# Instructor guide: Heat-engine boundary and efficiency ledger

Course: Thermodynamics and statistical reasoning

Suggested time: 45–60 minutes

## Learning target

Learners close a cyclic energy ledger and distinguish measured efficiency from the reversible Carnot ceiling.

## Prepare

- Define heat into the engine as positive.
- Draw hot reservoir, engine, and cold reservoir.
- Prepare a run with an intentionally omitted rejected-heat term.

## Facilitation moves

- Require kelvin before computing a ratio.
- Ask whether the device returned to its starting state.
- Treat above-limit results first as boundary or measurement failures.

## Misconception checks

- **Efficiency below 100% means energy disappeared.** The remainder is rejected heat or another accounted transfer, not missing energy.
- **A fluctuation can power a passive one-reservoir cycle indefinitely.** Equilibrium fluctuations obey detailed balance; preparation, feedback, and resetting costs belong in the cycle.

## Accessibility and participation

- Use a three-box energy-flow diagram with numeric labels.
- Offer a unit-conversion reminder for Celsius to kelvin.
- Let learners submit an annotated ledger instead of a long prose response.

## Evidence of learning

- A closed first-law ledger
- A valid Carnot comparison
- A clear complete-cycle boundary

## Extension

Add a finite-rate loss model and explain the gap between reversible and practical efficiency.

## Evidence boundary

Assess the learner's reasoning only within the declared model and recorded observations. Do not upgrade a simulation result into a claim about an unmodeled physical system.