**Unit 4: The Second Law of Thermodynamics**
*The second law of thermodynamics reflects the universal observation
that moving things eventually stop and broken eggs never can become
whole again. The law expresses this observation in terms of a
thermodynamic parameter known as entropy, which is a measure of the
disorder in a system. Renowned British physicist Sir Arthur Eddington
believed that the second law of thermodynamics is the most fundamental
law of science and that, at its foundation, it is a far broader concept
than is required by the narrow physical laws of our particular
universe. *

**Unit 4 Time Advisory**

Completing this unit should take approximately 21.5 hours.

☐ Subunit 4.1: 8 hours

☐ Subunit 4.2: 6 hours

☐ Subunit 4.3: 3 hours

☐ Subunit 4.4: 1 hour

☐ Subunit 4.5: 3.5 hours

**Unit4 Learning Outcomes**

Upon successful completion of this unit, you should be able to:
- state the second law of thermodynamics and its implications for
chemical reactions;
- perform entropy calculations around reversible and irreversible
cycles;
- state the Clausius inequality, and describe its relationship to
entropy;
- describe the relationship between entropy, irreversibility, and the
direction of spontaneous change;
- describe Maxwell’s demon and the relationship between entropy and
information; and
- define *statistical entropy,* and explain how this quantity provides
a bridge between the microscopic and macroscopic perspectives of the
thermodynamic property of state, entropy.

**4.1 The Second Law of Thermodynamics**
- **Lecture: The Massachusetts Institute of Technology OpenCourseWare:
Dr. Moungi Bawendi and Dr. Keith Nelson’s “Lecture 8: Second Law”**
Link: The Massachusetts Institute of Technology OpenCourseWare: Dr.
Moungi Bawendi and Dr. Keith Nelson’s “Lecture 8: Second
Law”

```
Also available in:
[iTunesU](http://ocw.mit.edu/courses/chemistry/5-60-thermodynamics-kinetics-spring-2008/video-lectures/lecture-8-second-law/)
[MP4](http://ocw.mit.edu/courses/chemistry/5-60-thermodynamics-kinetics-spring-2008/video-lectures/lecture-8-second-law/)
Instructions: Watch the video (approximately 50 minutes in length)
on the second law of thermodynamics. This lecture begins with a
discussion of the relationship between enthalpies of formation and
bond energies, following up on the lectures on thermochemistry. You
also will learn about how the second law complements the first. You
can find the lecture notes for this video here (PDF).
Watching this lecture should take approximately 1 hour.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 United States
license](http://creativecommons.org/licenses/by-nc-sa/3.0/us/).
```

**Reading: Dr. Howard DeVoe’s**Link: Dr. Howard DeVoe’s*Thermodynamics and Chemistry*(2nd ed.): “Chapter 4: The Second Law”*Thermodynamics and Chemistry*(2^{nd}ed.): “Chapter 4: The Second Law” (PDF)Instructions: Navigate to chapter 4, which begins on page 102, and read and work through the chapter, including completing the problems at the end of the chapter. The material in this chapter provides an exceptional foundation for studying the remaining concepts in this subunit of the course. Be sure to work through all of chapter 4 before moving on to the subsequent assignments in this unit.

Reading this material should take approximately 4 hours.

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDervis 3.0 Unported License.

**Reading: The University of Windsor:**Link: The University of Windsor:*Introductory Physical Chemistry*: Dr. Rob Schurko’s Course Notes: “Lecture 10: The Second Law: The Concepts” and “Lecture 11: Entropy Changes & Processes”*Introductory Physical Chemistry*: Dr. Rob Schurko’s Course Notes: “Lecture 10: The Second Law: The Concepts”and “Lecture 11: Entropy Changes & Processes” (PDF)Instructions: Read these notes, but pay particular attention to the illustrations shown and consider how they are related to the accompanying mathematical formulation of the second law of thermodynamics.

Reading this material should take approximately 3 hours.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.

**Optional: The University of Notre Dame OpenCourseWare: Dr. Joseph M. Powers’s Lecture Notes on Thermodynamics: “Chapter 7: The Second Law of Thermodynamics” and “Chapter 8: Entropy” (PDF)**Link: The University of Notre Dame OpenCourseWare: Dr. Joseph M. Powers’s*Lecture Notes on Thermodynamics*: “Chapter 7: The Second Law of Thermodynamics”and “Chapter 8: Entropy” (PDF)Instructions: Read Dr. Powers’s lecture notes. You may find this optional reading especially useful for helping you to understand the various statements of the second law that are found in the thermodynamics literature.

Terms of Use: This resource is licensed under a Creative Commons Attribution 2.5 Generic license.

**Optional: McGill University: Dr. David Ronis’s “The Second Law of Thermodynamics” (PDF)**Link: McGill University: Dr. David Ronis’s “The Second Law of Thermodynamics” (PDF)Instructions: Read Dr. Ronis’s brief handout. This optional reading provides you with a concise summary of principles related to the second law of thermodynamics.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**4.2 Entropy and the Clausius Inequality**
- **Lecture: The Massachusetts Institute of Technology OpenCourseWare:
Dr. Moungi Bawendi and Dr. Keith Nelson’s “Lecture 9: Entropy and
the Clausius Inequality”**
Link: The Massachusetts Institute of Technology OpenCourseWare: Dr.
Moungi Bawendi and Dr. Keith Nelson’s “Lecture 9: Entropy and the
Clausius
Inequality”

```
Also available in:
[iTunesU](http://ocw.mit.edu/courses/chemistry/5-60-thermodynamics-kinetics-spring-2008/video-lectures/lecture-9-entropy-and-the-clausius-inequality/)
[MP4](http://ocw.mit.edu/courses/chemistry/5-60-thermodynamics-kinetics-spring-2008/video-lectures/lecture-9-entropy-and-the-clausius-inequality/)
Instructions: Watch this video (approximately 50 minutes in
length). In this lecture, you will revisit some of the thermodynamic
cycles and their corresponding engines—concepts you saw in Unit 3 of
this course. You also will learn about entropy around thermodynamic
cycles in which there are reversible and irreversible paths
involved. You can find the lecture notes for this video here
(PDF).
Watching this lecture should take approximately 1 hour.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 United States
license](http://creativecommons.org/licenses/by-nc-sa/3.0/us/).
```

**Reading: The University of Notre Dame OpenCourseWare: Dr. Joseph M. Powers’s Lecture Notes on Thermodynamics: “Chapter 8: Entropy”**Link: The University of Notre Dame OpenCourseWare: Dr. Joseph M. Powers’s*Lecture Notes on Thermodynamics*: “Chapter 8: Entropy” (PDF)Instructions: Read through chapter 8 of Dr. Powers’s lecture notes. Note that this chapter has been assigned previously in this course; as you review the material this time, be sure to work through all the example problems provided in the text.

Reading this material should take approximately 3 hours.

Terms of Use: This resource is licensed under a Creative Commons Attribution 2.5 Generic license.

**Reading: The University of Windsor:**Link: The University of Windsor:*Introductory Physical Chemistry*: Dr. Rob Schurko’s Course Notes: “Lecture 11: Entropy Changes & Processes” (PDF)*Introductory Physical Chemistry*: Dr. Rob Schurko’s Course Notes: “Lecture 11: Entropy Changes & Processes” (PDF)Instructions: Read Dr. Schurko’s course material. Note that you have been assigned this reading previously in this course; as you read this time, focus on understanding how entropy changes are determined for various kinds of physical and chemical processes. Read the material and be sure to work through all the exercises and example problems provided in the text.

Reading this material should take approximately 2 hours.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**Optional: McGill University: Dr. David Ronis’s “Why the Efﬁciency of a Carnot Engine Is Independent of the Kind of Working Material” and “The Clausius Inequality and the Mathematical Statement of the Second Law of Thermodynmamics”**Link: McGill University: Dr. David Ronis’s “Why the Efﬁciency of a Carnot Engine Is Independent of the Kind of Working Material”and “The Clausius Inequality and the Mathematical Statement of the Second Law of Thermodynmamics” (PDF)Instructions: Read Dr. Ronis’s course notes. Please note that this reading is optional. The first handout offers a concise description of the Carnot heat engine and a thermodynamic analysis of its operation. The second handout provides you with an overview of the profound significance of the Clausius inequality.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.

**4.3 Entropy and Irreversibility**
- **Lecture: The Massachusetts Institute of Technology OpenCourseWare:
Dr. Moungi Bawendi and Dr. Keith Nelson’s “Lecture 10: Entropy and
Irreversibility”**
Link: The Massachusetts Institute of Technology OpenCourseWare: Dr.
Moungi Bawendi and Dr. Keith Nelson’s “Lecture 10: Entropy and
Irreversibility”

```
Also available in:
[iTunesU](http://ocw.mit.edu/courses/chemistry/5-60-thermodynamics-kinetics-spring-2008/video-lectures/lecture-10-entropy-and-irreversibility/)
[MP4](http://ocw.mit.edu/courses/chemistry/5-60-thermodynamics-kinetics-spring-2008/video-lectures/lecture-10-entropy-and-irreversibility/)
Instructions: Watch the video (approximately 53 minutes in length),
which continues entropy calculations around cycles that involve
reversible and irreversible processes, with particular emphasis on
the direction of spontaneous change. You can find the lecture notes
for this video here (PDF).
Watching this lecture should take approximately 1 hour.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 United States
license](http://creativecommons.org/licenses/by-nc-sa/3.0/us/).
```

**Reading: Connexions: “Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy”**Link: Connexions: “Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy” (HTML)Instructions: Read the webpage. This source has a particularly good set of questions and problems to be addressed. Work through all the questions and problems in this reading—both the conceptual problems and those requiring numerical calculations.

Reading this material should take approximately 2 hours.

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDervis 3.0 Unported License.

**4.4 Maxwell’s Demon**
- **Reading: The Institute of Mathematical Sciences: Dr. Sitabhra
Sinha, Brajendra Kumar Singh, and Albert Smith’s “Maxwell’s Demon”**
Link: The Institute of Mathematical Sciences: Dr. Sitabhra Sinha,
Brajendra Kumar Singh, and Albert Smith’s “Maxwell’s
Demon” (Java)

```
Instructions: Explore this Java applet, which is based on a thought
experiment that Scottish physicist James Clerk Maxwell devised
nearly 150 years ago in an attempt to disprove the second law of
thermodynamics. Although Maxwell did not succeed, his idea raised
interesting questions about the relationship between information and
entropy. As you explore the applet, try to separate the fast from
the slow molecules. Are you violating the second law of
thermodynamics when you attempt this? No, because the amount of
information needed to do this separation requires quite a large
energy input!
Completing this web media assignment should take approximately 1
hour.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**4.5 Statistical Entropy: Microscopic vs. Macroscopic Viewpoints**
- **Reading: The University of Notre Dame OpenCourseWare: Dr. Joseph
M. Powers’s Lecture Notes on Thermodynamics: “Chapter 8: Entropy
(Sections 8.9 and 8.10)”**
Link: The University of Notre Dame OpenCourseWare: Dr. Joseph M.
Powers’s

*Lecture Notes on Thermodynamics*: “Chapter 8: Entropy (Sections 8.9 and 8.10)” (PDF)

```
Instructions: Review chapter 8 of Dr. Powers’s lecture notes, which
have been assigned previously in this course. As you read this time,
focus specifically on sections 8.9 (“Probablistic approach to
entropy”) and 8.10 (“Summary statement of thermodynamics”) of the
chapter. Most of the material in this reading will be familiar to
you from previous assignments in this course. However, whereas
previously the emphasis was on the definition and interpretation of
entropy as a macroscopic property of state, here the entropy state
function is defined in terms of microscopic material properties.
Reading this material should take approximately 1.5 hours.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution 2.5 Generic
license](http://creativecommons.org/licenses/by/2.5/).
```

**Reading: Dr. Howard DeVoe’s**Link: Dr. Howard DeVoe’s*Thermodynamics and Chemistry*(2nd ed.): “Chapter 4: The Second Law (Section 4.8)”*Thermodynamics and Chemistry*(2^{nd}ed.): “Chapter 4: The Second Law (Section 4.8)” (PDF)Instructions: Navigate to section 4.8, titled “The Statistical Interpretation of Entropy,” on page 130, and read through page 132. Please note that chapter 4 of this textbook has been previously assigned in this course; as you review section 4.8 this time, note that only the conceptual basis of the term

*statistical entropy*is addressed here. You will encounter a more rigorous treatment of statistical entropy in Unit 9 of this course.Reading this material should take approximately 1 hour.

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDervis 3.0 Unported License.

**Reading: Tim Thompson’s “Adventures in Entropy”**Link: Tim Thompson’s “Adventures in Entropy” (HTML)Instructions: Access and peruse the hyperlinked material on this website. The material presented here will help you gain some exposure to “thinking outside the box” about thermodynamic entropy. The information on this site is intellectually sound, enormously thought-provoking, and one heck of a lot of fun to ponder.

Reading this material should take approximately 1 hour.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.