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### Unit: Math Bits

• Differentials
• Zapping with d
• Small Group Activity: Exploring the Partial Derivative Machine
• Partial Derivative Machine dictionary
• dU
• Numerical Integration
• Chain Rules
• Small Group Activity: PDM Derivatives
• Chain Rule Diagrams
• 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

• Intro to Thermodynamic Properties
• Lab: Ice Lab I
• Comparing Thermodynamic Properties
• QUIZ
• Jargon
• First Law
• Snapping a Rubber Band
• Second Law
• Thermodynamic Identity
• Name the Experiment
• Heat Capacity
Hour 11: Ice Lab II
• Lab: Ice Lab II
Hour 12: Free Expansion
• Free expansion not-quiz
• Discussion of not-quiz
Hour 13-14: Elevator
• Elevators
• Small Group Activity: The Elevator Cycle
Hour 15: Holiday
• QUIZ
• Work
• Heat
• Using $p V$ and $T S$ Plots
Hour 17: A Simple Curve
• Analyzing a Simple Curve

### Unit: Internal Energy

• Name the Experiment II (Heat and/or First Law)
• Legendre Transformations on PDM
• Legendre Transformations
• Maxwell Relations
• Maxwell Relation Activities
• QUIZ
• Name The Experiment III
Hours 23-24: Rubber Band Lab
• Lab: Rubber Band Lab
• Sometimes Always Never True (1st half)
Hours 26-28: Holiday

### Unit: Statistical Mechanics

• QUIZ
• Fairness Function and Probability
• Maximizing S
• Lagrange Multipliers
Hour 31: Boltzman Ratio
• Weighted Averages
• Derive Boltzman Ratio and connect to Thermo ($U = \sum p_iE_i$)
Hour 32: Free
• Free
• Diatomic Gas
Hour 35: Review
• Review

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