression for the Dissociation Energy of the Molecule 
8:29  
 
Example II: Part B  Equation for ∆G( r ) 
14:00  
 
Example III: How Many Vibrational States are There for Br₂ before the Molecule Dissociates 
18:16  
 
Example IV: Find the Difference between the Two Minima of the Potential Energy Curves 
20:57  
 
Example V: Rotational Spectrum 
30:51  
XXIV. Statistical Thermodynamics 

Statistical Thermodynamics: The Big Picture 
1:01:15 
 
Intro 
0:00  
 
Statistical Thermodynamics: The Big Picture 
0:10  
 
 Our Big Picture Goal 
0:11  
 
 Partition Function (Q) 
2:42  
 
 The Molecular Partition Function (q) 
4:00  
 
 Consider a System of N Particles 
6:54  
 
 Ensemble 
13:22  
 
 Energy Distribution Table 
15:36  
 
 Probability of Finding a System with Energy 
16:51  
 
 The Partition Function 
21:10  
 
 Microstate 
28:10  
 
 Entropy of the Ensemble 
30:34  
 
 Entropy of the System 
31:48  
 
Expressing the Thermodynamic Functions in Terms of The Partition Function 
39:21  
 
 The Partition Function 
39:22  
 
 Pi & U 
41:20  
 
 Entropy of the System 
44:14  
 
 Helmholtz Energy 
48:15  
 
 Pressure of the System 
49:32  
 
 Enthalpy of the System 
51:46  
 
 Gibbs Free Energy 
52:56  
 
 Heat Capacity 
54:30  
 
Expressing Q in Terms of the Molecular Partition Function (q) 
59:31  
 
 Indistinguishable Particles 
62:16  
 
 N is the Number of Particles in the System 
63:27  
 
 The Molecular Partition Function 
65:06  
 
 Quantum States & Degeneracy 
67:46  
 
 Thermo Property in Terms of ln Q 
70:09  
 
 Example: Thermo Property in Terms of ln Q 
73:23  

Statistical Thermodynamics: The Various Partition Functions I 
47:23 
 
Intro 
0:00  
 
Lesson Overview 
0:19  
 
Monatomic Ideal Gases 
6:40  
 
 Monatomic Ideal Gases Overview 
6:42  
 
 Finding the Parition Function of Translation 
8:17  
 
 Finding the Parition Function of Electronics 
13:29  
 
 Example: Na 
17:42  
 
 Example: F 
23:12  
 
 Energy Difference between the Ground State & the 1st Excited State 
29:27  
 
 The Various Partition Functions for Monatomic Ideal Gases 
32:20  
 
 Finding P 
43:16  
 
 Going Back to U = (3/2) RT 
46:20  

Statistical Thermodynamics: The Various Partition Functions II 
54:09 
 
Intro 
0:00  
 
Diatomic Gases 
0:16  
 
 Diatomic Gases 
0:17  
 
 ZeroEnergy Mark for Rotation 
2:26  
 
 ZeroEnergy Mark for Vibration 
3:21  
 
 ZeroEnergy Mark for Electronic 
5:54  
 
 Vibration Partition Function 
9:48  
 
 When Temperature is Very Low 
14:00  
 
 When Temperature is Very High 
15:22  
 
 Vibrational Component 
18:48  
 
 Fraction of Molecules in the r Vibration State 
21:00  
 
 Example: Fraction of Molecules in the r Vib. State 
23:29  
 
 Rotation Partition Function 
26:06  
 
 Heteronuclear & Homonuclear Diatomics 
33:13  
 
 Energy & Heat Capacity 
36:01  
 
 Fraction of Molecules in the J Rotational Level 
39:20  
 
 Example: Fraction of Molecules in the J Rotational Level 
40:32  
 
 Finding the Most Populated Level 
44:07  
 
Putting It All Together 
46:06  
 
 Putting It All Together 
46:07  
 
 Energy of Translation 
51:51  
 
 Energy of Rotation 
52:19  
 
 Energy of Vibration 
52:42  
 
 Electronic Energy 
53:35  
XXV. Statistical Thermodynamics Example Problems 

Example Problems I 
48:32 
 
Intro 
0:00  
 
Example I: Calculate the Fraction of Potassium Atoms in the First Excited Electronic State 
0:10  
 
Example II: Show That Each Translational Degree of Freedom Contributes R/2 to the Molar Heat Capacity 
14:46  
 
Example III: Calculate the Dissociation Energy 
21:23  
 
Example IV: Calculate the Vibrational Contribution to the Molar heat Capacity of Oxygen Gas at 500 K 
25:46  
 
Example V: Upper & Lower Quantum State 
32:55  
 
Example VI: Calculate the Relative Populations of the J=2 and J=1 Rotational States of the CO Molecule at 25°C 
42:21  

Example Problems II 
57:30 
 
Intro 
0:00  
 
Example I: Make a Plot of the Fraction of CO Molecules in Various Rotational Levels 
0:10  
 
Example II: Calculate the Ratio of the Translational Partition Function for Cl₂ and Br₂ at Equal Volume & Temperature 
8:05  
 
Example III: Vibrational Degree of Freedom & Vibrational Molar Heat Capacity 
11:59  
 
Example IV: Calculate the Characteristic Vibrational & Rotational temperatures for Each DOF 
45:03  