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### Unit: Math Bits

**Hour 1: Math Bits - Differentials**- Differentials
- Zapping with d

**Hours 2-3: Math Bits - Variables and Representations***Small Group Activity: Exploring the Partial Derivative Machine*- Partial Derivative Machine dictionary

**Hour 4: Math Bits - Energy and Integrals***dU*- Numerical Integration

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

- Chain Rule Diagrams

**Hour 7: Math Bits - The Elevator Cycle***Small Group Activity: The Elevator Cycle*

- Some notes on how Math Bits might change:
- The elevator/cycles problem is now done below, so can be dropped
- There are two surfaces activities that fit well with Math Bits
*Thermodynamic States*(I would do this one before starting the PDM)*Covariation in Thermal Systems*(I would do this one on Friday as a bridge back to Thermodynamics)- We also have
*Quantifying Change in Thermal Systems*which is quick and could go anywhere or be left out (it is primarily a contour map activity).

- Something else probably needs to be dropped. I would probably recommend Numerical Integration (or at least it can be minimized), though the ideas here should be brought back for the elevator cycle activity, which looks to have 2 hours below which is more than we gave it.
- Other surfaces activities that fit well below:
*Heat Capacity of Water Vapor**“Squishability” of Water Vapor*

### Unit: First and Second Laws of Thermodynamics

**Hour 8: Heat and Temperature**- Intro to Thermodynamic Properties
*Lab: Ice Lab I*

- Comparing Thermodynamic Properties

**Hour 9: The First and Second Law**- QUIZ
- Jargon
- Intensive and Extensive
- T, S, V, p, U
- Work, Heat
- First Law
- Second Law
- Reversible and Irreversible
- Adiabatic

- Snapping a Rubber Band
- Second Law

- Thermodynamic Identity
- Name the Experiment I
- Heat Capacity

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

- Free expansion not-quiz
- Discussion of not-quiz

**Hour 13-14: Mechanical cycles**- Elevators
*Small Group Activity: The Elevator Cycle*

**Hour 15: Holiday**

**Hour 16: Heat, work, and processes**- QUIZ
- Work
- Heat
- Using $p V$ and $T S$ Plots

**Hour 17: A simple cycle**- Analyzing a Simple Curve

### Unit: Internal Energy

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

**Hours 19-20: Legendre Transformations****LINKS THAT WORK:****LINKS THAT DO NOT WORK:**- Legendre Transformations

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

- QUIZ
- Name The Experiment III

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

- Sometimes Always Never True (1st half)

**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