### Course Overview

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

##### Students will be able to:

- Use both dimensional reasoning and intensivity/extensivity to make sense of mathematical expressions involving thermodynamic variables
- Interpret phase diagrams and reason about processes involving phase transitions
- Explain how a given partial derivative relation relates to a particular experimental measurement
- Distinguish between state properties and quantities such as heat and work that arise from inexact differentials
- Use terms from thermodynamics such as quasistatic, reversible, adiabatic, intensive, extensive, and isothermal in physical context
- Use the laws of thermodynamics to solve problems both for generic systems (for with the equation of state is not known) and for specific systems such as the ideal gas
- Reason about thermodynamic processes and cycles, including integrating along paths
- Use the methods of statistical mechanics (in particular, the Boltzmann ratio, and summation over probabilities) to solve for thermal properties in equilibrium
- Describe the Gibbs and Boltzmann statistical formulations for entropy

##### Previous 3-week E&E 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**

### Sample Syllabus

##### Textbook

An Introduction to Thermal Physics - Daniel V. Schroeder

Alternative text:

Thermal Physics Concepts and Practice - Allen Wassermann

##### Sample Syllabus

# Course Content

This link will take you to the original version of the Energy and Entropy page.

### Unit: Math Bits

**Hour 1: Math Bits - Differentials**- Differentials
- Zapping with d
*Surfaces Activity: Covariation in Thermal Systems*

- QUIZ
*Small Group Activity: Exploring the Partial Derivative Machine*- Contour Graphs
*Surfaces Activity: Thermodynamic States*

*Small Group Activity: Exploring the Partial Derivative Machine*- Partial Derivative Machine dictionary

**Hour 4: Math Bits - Energy and Integrals***dU*- Numerical Integration
*Surfaces Activity: Quantifying Change in Thermal Systems*

**Hours 5-6: Math Bits - Derivatives and Chain Rules**- Chain Rules
*Small Group Activity: PDM Derivatives*

- Chain Rule Diagrams

*Surfaces Activity: “Squishability” of Water Vapor*

### Unit: First Law of Thermodynamics

**Hour 8: Heat and Temperature***Lab: Ice Calorimetry Lab**SWBQ: Comparing Thermodynamic Properties**Lecture: Dulong and Petit Rule*

**Hour 9: The first law**- QUIZ
*Activity: Comparing the System and Surroundings**Lectures: Jargon*- Intensive and Extensive
- T, S, V, p, U
- Work, Heat
- The First Law

*Lecture: Snapping a Rubber Band*

- Thermodynamic Identity
- Name the Experiment I
- Heat Capacity

**Hour 11: Heat capacity and latent heat***Lab: Ice Lab II*

: This should go somewhere around here once things get rearranged:

*Heat Capacity of Water Vapor*

**Hour 12: Mechanical cycles**Needs Content- Elevators
*Small Group Activity: The Elevator Cycle*

**Hour 13: Heat, work, and processes**Needs Prereqs- Work
- Heat
- Using $p V$ and $T S$ Plots

**Hour 14: A simple cycle**Needs Prereqs- Analyzing a Simple Curve

**Hour 15: Holiday**

### Unit: Internal Energy

- Quiz
- Name the Experiment II (Heat and/or First Law)

**Hour 17: The second law**Needs Prereqs- Lectures: Jargon
- Second Law
- Reversible and Irreversible
- Adiabatic
- Quasistatic

**Hour 18: Entropy, expansion, and the Second Law**Needs Prereqs- Free expansion not-quiz
- Discussion of not-quiz

**Hours 19-20: Legendre Transformations**Needs Prereqs

**Hour 21: Maxwell relations**- Maxwell Relations
- Maxwell Relation Activities

- Name The Experiment III

**Hours 23-24: Using a Maxwell relation to make an entropy change**- QUIZ
*Lab: Rubber Band Lab*

- Sometimes Always Never

**Hours 26-28: Holiday**

### Unit: Statistical Mechanics

**Hour 29: Statistical view of entropy**- QUIZ
- Fairness Function and Probability

**Hour 30: Maximizing Entropy**- Maximizing S
- Lagrange Multipliers

- Weighted Averages
- Derive Boltzman Ratio and connect to Thermo ($U = \sum p_iE_i$)

**Hour 32: Free**- Free

**Hours 33-34: Exploring a Diatomic Gas**- Diatomic Gas

**Hour 35: Review**- Review

- (HotMetal)
*No HW problem by this name on archive.*

### Activities Included

- All activities for Energy & Entropy