## Energy & Entropy

: Course site under construction.

The Energy and Entropy Paradigm introduces both classical thermodynamics and statistical mechanics, with an information theory emphasis. This course is designed to follow the interlude course that presents a series of mathematical techniques necessary to solve numerous thermodynamics problems including work with partial derivatives, total differentials, exact and inexact differentials, and the cyclic chain rule. In the beginning of the course, students will be introduced to the terminology necessary to understand thermodynamic processes. The course will then present the first and second thermodynamic laws. Utilizing the techniques learned in the interlude, students will use the first thermodynamic law, in conjunction with Legendre Transforms, to derive Maxwell's relations. Throughout Energy and Entropy, the class will frequently be placed in small groups and asked to physically present how thermodynamic partial derivatives could be measured (see name the experiment). These activities collaborate with the integrated laboratory exercises to present thermodynamics with a physically observable approach. After working with classical thermodynamics, the course provides an introduction to statistical mechanics, exposing students to the concepts of maximum fairness and the probability of microstates. The course concludes with a culmination of thermodynamics and statistical mechanics in a calculation of the total internal energy of a diatomic gas.

### Course Goals

- For students to understand
**(be able to apply and interpret) the concepts of heat and temperature** - For students to understand
**(be able to apply and interpret) the concepts of work and internal energy** - For students to understand
**(be able to apply) the concepts of heat, temperature, work, and internal energy to the concept of an engine** - For students to understand
**(be able to apply and interpret) the First, Second, and Third Thermodynamic Laws** - For students to understand
**(be able to apply and interpret) black body thermodynamics** - For students to understand
**(be able to use and interpret) statistical mechanics**

##### Textbook

An Introduction to Thermal Physics - Daniel V. Schroeder

Alternative text:

Thermal Physics Concepts and Practice - Allen Wassermann

##### Sample Syllabus

# Course Content

### Unit: First & Second Laws of Thermodynamics

#### Heat and Temperature (40 minutes)

- Ice calorimetry lab (Integrated Laboratory, 30 minutes)
- Comparing Thermodynamic Properties (SWBQs, 15 minutes)
- Dulong-Petit Law (Lecture, 5 minutes)

#### Introducing the First & Second Thermodynamic Laws (2 hours 55 minutes)

- Comparing Systems and Surroundings (Small Groups, 10 minutes)
- The First Thermodynamic Law (Lecture, 10 minutes)
- Snapping a Rubber Band (SWBQ and Lecture, 15 minutes)
- Hot Metal in Room Temperature Water (SWBQ, 3 minutes) (sometimes? could be skipped)

- The Second Thermodynamic Law (Lecture, 5 minutes)
- Thermodynamic Terminology (Thermodynaic Potentials) (Lecture, 7 minutes)
- The Thermodynamic Identity (Lecture, 5 minutes)
- Name the experiment (Activity, 25 minutes)
- Heat Capacity (Lecture, 10 minutes)
- Second ice calorimetry lab (Integrated Laboratory, 45 minutes)

#### Heat and Work (3 hours 40 minutes)

- Free expansion quiz and discussion (Activity, 40 minutes)
- Work in Thermodynamics (Lecture, 5 minutes)
- Using $pV$ and $TS$ Plots (Small groups, 35 minutes)
- Analyzing a Simple Cycle using a $pV$ Curve (Small groups, 65 minutes)
- Name the Experiment: Changing Entropy (Small groups, 15 minutes)
- Deriving the Carnot Efficiency (Lecture, 30 minutes)

### Unit: Internal Energy

#### Maxwell Relations (1 hour 35 minutes)

- Monotonicity and State Functions (Lecture, 10 minutes) (CUT???)
- Legendre Transforms (Lecture, 5 minutes)
- Maxwell Relations (Lecture, 10 minutes)
- Seeking the right Maxwell Relation (Small groups, 20 minutes)
- Name the Experiment: Maxwell Relations (Small groups, 20 minutes)
- Name the (often skipped)Experiment: More Maxwell Relations (Small groups, 30 minutes) (Join with previous one, unify with paper)

#### Rubber Band Lab ()

- Rubber band lab (Integrated Laboratory, 1 hour 50 minutes)

#### Simple Cycles & Analyzing Thermodynamic Processes ()

- Always, Sometimes, or Never True (Small groups, 60 minutes) (could be skipped?)

#### Black Body Thermodynamics (30 minutes)

- Two Interacting Black Body Objects (Small groups, 30 minutes) (often skipped)

### Unit: Statistical Mechanics

#### The Statistical Approach ()

- Comparing Statistical Mechanics to Thermodynamics (Lecture, 5 minutes)
- The Fairness Function (Lecture, 10 minutes)
- Combining Probabilities (Small Groups, 20 minutes)

#### Optimizing the Fairness ()

- Students as molecules dice activity (Kinesthetic, 25 minutes) (can be skipped, hard to manage, add for getting energy constraints and microcanonical ensembles, could split?)
- Maximizing a Function (SWBQ, 5 minutes)
- Method of Lagrange Multipliers (Lecture, 10 minutes)
- Weighted Averages (Lecture, 10 minutes)
- Energy Constraints (Lecture, ?? minutes)
- Two Non-interacting Systems (SWBQs, 15 minutes)
- The Partition Function (Lecture, 10 minutes)

#### Moving from Statistics to Thermodynamics ()

- Fairness and Entropy (Lecture, 5 minutes)
- Relating the Internal Energy and Fairness (Lecture, 15 minutes)

#### Internal Energy of a Diatomic Gas (2 hours 10 minutes)

- Reviewing Several Energy Eigenvalues (Lecture, 10 minutes)
- Internal Energy of a Diatomic Ideal Gas (Lecture, 20 minutes)
- Calculating the Internal Energy of a Diatomic Ideal Gas (Small groups, 100 minutes)

#### The Third Thermodynamic Law (20 minutes)

- Third Law of Thermodynamics (Lecture, 20 minutes) (optional)

### Activities Included

- All activities for Energy & Entropy