×
Start learning today, and be successful in your academic & professional career. Start Today!

Raffi Hovasapian

Energy & the First Law I

Slide Duration:

Section 1: Classical Thermodynamics Preliminaries
The Ideal Gas Law

46m 5s

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

46m 2s

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
Section 2: Energy
Energy & the First Law I

1h 6m 45s

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
1:00:50
Convention for Heat
1:02:40
Convention for Work
1:04:24
Schematic Representation
1:05:00
Energy & the First Law II

1h 6m 33s

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
Pressure-Volume 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 Pressure-Volume 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

1h 2m 17s

Intro
0:00
Compression
0:20
Compression Overview
0:34
Single-stage compression vs. 2-stage Compression
2:16
Multi-stage Compression
8:40
Example I: Compression
14:47
Example 1: Single-stage Compression
14:47
Example 1: 2-stage 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

1h 4m 39s

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
1:02:06
Joule's Experiment

16m 50s

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

43m 40s

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

32m 23s

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

39m 15s

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
Joule-Thompson Coefficient
29:50
Changing Temperature & Pressure in Such a Way that Enthalpy Remains Constant
31:44
Joule Thompson Inversion Temperature
36:26
Positive & Negative Joule-Thompson Coefficient
36:27
Joule Thompson Inversion Temperature
37:22
Inversion Temperature of Hydrogen Gas
37:59

35m 52s

Intro
0:00
0:10
0:18
Work & Energy in an Adiabatic Process
3:44
Pressure-Volume 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
18:08
18:09
21:54
22:34
Fundamental Relationship Equation for an Ideal Gas Under Adiabatic Expansion
25:00
More on the Equation
28:20
Important Equations
32:16
32:17
Reversible Adiabatic Change of State Equation
33:02
Section 3: Energy Example Problems
1st Law Example Problems I

42m 40s

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
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

1h 23s

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

44m 34s

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

59m 7s

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
Section 4: Entropy
Entropy

49m 16s

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

33m 59s

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

54m 37s

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
Temperature-dependence of Entropy
24:00
Example I
26:19
Entropy As a Function of Temperature & Volume, Cont.
31:55
Volume-dependence 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 Volume-dependence of Entropy for Liquids & Solids
52:52
Entropy as a Function of Temperature & Pressure

31m 18s

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
Temperature-dependence
7:08
Pressure-dependence
9:04
Differentiate with Respect to Pressure & Holding Temperature Constant
9:54
Differentiate with Respect to Temperature & Holding Pressure Constant
11:28
Pressure-Dependence of Entropy for Liquids & Solids
18:45
Pressure-Dependence of Entropy for Liquids & Solids
18:46
Example I: ∆S of Transformation
26:20
Summary of Entropy So Far

23m 6s

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
Temperature-dependence of Entropy
19:49
Entropy Changes for an Ideal Gas

25m 42s

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
Section 5: Entropy Example Problems
Entropy Example Problems I

43m 39s

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/mol-K, 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

56m 44s

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

57m 6s

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
Section 6: Entropy and Probability
Entropy & Probability I

54m 35s

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

35m 5s

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
Section 7: Spontaneity, Equilibrium, and the Fundamental Equations
Spontaneity & Equilibrium I

28m 42s

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
Pressure-volume Work
22:02
Spontaneity & Equilibrium II

34m 38s

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

30m 50s

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 Volume-Dependence of Entropy & Isothermal Pressure-Dependence of Entropy
26:21
The General Thermodynamic Equations of State

34m 6s

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 Joule-Thomson Coefficient
30:44
Joule-Thomson Inversion Temperature
32:12
Properties of the Helmholtz & Gibbs Energies

39m 18s

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

19m 40s

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
Section 8: Free Energy Example Problems
Free Energy Example Problems I

54m 16s

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

31m 17s

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

45m

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

58m 5s

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
Section 9: Equation Review for Thermodynamics
Looking Back Over Everything: All the Equations in One Place

25m 20s

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 & Joule-Thomson 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 & Joule-Thomson Coefficient
21:59
Relationship Between Constant Pressure & Constant Volume Heat Capacities
23:14
One Final Equation - Just for Fun
24:04
Section 10: Quantum Mechanics Preliminaries
Complex Numbers

34m 25s

Intro
0:00
Complex Numbers
0:11
Representing Complex Numbers in the 2-Dimmensional Plane
0:56
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

59m 57s

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

42m 5s

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

30m 26s

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

21m 34s

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
Section 11: The Particle in a Box
The Particle in a Box Part I

56m 22s

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

45m 24s

Intro
0:00
Free Particle in a Box
0:08
Free Particle in a 1-dimensional 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

48m 43s

Intro
0:00
2-Dimension
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 1-dimensional Case
16:31
Normalization Constant
22:32
3-Dimension
28:30
Particle in a 3-dimensional 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
Section 12: Postulates and Principles of Quantum Mechanics
The Postulates & Principles of Quantum Mechanics, Part I

46m 18s

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

39m 28s

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

35m 32s

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

29m 55s

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
Section 13: Postulates and Principles Example Problems, Including Particle in a Box
Example Problems I

54m 25s

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

46m 58s

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

44m 11s

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
Section 14: The Harmonic Oscillator
The Harmonic Oscillator I

35m 33s

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

43m 4s

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 1-dimensional Quantum Mechanic Oscillator
14:14
Quantized Values for the Energy Level
15:46
Ground State & the Zero-Point 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

26m 30s

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 Wave-Functions
6:37
Plotting the Probability Density of the Wave-Functions
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
Section 15: The Rigid Rotator
The Rigid Rotator I

41m 10s

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

30m 32s

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

35m 19s

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
Section 16: Oscillator and Rotator Example Problems
Example Problems I

33m 48s

Intro
0:00
Equations Review
0:11
Energy of the Harmonic Oscillator
0:12
Selection Rule
3:02
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 Zero-Point 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

46m 43s

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
Section 17: The Hydrogen Atom
The Hydrogen Atom I

40m

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
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

35m 58s

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

36m 18s

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 xy-plane
33:24
The Hydrogen Atom IV

33m 55s

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

51m 53s

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
28:02
Example: 1s Orbital
28:34
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

51m 53s

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

34m 29s

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
Section 18: Hydrogen Atom Example Problems
Hydrogen Atom Example Problems I

43m 49s

Intro
0:00
Example I: Angular Momentum & Spherical Harmonics
0:20
Example II: Pair-wise 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

1h 1m 57s

Intro
0:00
Example I: Normalization & Pair-wise Orthogonal
0:13
Part 1: Normalized
0:43
Part 2: Pair-wise 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
1:00:16
The Hydrogen Atom Example Problems III

48m 33s

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 Hydrogen-like Atom
36:33
The Hydrogen Atom Example Problems IV

48m 33s

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

48m 33s

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
Section 19: Spin Quantum Number and Atomic Term Symbols
Spin Quantum Number: Term Symbols I

59m 18s

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
Multi-electron Atoms
11:08
Term Symbols
18:08
Russell-Saunders 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

34m 54s

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

38m 3s

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

57m 49s

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
Spin-Orbit 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
Section 20: Term Symbols Example Problems
Example Problems I

1h 1m 20s

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

56m 34s

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
Section 21: Equation Review for Quantum Mechanics
Quantum Mechanics: All the Equations in One Place

18m 24s

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 1-Dimensional Box of Length a
3:09
The Particle in a 2-Dimensional Box of Area a x b
3:48
The Particle in a 3-Dimensional 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
z-component of the Angular Momentum of the Electron
16:53
Atomic Spectroscopy: Term Symbols
17:14
Atomic Spectroscopy: Selection Rules
18:03
Section 22: Molecular Spectroscopy
Spectroscopic Overview: Which Equation Do I Use & Why

50m 2s

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 Oscillator-Rigid Rotor Approximation (Making Corrections)
28:37
Harmonic Oscillator-Rigid Rotor Approximation (Making Corrections)
28:38
Vibration-Rotation 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 Oscillator-Rigid Rotor Approximation
47:33
Vibration-Rotation Interaction
48:14
Centrifugal Distortion
48:20
Anharmonicity
48:28
Correcting for All Three Simultaneously
48:44
Vibration-Rotation

59m 47s

Intro
0:00
Vibration-Rotation
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 Vibration-Rotation
37:42
Frequency of Absorption
39:32
Diagram: Energy Transition
45:55
Vibration-Rotation Spectrum: HCl
51:27
Vibration-Rotation Spectrum: Carbon Monoxide
54:30
Vibration-Rotation Interaction

46m 22s

Intro
0:00
Vibration-Rotation Interaction
0:13
Vibration-Rotation 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 Vibration-Rotation 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 Non-Rigid Rotator

29m 24s

Intro
0:00
The Non-Rigid 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
21:31
Observed Frequencies of Absorption
26:26
The Anharmonic Oscillator

30m 53s

Intro
0:00
The Anharmonic Oscillator
0:09
Vibration-Rotation 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

1h 1m 33s

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 Zero-point 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
Franck-Condon 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
Section 23: Molecular Spectroscopy Example Problems
Example Problems I

33m 47s

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 Vib-Rot Spectrum of HBr
26:28
Example Problems II

1h 1m 5s

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: Vib-Rot Interaction, Centrifugal Distortion, & Anharmonicity
54:47
Example Problems III

33m 31s

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
Section 24: Statistical Thermodynamics
Statistical Thermodynamics: The Big Picture

1h 1m 15s

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
1:02:16
N is the Number of Particles in the System
1:03:27
The Molecular Partition Function
1:05:06
Quantum States & Degeneracy
1:07:46
Thermo Property in Terms of ln Q
1:10:09
Example: Thermo Property in Terms of ln Q
1:13:23
Statistical Thermodynamics: The Various Partition Functions I

47m 23s

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

54m 9s

Intro
0:00
Diatomic Gases
0:16
Diatomic Gases
0:17
Zero-Energy Mark for Rotation
2:26
Zero-Energy Mark for Vibration
3:21
Zero-Energy 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
Section 25: Statistical Thermodynamics Example Problems
Example Problems I

48m 32s

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

57m 30s

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

• ## Related Books

 1 answerLast reply by: Professor HovasapianFri Apr 7, 2017 6:34 PMPost by Sunanda Eluri on April 4, 2017If w amount of work is done by the system and q amount of heat is supplied to the system. What type of system would it be? 1 answerLast reply by: Professor HovasapianSat Sep 5, 2015 3:56 PMPost by Shukree AbdulRashed on September 5, 2015Hello. I have a question about the the ideas presented at the 40:00 min mark. In my lecture notes, it states that when the system gains heat - q is positive. When the system loses heat - q is negative. Doesn't this directly contradict what is presented in you lecture. From my understanding, if a mass of water is cooled, doesn't that mean that the surroundings were at a lower temperature than the water itself? Thus, heat has flown from the system (the mass of water) to the surroundings (the air outside the beaker). However, it is stated that the heat has flown from the surroundings. I'm afraid I don't understand. Thank you. 3 answersLast reply by: Professor HovasapianSat Dec 27, 2014 10:02 PMPost by Kweku Konadu on October 25, 2014Is there a way to increase the speed of the videos?

### Energy & the First Law I

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Properties of Thermodynamic State 1:38
• Big Picture: 3 Properties of Thermodynamic State
• Enthalpy & Free Energy
• Associated Law
• Energy & the First Law of Thermodynamics 7:13
• System & Its Surrounding Separated by a Boundary
• In Other Cases the Boundary is Less Clear
• State of a System 12:37
• State of a System
• Change in State
• Path for a Change in State
• Example: State of a System
• Open, Close, and Isolated System 18:26
• Open System
• Closed System
• Isolated System
• Important Questions 20:38
• Important Questions
• Work & Heat 22:50
• Definition of Work
• Properties of Work
• Definition of Heat
• Properties of Heat
• Experiment #1
• Experiment #2
• More on Work & Heat 54:50
• More on Work & Heat
• Conventions for Heat & Work 1:00:50
• Convention for Heat
• Convention for Work
• Schematic Representation

### Transcription: Energy & the First Law I

Hello and welcome back to www.educator.com and welcome back to Physical Chemistry.0000

Today, we are going to begin our discussion of thermodynamics and we are going to begin with energy and the first law of thermodynamics.0004

The next several lessons, what they are going to be is primarily just a theoretical discussion, back ground discussion, basic information.0013

Some of this information you already will know from general chemistry.0022

Some of it may be new to you or some of that maybe we will be looking at it in a way that perhaps you have not looked at before.0026

For the most part, this is just a collection of definitions and facts and things that we are going to be using.0033

Terms that we are going to be using, making sure that everything is defined well so that when we run into these things and use them on a regular basis,0039

we will know what it is that we are talking about.0046

One thing I would like you to know about the nature of Physical Chemistry in general, we are going to be doing a lot of example problems in this course.0049

A lot, I mean a lot.0056

We will be doing them in the lessons themselves, although the nature of the course, what is going to be happening is,0059

many of the lessons are going to be presented and there is a lot of theoretical discussion or just a general discussion of principles and processes.0067

Although, we will be doing some of the example problems within the lessons themselves,0079

I’m going to save the bulk of the example problems to do in separate lessons altogether.0083

It simply works out better that way given the nature of this particular course.0088

Having said that, let us go ahead and jump right on in.0093

Let us see what we have here.0099

What I'm going to do is to start off by discussing the big picture of thermodynamics.0101

Something that is not often talked about in most of general chemistry course or most thermodynamics courses.0107

But we want you to have the big picture and we want to close in.0113

The big picture, there are 3 properties.0118

Let me write this to get a little bit more room.0126

In fact, I think I’m going to go with blue.0132

The big picture, 3 properties completely describe the thermodynamic state of any system.0143

This might be a bit of a surprise when you see this state of any system.0158

They are the temperature T, the energy we will use a variable u for energy, and the entropy.0179

You have heard these terms before, entropy we are going to use S.0196

If you know the temperature of the system, if you know how much energy the system contains, and if you know the entropy of the system,0200

that these 3 are all you need for complete thermodynamic description.0207

Now you are probably wondering what happened to enthalpy, what happened to free energy?0211

Properties such as enthalpy, which you know as SH or δ H the change in enthalpy, and free energy which you know as g, that gives free energy.0217

These are actually derive properties.0242

They are accounting devices used to either simplify calculations, make something more experimentally easy to deal with.0253

They are not actual thermodynamic properties.0266

I will just call them, they are accounting devices and you will see what we mean when we actually discuss them.0269

Each of the 3 fundamental thermodynamic properties it has an associated law.0287

Again, this might be a bit of a surprise when I'm about to write down.0311

You have heard the first law of thermodynamics, the second law, the third law.0317

You might not remember what it is that they are but you know that there is a first, a second, and a third law.0321

However, temperature, energy, and entropy, are not the first, second, and the third law.0325

As it turns out, the temperature is associated with something that we call the zero flaw.0329

We are not concern what it is right now, it just happens to do with temperature.0336

Energy is the one that is associated with the first law.0341

Entropy is associated with the second law.0346

When thermodynamics developed, the reason we call the zero of law is it was sort of a logical realization.0353

Once the first, second, and third laws were established, the thermodynamic, classical thermodynamics, was set in place,0360

we stopped and says wait a minute, we need to somehow deal with this notion of temperature just to form this formal system,0365

that the logic behind what is an empirical study.0373

That is classical thermodynamics is entirely empirical.0379

We went back and said let us tighten up a little bit.0383

We need to logically go back and talk about this thing called temperature before we can actually move forward.0387

Because they already used the number 1, they have decided to call this the zero of law.0394

Temperature is zero of law, energy first law, and entropy second law.0398

The third law is less general and it only applies just to one class of substance, a crystal under specific set of conditions, basically, 0° K.0405

These are general laws, the zero, the first, and second, the third law is less general.0419

We will be discussing it but as far as the properties themselves are concerned , this is the relationship.0425

We are going to begin our discussion with energy and the first law.0433

We will begin with energy and the first law.0442

Let us go ahead and get started.0456

When we speak about thermodynamic scenario, we speak of the system and its surroundings separated by a boundary.0459

Schematically, we know we have something like this.0484

We can do it over here, it is not a problem.0493

This is going to be our system, this is going to be our surroundings, and this is going to be our boundary.0499

It is up to us what we want to describe as our system, what we want to choose is our surroundings.0512

What we want to choose is our boundary.0517

The system + the surroundings = what we call the universe, that is it.0520

Now in some cases, the distinction between system and surroundings is very clear.0530

For example, if I had a beaker of water let us say at 100°C, this is our system.0534

And the surroundings would be the air outside, the boundary would be the actual beaker itself, the glass.0550

Technically, the boundary is the inside surface of the glass.0557

Technically, it is where the system just separates from the surroundings.0562

The glass itself is actually considered part of the surroundings where they meet the inside surface where the water touches the glass.0567

That is actually the boundary.0579

You know that in certain circumstances, let us say if you have some beaker and you are running some endothermic reaction on that.0583

Endothermic reaction is a reaction that absorbs heat.0589

What happens is, the beaker gets cold to your touch.0593

What is happening here is that the heat that is required, that is being absorbed by the particular reaction,0598

is being absorbed initially not from the surrounding air, it is being absorbed from the glass itself.0604

Heat is being pulled from the glass, which is why when you touch it, it feels cold.0612

Eventually, heat from the surrounding air will move into the glass, that will happen.0616

By some process, yes, heat is coming in from the surroundings but the initial heat is actually coming from the glass itself, which is why the glass feels cold.0625

The inside surface of the particular beaker is the technical boundary.0633

For practical purposes, it does not matter.0638

In other cases, it is not so clear what the boundary is, this is often the case in chemistry.0640

In other cases, the boundary is less clear.0648

A perfect example of that is the reaction of potassium hydroxide + hydrochloric acid giving us water.0663

I tend to write water as HOH just to remind myself that it is an H and OH in neutralization reaction + potassium chloride.0675

In this particular case, the surroundings is the water, the system is the reaction itself.0685

There is no clear distinct boundary that we can see when it comes for reaction.0695

We are running a reaction in aqueous medium, the reaction is either going to be endothermic or exothermic, it is going to absorb heat or release heat.0699

When we draw it schematically, we can draw a little box or a circle, whatever you want.0708

It is the reaction, that is the system.0713

And in this particular case, the aqueous environment around it that is the surroundings.0715

There is no clear distinct boundary but we can always choose an appropriate boundary or an idealized boundary in this case, in order to discuss it.0720

The reaction is the system and the aqueous environment is the surroundings.0731

The boundary is not so clear but it is there in some sense.0751

Let us go ahead, we speak about the state of the system.0757

We are going to hear the word state a lot in thermodynamics.0767

We speak about the state of the system and the state is when each of the systems properties has a given value.0771

A particular system itself will decide what those properties are.0805

In the case of let us say a gas, pretty much all we need is the pressure, the volume, the temperature, and0812

let us go ahead and use the Pv=nrt and the number of moles.0820

If we know the pressure, the volume, the temperature, the number of moles, we know the gases in that particular state.0824

If we change any of those variables, we have a change of state.0831

There is a new pressure, a new temperature, a new volume, and possibly a new number of moles.0834

We speak of the change in state or change of state, that is when the initial and final states are specified.0846

I think you already know but we do want to formalize it to a fair extent.0876

Being precise is going to be very important in thermodynamics.0883

There is a lot of definitions are very restricted meanings.0886

We speak of the path, it is going to be very important, the path for a change in state.0892

The path that is exactly what you think it is.0917

It is the individual steps taken by a system in going from state initial to state final.0923

If we want to take a look, let us see, let us do a quick 4 example and we will go ahead and use something that we are going to be using a lot of the pressure volume graph.0948

Pressure and volume, let us use one of the isotherms.0964

You remember the isotherms?0969

If you are going to keep the temperature constant, you are going to end up getting a graph the relationship between pressure and volume.0971

As pressure decreases, volume increases, or as volume increases, pressure decreases.0977

This if you do, if you perform the change in volume, change in pressure, and keep the temperature constant, it is going to follow something called a isothermal.0982

Let us call this as our initial state, let us call this as our final state.0993

Let me go ahead and do SI and SF, initial and final state, the path in going from initial state to final state, I can do this many ways.0998

I can go that way and then this way, I can go this way and that one.1008

I can actually follow the isotherm, I can go this way.1019

Let me go ahead and put arrows like this.1024

I can maybe go in all kinds of ways and if I want I can go this way and that way and backup and that way.1027

Finally, end up here.1037

There are different paths that I can actually take in going from initial state to final state.1038

The path is going to be very important later when we discuss work and heat.1044

As it turns out, work and heat are path functions.1048

How much work a system does or is done to, or how much is transfer to a system or from a system, actually depends on1053

the path that we take in going from an initial state to a final state.1062

As it will turn and we will see, energy itself does not matter what path we take.1066

All that matters is the initial state and the final state.1071

In the case of work and heat, path is very important.1074

If I want to fly from here to New York, I can do a couple ways.1080

I can just fly straight or I can fly to Seattle first then to Miami, then go to New York.1085

The initial and final states are the same but clearly I’m going to end up spending a lot more time, a lot more gas going to Seattle first then to Miami then to New York.1089

The path actually makes a difference.1099

Let us go ahead and let us see, I think I’m going to go ahead and go to a change of pace here.1104

Let us define an open system.1112

An open system is where both mass and energy can transfer to and from the system.1117

In other words, it can cross the boundary.1123

Both mass and energy can cross the boundary.1127

By boundary, we are talking about the boundary between system and surroundings.1140

A close system is one where only energy can cross the boundary, no mass can cross the boundary.1144

We have a final which we call an isolated system, that is exactly what you think it is.1163

It is where neither mass nor energy can cross the boundary.1172

It is very important.1193

An isolated system does not produce any observable effect in the surroundings.1197

This is obvious but we do want to state it.1205

An isolated system does not produce any observable effect in its surroundings, profoundly important.1212

Let me go ahead and go back to blue, I like blue a lot better.1240

Important questions to ask for every scenario that you come across, every problem that you do, these are questions that you want to keep in mind.1248

You want to ask many questions but these are the basic fundamental questions that you always want to be aware of.1271

The scenario is either explicitly or implicitly, what is the system? What is the surroundings? What is the boundary?1281

You have to be very clear on these things.1314

What is the boundary? What is the initial state? What is the final state? What is the path?1321

It is profoundly important.1334

I will just put ETC for etcetera, several questions depending on the particular scenario.1336

We definitely keep these things in mind.1341

Any time you face a new problem, make sure that you know what your system is, what your surroundings are,1343

what your boundary is, what your initial state is, what your final state is, what path you are taking.1348

If you have these things then you can go ahead and work out the rest, hopefully.1354

That is going to be the test.1358

Let us talk about work and heat.1364

Let us go ahead and talk about work and heat, profoundly important.1372

Let us go ahead and begin with work, let us give a nice definition here.1383

I think I’m going to start on the next page.1387

These are very specific definitions.1397

They are going to seem self evident to some extent, some of the things that I say maybe flagrantly obvious1400

but we want to be very clear about them, which is why we are laying them out like this in such a formal manner.1408

Work is the process by which the quantity of energy flows, we will also use the term transferred, is transferred,1414

flows or transferred across the boundary between system and surroundings and which can be converted to the lifting of a weight in the surroundings.1454

This is the most important part, in the surroundings.1497

When we would talk about work that flowed, work is energy.1501

It is a quantity of energy that flows between a system and surroundings.1504

As it turns out, this particular energy that flows is energy that can be used to lift a weight in the surroundings or1509

if the work happens to flow from the surroundings to the system, leaves the surroundings the weight itself will go down.1520

When we talk about lifting a weight, we are talking either positive or negative.1529

Some notes on work, things to definitely keep in mind.1536

Work appears only during the change of state.1551

In other words, if there is a change of state, some kind of energy is used, if work shows up that means the final state1568

is not the same as the initial state of system or surroundings.1574

Work appears only during the change of state.1578

Work is recognized, identified as work by an effect in the surroundings.1587

This is probably the most important part.1603

In the surroundings, what happens, what we observe in the surroundings that let us know what actually is happening in the system.1609

It is indirect, we do not actually observe the system, we observe the effect of the surroundings and that tells us what is happening in the system.1617

The third part, the magnitude, in another words, the quantity itself, the magnitude of the work is mgh, mass × acceleration of gravity × the height,1627

through which the particular weight in the surroundings has gone up or down.1648

Work is a quantity because it is a quantity, therefore, these 3 dots means therefore, it can be positive or it can be negative.1658

Work can flow from the surroundings to the system.1677

Work can flow from the system to the surroundings.1680

In thermodynamics, we take a point of view.1682

In thermodynamics, when we talk about energy that is flowing in the form of work or heat, we are talking about a direction.1685

Positive and negative signs of thermodynamics they have to do with direction.1692

Either themselves are not that important as long as we can keep track of the direction.1696

We can speak qualitatively it is going from the system to the surroundings, from the surroundings to the system.1700

We can keep that straight then we just have to deal with magnitudes, positive and negative signs do not matter.1707

When we do the mathematics, any negative sign means that it is moving a particular direction depending on what point of view we have taken first.1711

We have to decide, am I taking the surroundings point of view or am I taking the systems point of view?1721

As it turns out, it does not really matter what point of view you take, as long as you have a convention and stick with that convention.1726

And if the convention is different than anything that you have learned before or is a new convention that you come across, all you really doing is switching the signs.1733

As all you are doing is taking a positive and putting a negative sign in front of it.1741

Do not worry so much about conventions, we will talk a little bit about that in a while.1744

Let me see, work is a quantity and therefore, it can be positive or negative.1751

It is positive if a mass has been lifted in the surroundings.1756

In other words, if h is positive, if the height through which the mass moves.1778

If h is positive.1785

In this particular case, we say work has flowed or flown to the surroundings or work has been produced in the surroundings.1792

When we talk about work, it is going to be positive from the surroundings point of view.1827

If a weight has been lifted in the surroundings, work is positive, that means work has flown into the surroundings normally from the system.1842

Or work has been produced in the surroundings.1854

We would use both of those descriptions.1857

Work is negative if a mass is lowered in the surroundings.1863

In other words, if the height is negative, if a weight has dropped in the surroundings.1880

This particular case, we say work has flowed from the surroundings or work has been destroyed.1894

We will use both descriptions.1917

Work has been destroyed in the surroundings, clearly prepositions.1921

It is very important in thermodynamics, from ,to, in.1926

Do not worry we will actually be discussing this in a lot more detail.1933

Heat is the process, notice that I’m using the word process in the definition of work and a definition of heat.1944

It is the process by which the quantity of energy flows across the boundary between system and surroundings1953

due to the difference in temperature between the system and surroundings.1989

The heat itself flows from the regions of higher temperature to regions of lower temperature.2010

If you have something that is 100° and if you have something that is 50° and you put them into contact with each other, heat is going to flow from the 100° to 50°.2032

The temperature the 100° is going to drop, the 50° of temperature is going to rise and it is going to come to some sort of thermal equilibrium.2045

There is going to be a final temperature that both of them will reach.2053

Heat is not a thing, it is a quantity but it is a process.2058

It is what happens when you put two things in contact that are of different temperatures.2062

All of the sudden there is some spontaneous flow of energy so that is what heat is.2067

It is the process by which a quantity of energy flows across the boundary between the system and surroundings due to the difference in temperature between the two.2072

Heat flows from regions of higher temperature to regions of lower temperature.2080

Let us go ahead and say a few words about heat itself.2087

So notes on heat, not altogether different than work.2091

Heat appears only during the change of state and heat is recognized by an effect in the surroundings.2103

That is how we recognize heat, that heat is flowed.2144

By what happens when we observe the surroundings, we observe the system.2154

This next one, I will write it down, not something that you really have to remember, keep in mind.2162

As more of a formality, the magnitude of the heat is proportional to the mass of water in the surroundings that increases or decreases in temperature by 1°C.2167

When we say 1°, when we are working to thermodynamics we are going to work in K.2224

I will make it 1° to make it more generic.2230

We have set the work, the magnitude of the work was mass × acceleration × the height, to which the particular weight in the surroundings moved.2237

Analogously, the magnitude of the heat is going to be proportional to the mass of water in the surroundings that increases or decreases in temperature by 1°.2247

If there is a certain mass of water in the surroundings that ends up getting 2° hotter,2255

those 2 units of heat was going to be proportional to the amount of water that is actually there.2262

It is going to be different as 10g or if it is going to be 100g.2269

Again, this is more just a formal definition to keep in line with the fact that we need some sort of physical apparatus,2274

in this case water, by which decide that heat has flowed.2283

This is how we decide if in the surroundings water has gotten hotter or colder.2287

Let us continue on, heat is a quantity like work.2306

Therefore, it can be positive or negative.2316

Now in the case of heat, it is positive if the mass of water has cooled.2325

This mass of water is in the surroundings, if the water cools down that means heat has flowed away from it.2338

Heat has flowed from the surroundings.2350

It is flowing from the surroundings, it is flowing to the system.2362

The surroundings systems, it will not go anywhere else.2364

Heat is negative if a mass of water has warmed.2369

Heat has flowed to the surroundings.2390

In the case of heat flow to the surroundings, it is flowed from the system.2403

In chemistry, you are accustomed always taking the systems point of view.2407

Heat, the way we have defined here is the point of view that you are accustomed to.2412

When we talk about heat being positive, that means heat has flowed into the system.2418

If heat is negative that means the system has lost energy as heat.2425

Heat has flowed away from the system.2428

This is the convention that you are most accustomed to in chemistry, taking from the systems point of view.2431

If it is positive and it is flowing, that means heat is flowing to the system.2437

It is flowing from the surroundings.2441

It is just a question of perspective because we always recognize these things by what we observe in the surroundings.2443

This is why we are using the surroundings as our point of view, as opposed to the systems point of view.2452

It does not matter because you have to decide where you are standing in order to decide whether something is coming or going, that is the whole idea.2459

We will talk a little bit more about convention in just a minute.2466

Let us see what else we have got.2471

This is going to be very important.2477

I’m going to write this down, I’m going to go ahead and say it.2482

Deciding whether or not heat or work has flowed during the change of state is based strictly on observations of effect in the surroundings.2489

This is profoundly important.2498

Let us clarify this.2501

I’m going to write a couple of experiments.2503

When we have to decide whether heat has flowed or work has flowed, we do not look at the system, we look at the surroundings.2509

I am sorry to keep elaborating that point but this is what we do in thermodynamics.2517

We need to be very clear about what is going on.2521

Yes, we are going to be talking about systems and especially, this is physical chemistry and in chemistry we are going to talk about chemical systems.2524

We will be concerned with the system but we do not just want to ignore the surroundings.2530

It is very important to know the information we get about the system comes from information that we observe in the surroundings.2536

I want to clarify this point.2542

Let us run a couple of experiments here.2545

Experiment number 1, I'm going to go ahead and take a beaker of water and have 25g of water in here and it is going to be at 25°C.2547

I’m going to go ahead and immerse that in a larger beaker of water.2565

In this particular case, this is going to be 100 g of water and it is going to be at 80°C, this is our surroundings.2574

This right here, the small beaker, the 25 g of water that is going to be our system and the boundary is that right there.2587

It is going to be the glass, the small beaker.2597

That is our boundary.2599

We already know what is going to happen, due to the temperature difference, the 80° and the 25° heat is going to flow from hotter region to a colder region.2601

Heat is going to flow from the surroundings into the system.2614

Let us see what goes.2622

Here is what we do, we left the surroundings, we wait a little bit of heat flows.2626

We let the surroundings drop from 80°C to 79°C, so we let it drop by 1°.2638

And we take out the beaker and then we take out the small beaker.2659

Let us go ahead and do some calculations here.2667

We know that the amount of heat that flows is equal to the mass × that heat capacity × the change in temperature.2669

Let us go ahead and call q out, this is going to be the heat that flowed from the 100 g of water, that is going to equal MC δ T.2676

Well, that is going to equal, there is 100 g of water, the heat capacity of water I’m going to go ahead and use just calories instead of J, for right now.2688

It is going to be 1 cal/ g/ °C, that is the amount of heat energy that is required to raise 1 g of water by 1°C.2697

We let it drop by 1°C so we have 1°C when we go ahead and we do this math, 100 cal of heat have flowed from the surroundings to the system.2712

To the system which is the small beaker.2744

Let us go ahead and calculate the amount of heat that has flown into the beaker and find out what its temperature is.2746

Q in, the system is equal to MC δ T.2753

In this particular case, we know what q is, q was 100 cal of heat.2759

A 100 cal have flowed.2764

We flowed into 25 g of water.2766

Specifically, it is the water so it is just 1 cal/g/ °C, we want δ T.2772

When we solve for δ T, we are going to find out the δ T is 4°C.2781

The small beaker of water is at 29°C, 1°C drop in the surroundings now the beaker is at 29°C.2790

That is our first experiment ,with a small beaker we raised from 25° to 29° by a flow of heat.2808

To our second experiment, let us go here and move forward a little bit.2821

This is called a joule apparatus.2827

Basically, if I take that small beaker I can set up this kind of apparatus.2831

This is going to be our beaker of water right here.2837

What I can do is I can set up the system right here.2841

Basically, what it is, is I can put a paddlewheel inside that beaker and I can wrap a string around the paddlewheel and I can attach the string to a weight.2844

Notice there is a little ruler here.2853

I can go ahead and adjust the height for which you know what is going to happen.2856

The weight is going to fall down, when it falls it is going to turn this handle, that handle is going to turn the paddlewheel.2862

The paddlewheel is going to stir up the water and it is going to raise its temperature.2869

I can go ahead and pick a particular weight and I can pick a particular height and arrange to stir up the water enough to raise the temperature from 25° to 29°.2875

That just comes from a choice, a little bit of trial and error.2888

I can raise it so we can arrange the mass and height for which this mass drops such that we get the 4° rise in temperature for our 25 g of water.2891

Notice, experiment 1, I have 25 g of water that is now in the final state of 29°C.2934

Experiment 2, I have 25 g of water that is now with 29°C.2950

This, in experiment 1, it reached 29°C by a flow of heat.2963

In experiment 2, clearly there is no heat flowing here, what we are doing is work.2968

We are actually doing work on the water and by doing work on the system, we are actually raise this temperature to 29°C.2973

If you did not see these experiments, let us say you are out of the room and let us say you came into the room,2982

notice that I have presented two beakers both of them 25 g of water at 29°C, what can you do to decide which beaker had the heat flow, which beaker had the work flow?2987

Without knowing the experiment, there is no way to decide.2998

Just looking at the system, there is no way to decide whether a flow of heat has raised the temperature3006

or whether a flow of work has been done up or whether flow of work is actually raised the temperature.3012

However, if you observe the surroundings there is a way to tell.3017

By observing the system, you cannot tell.3034

All you see is this beaker at 29°C and the other beaker at 29°C.3045

The question is undecidable.3050

However, if you look at the surroundings or observing the surroundings, you will notice two things.3052

The experiment 1, the surrounding is 1° cooler because it is 1° cooler that means heat has flown from the surroundings.3070

Therefore, you know that the particular beaker rose in temperature because of flow of heat, a transfer of heat.3084

Experiment 2, the mass in the surroundings is lower.3092

You can see with your own eyes, you look and you see that the mass is actually lower than it was before.3109

Because you are observing the surroundings, if the mass is lower in the surroundings that means work has been done.3118

And since the mass is lower, that means work has been done on the system.3124

Work has flown from the surroundings to the system, that is how you can tell.3131

What we are trying to make is that you cannot tell just by looking at a system what has happen, whether heat has flowed or whether work has flowed.3139

However, if you observe the surroundings you can tell.3147

1° cooler in the surroundings, it is heat that has flown.3150

A mass is lower in the surroundings, it is work that has flown.3153

Again, it is the effect observed in the surroundings that tell us what has happened in the system.3160

In chemistry, we always take the systems point of view.3190

What is the problem with that?3194

We will get so wrapped up in the system, we forget about the surroundings.3196

Most of the time, we have to look to the surroundings to let us know what was happening in the system, it is indirect.3203

As it turns out, you already know this.3207

This is not something that is new to you.3210

When you are doing thermodynamic experiments, you remember the experiments that you did in general chemistry.3213

In order to find out what the other particular reaction is, what the heat or release of heat absorbed is, you are not looking at the reaction itself,3222

what you are doing is you are running the reaction of aqueous medium or in a calorimeter.3230

What you are measuring is the temperature of the water change, that is what you are doing.3234

You are taking a look at what is happening in the system by taking a look at what is happening in the surroundings, in the water.3241

You are taking a look at whether the temperature of the water rises or goes down and the extent to which it rises3246

or goes down tells you how much energy is absorbed or released in the system.3251

If the temperature of the solution of the aqueous environment goes up that means that heat has flown into the surroundings to make it hotter.3257

If heat has flown into the surroundings that means that heat has flown out of the system.3266

And since our reaction is the system that means this is an exothermic reaction.3272

You know this already, we do not observe the system, we observe the surroundings that tell us what is happening in the system.3276

Let us go ahead and say a couple more.3286

A little bit more on work and heat.3292

Work and heat, they are energy and they are quantities.3296

As we said, algebraic quantities.3311

They are positive or negative depending on the direction of flow but they are not properties that are possessed by a system.3314

They are processes by which energy is transferred.3346

We never speak of the system having x J of heat or y J of work.3371

What we do say, we speak of the system having a given energy and in the change of state, if the change of state takes place,3379

we say x J is gained or lost as heat, or y J is gained or lost as work.3445

When we actually start talking about this, I’m just generally doing the problems and things like that.3474

We are going to be a little more loose with the language.3478

We are going to say x J of heat have flowed, y J of work has flowed.3482

They are things but they are processes by which energy is transferred.3489

That is what is important.3495

A system does not possess heat or work.3497

Work and heat are things that happen upon the change of state, its energy that changes.3499

There is beginning given amount of energy in a system, work or heat has flowed and there is a final energy of the system.3505

The system possesses energy.3512

Heat and work are the processes by which energy is actually transferred, by which the energy of the system changes.3514

1 J gained was work.3524

Of course, now the system has a new amount of energy, either more or less.3529

New amount of energy which is in its final state.3553

Energy moves via heat and work.3565

I’m sorry I keep elaborating the point, you are probably getting sick of this but it is really important to differentiate.3572

I guess the best analogy that I can think of is the money analogy.3579

You can go to a bank and you can deposit money or you can withdraw money.3584

Money can be transferred.3588

You can deposit money as paper money or you can deposit is as coin money, it is the dollars that matter.3590

You want to start off with a \$800 in your bank account.3597

Let us say you bring in \$50.00 of paper and you bring \$25.00 in coin.3600

The final dollar amount in your account is the 100 + 75 that you brought in.3605

You have \$175.3612

The money is energy, that is how much money you have, that is the dollars.3615

The paper is the heat and the coin is the work.3620

You can bring money in as paper or as coin.3625

It is not money itself, it is not the actual value, it is just the means by which you are actually transferring it.3630

If that makes sense.3640

Again, money is the energy, paper is the heat, and coin is the work.3641

I hope that makes sense.3649

Do not worry about conventions, they are not a big deal.3665

Like I have said before, chemistry convention is we always take the systems point of view.3672

Our conventions are going to be slightly different.3677

However, when I do the problems I'm going to show you, I'm going to do with our convention and3680

I'm going to show you just how easy it is to actually do it with what you would call the purely chemist's convention.3685

Literally, all that I’m going to be doing is changing sign.3690

If I come up with a value of work, for let us say 50 J, from the chemist point of view, it is going to be -50 J.3693

The math itself does not change.3699

All the changes is positive and negative signs, that is all.3702

To again, I'm going to list it, it is going to seem like it is a big deal but is absolutely not a big deal, I promise you.3704

Nothing is lost, the math is exactly the same, all the derivatives are the same, the integrals are the same.3711

The only difference is a positive and negative sign.3716

As long as you understand what the system is, what the boundary is, and the direction of heat flow and workflow,3719

as long as you understand those things that is what matters.3725

When you give your answers on a quiz or a test, if you forget a negative sign that is not a problem.3730

You can always say heat is flowing from the system to the surroundings, as long as you specify the direction of flow,3735

you actually do not even need to worry about a point of view.3742

You do not need to worry about the positive and negative signs.3745

The math itself is not that relevant.3748

What was relevant is the magnitude of the change and the direction of the change.3751

If you can keep track of that, everything will be fine.3756

Having said that let us talk about our conventions.3758

Our convention for heat.3761

We will say that heat is positive if it flows into the system which means from the surroundings.3766

It just depends on what your perspective is.3783

We will call heat negative, if it flows from the system.3788

In other words, it flows to the surroundings.3798

By not picking a particular point of view, by not getting the locked into quote the chemists point of view,3803

or the engineer’s point of view, or the physicist point of view.3807

What you are doing is freeing yourself up to actually just take a look a thermodynamics scenario in general.3813

If you understand that, point of view becomes completely secondary and irrelevant.3818

Afterward, once you decide what is going, where energy has flowed, where it ended up, what the final temperature is of the system,3822

what the initial temperature is and the final temperature is of the surroundings.3829

Once you have the bird's eye view of the big picture, you can decide yourself what point of view take if you have to give a final answer.3833

It is the scenario, the process that we want to understand.3841

We just do not want to get locked into a particular point of view.3845

All know I have to take the system's point of view, you do not.3847

I just want to pull you back to give you the bigger picture, that is what is important.3851

Negative, it flows from the system or to the surroundings.3856

Our conventions for work.3865

Work is positive if it flows to the surroundings which means from the system.3871

And the work is negative when it flows from the surroundings or flows to the system.3887

Let us go ahead and give a schematic representation of what it is we are talking about here.3903

We have our surroundings, we have our system here, we have our surroundings here,.3908

Heat is positive, heat negative.3920

Heat is positive when it goes into the system from the surroundings.3926

Heat is negative when it goes out of the system to the surroundings.3929

Work is positive when it comes to the surroundings from the system.3938

Work is negative when it goes from the surroundings to the system.3943

This is a schematic of our particular convention.3947

Again, do not worry about the convention.3956

All of this will make sense when we actually start with the problems and you will see that it does not matter what convention you take.3958

A physicist takes one point of view, engineer’s take another point of view, chemist take another point of view.3965

If you understand the thermodynamics, the conventions become irrelevant, they become secondary.3968

They become important only when you have to give a final answer for a final thing.3973

If I ask you about a system then once you know what is happening, you can tell me yes, heat has flowed to the system,3978

work has flown out of the system, and the final energy of the system is this amount.3985

Thermodynamics you want to understand.3990

The flow that we want to understand, we do not want to get locked into just one point of view and feel that if I do not take the point of view everything is going to fall apart.3992

It will not fall apart, I promise you.4001

Thank you for joining us here at www.educator.com.4003

We will see you next time, bye.4004

OR

### Start Learning Now

Our free lessons will get you started (Adobe Flash® required).