High School / HS-16

Heat Engine & Thermodynamics Lab

Available Grades 9–12 Energy

Run a hot-water Stirling engine, log temperatures, pressure, and RPM, reconstruct its P–V cycle, and compare its efficiency with the Carnot limit.

Overview & learning outcomes

Students instrument a hot-water (low-temperature-difference) Stirling engine with an ESP32 logger: a ported pressure sensor in the displacer chamber, a once-per-turn hall sensor on the flywheel, and temperature probes in the water and on the top plate. They reconstruct the P–V loop, compute work per cycle and indicated power, check it against a spin-down friction measurement, measure heat input by water calorimetry, and compare the engine's efficiency with the Carnot and Curzon–Ahlborn limits and an isothermal Schmidt model built from their own measurements.

Students will:

  • Describe the ideal Stirling cycle (two isothermal and two constant-volume steps) and explain why a real engine's P–V loop is rounded
  • Compute work per cycle from the area of the measured P–V loop (W = ∮P dV) and power from work × cycles per second
  • Calculate the Carnot limit η = 1 − T_cold/T_hot in kelvin (for 80 °C water and 20 °C air, about 17%)
  • Compare measured efficiency with the Carnot limit and account for the losses

Every high school pack includes worked math and physics, prediction-versus-measurement labs, at least two design-and-test iterations, data logging, a rubric, and documentation templates, plus printable Builder's Corner build journal pages.

Bill of materials & where to buy

Parts, specs, quantities, and estimated unit costs, with places to buy. Prices change; anything marked as an estimate is an estimate. Links were checked when the BOM was written.

Estimated kit cost

  • A. Engine and instrumentation: $121.19 typical · $106.24 low-cost path
  • B. Heat source, water and fixtures: $76.50 typical · $21.50 low-cost path
  • C. Tools and safety (once per school): $104.09 typical · $15.59 low-cost path
  • Everything from zero: $301.78 typical · $143.33 low-cost path (low-cost path uses listed substitutes and assumes a school or makerspace already owns reusable tools)

Totals are computed from the line items below. Prices were read from vendor pages on the dates shown and will change. Rows tagged estimate have no verified link and are planning numbers only.

A. Engine and instrumentation

IDPart & specQtyUnit (typical)Line (typical)Where to buyCheaper substituteAdult handling / safety gear
E1Low-temperature-difference (coffee-cup) Stirling engine
EngineDIY 'Low Temperature Stirling Engine Coffee Cup' · page: aluminium, 136 g; 'Can not use with flame heating!'; runs on a cup of hot water. Kit uses water ≤ 50 °C.
1$24.99$24.99enginediy.com
EngineDIY
$24.99 · checked 2026-10-09 · Available (store data)
Engine Model Kit LTD engine with cup ($34.99, page shows Sold out on 2026-10-09); a second, unmodified engine as a control (+$24.99)Adult drills the 3 mm pressure port (build guide Part 2)
E2ESP32 Feather V2 (logger)
Adafruit PID 5400 · USB serial CSV logger; Wi-Fi/Bluetooth off
1$19.95$19.95adafruit.com
Adafruit
$19.95 · checked 2026-10-09 · In stock
Any Arduino with I²C + an interrupt pin (re-map pins)Header soldering: adult supervision
E3MPRLS ported pressure sensor, 0–25 PSI absolute
Adafruit PID 3965 · I²C 0x18, metal port for a tube; reads the engine's gas pressure
1$29.95$29.95adafruit.com
Adafruit
$29.95 · checked 2026-10-09 · In stock
——
E4STEMMA QT / Qwiic cable 100 mm
Adafruit PID 4210
1$0.95$0.95adafruit.com
Adafruit
$0.95 · checked 2026-10-09 · In stock
——
E5Waterproof DS18B20 temperature probe
Adafruit PID 381 · one in the water, one taped to the top plate
2$9.95$19.90adafruit.com
Adafruit
$9.95 · checked 2026-10-09 · In stock
10 kΩ NTC thermistors + calibration (cheaper, more work)—
E6Hall-effect sensor US5881LUA
Adafruit PID 158 · one pulse per flywheel turn
1$2.00$2.00adafruit.com
Adafruit
$2.00 · checked 2026-10-09 · In stock
IR break-beam pair through the flywheel spokes—
E7Small neodymium disc magnets 3 × 1 mm (pair)
One S-face-out (triggers), one N-face-out opposite (balances the flywheel, no second pulse)
1$3.00 estimate$3.00Craft/hardware store (no link)
—
Adafruit PID 9 rare-earth magnet ($2.50, page shows Out of stock on 2026-10-09; larger: check balance)Keep magnets away from young children (swallowing hazard)
E8Silicone tubing 3 mm ID, 1 m
Adafruit PID 4661 · use ≤ 5 cm between port and sensor (dead volume ≈ 0.35 cm³)
1$2.50$2.50adafruit.com
Adafruit
$2.50 · checked 2026-10-09 · In stock
——
E9Brass tube 3 mm OD × 15 mm + 2-part epoxy
Pressure port glued into the engine's top plate
1$6.00 estimate$6.00Hobby/hardware store (no link)
—
—Adult drills and glues; epoxy with gloves, ventilated
E104.7 kΩ + 10 kΩ resistors, half-size breadboard, jumper wires
DS18B20 pull-up (4.7 kΩ); hall pull-up to 3.3 V (10 kΩ); wiring
1$7.00 estimate$7.00School stock (no link)
—
——
E11USB-A to USB-C data cable
Adafruit PID 4474
1$4.95$4.95adafruit.com
Adafruit
$4.95 · checked 2026-10-09 · In stock
Classroom cable—
Subtotal$121.19Low-cost path: $106.24

B. Heat source, water and fixtures

IDPart & specQtyUnit (typical)Line (typical)Where to buyCheaper substituteAdult handling / safety gear
H1Double-wall insulated mug with a flat rim (≈ 300 mL)
The engine sits on the rim; same mug for engine and lid runs
1$10.00 estimate$10.00Retail (no link)
—
Foam cup in a beaker (less stable)—
H2Electric kettle with auto shut-off
ADULT ONLY. Heats water that the adult mixes down to ≤ 50 °C before it reaches the student station
1$25.00 estimate$25.00Retail (no link)
—
Hot tap water measured with the probe, ≤ 50 °C (often 45–50 °C)Adult only; kettle stays at the adult station
H3Spill tray (rimmed, heat-resistant) + towel
Mug and engine stand inside it
1$8.00 estimate$8.00Retail (no link)
—
Baking sheet—
H4Digital kitchen scale, 1 g
Water mass (heat input) and flywheel mass (inertia)
1$12.00 estimate$12.00Retail (no link)
—
Assumed owned—
H5XPS foam offcut 25 mm, ≈ 150 × 150 mm
Insulating lid for the lid run (template foam-lid.svg)
1$5.00 estimate$5.00Hardware store (no link)
—
Folded towel over a plate (less repeatable)Adult cuts
H6Baltic birch plywood 3 mm, 12 × 20 in
Wood Vault, 1/8" Laser/CNC grade variant; 1 sheet (base, uprights, sensor arm, probe clips, TDC pointer)
1$3.50$3.50woodvault.com
The Wood Vault
$3.50 per sheet (1/8" Laser/CNC grade variant) · checked 2026-10-09 · Not confirmed (variant page)
Any 3 mm laser plywoodTrained adult runs the laser cutter
H7M4 × 20 bolt + washer + wing nut (arm), Kapton or aluminum tape, thermal paste, zip ties
Sensor mounting
1$8.00 estimate$8.00Hardware store (no link)
—
——
H8Laser cutter access or cutting service
1 sheet (estimate)
1$5.00 estimate$5.00Makerspace / cut service (no link)
—
—Trained adult operates the laser cutter
Subtotal$76.50Low-cost path: $21.50

C. Tools and safety (once per school)

IDPart & specQtyUnit (typical)Line (typical)Where to buyCheaper substituteAdult handling / safety gear
T1Temperature-controlled soldering iron
Pinecil
1$68.50$68.50sparkfun.com
SparkFun
$68.50 · checked 2026-10-09 · Not recorded
Assumed owned in the low totalAdult supervision
T2Lead-free solder 15 g
SparkFun
1$4.95$4.95sparkfun.com
SparkFun
$4.95 (single-unit price) · checked 2026-10-09 · Not recorded
—Wash hands after soldering
T3Safety glasses, ANSI Z87.1 (Z87+) impact-rated, clear
3M SecureFit SF201AF · clear anti-fog polycarbonate lens marked Z87+ (ANSI Z87.1 impact-rated; 3M spec table on strobelssupply.com and safetycompany.com, read 2026-10-09); drilling, soldering, laser cutting, hot-water work (splash)
2$5.32$10.64platt.com
Platt Electric Supply
$5.32 EA · checked 2026-10-09 · 40 in stock (company-wide)
Any glasses marked Z87+ (ANSI Z87.1 high-impact). Not SparkFun SWG-11046: it lists only CE/EN 1836, a sunglass standard, not impact-ratedCheck the Z87+ marking on arrival
T4Drill + 3 mm bit, deburring tool, oven mitt
Pressure port (adult); mitt for the adult handling the kettle
1$20.00 estimate$20.00Hardware store (no link)
—
Assumed owned in the low totalAdult only
T5Laptop with Arduino IDE and Python 3 + numpy (+ matplotlib, pyserial)
Logger stream; heat.py
1$0.00 estimate$0.00School (no link)
—
——
Subtotal$104.09Low-cost path: $15.59

The pack is digital files only. Hardware is bought separately.

Standards map

These are standards the pack's activities are mapped to by Laue Labs. They are not a certification or endorsement by any standards body or state.

"Mapped to" means Laue Labs' alignment, not a certification.

Activity NGSS HS performance expectations Practices / crosscutting Common Core HS math
Lab 1 Carnot, models HS-PS3-1 (computational model of energy change), HS-PS3-2 Using mathematics; Developing models HSN-Q.A.1–3, HSA-CED.A.4
Lab 2 P–V loop HS-PS3-1, HS-PS3-3 (design a device that converts energy) Analyzing data; Energy and matter HSF-TF.A (sinusoids), numerical integration
Lab 3 temperatures HS-PS3-4 (second law: uniform energy distribution, thermal equilibrium) Planning investigations; Cause and effect HSS-ID.B.6
Lab 4 energy budget HS-PS3-1, HS-PS3-4 Analyzing and interpreting data; Systems and system models HSS-ID.B.6, error propagation
Lab 5 CER HS-ETS1-3 (trade-offs), HS-PS3-3 Engaging in argument from evidence —
Build HS-ETS1-2 Designing solutions HSG-MG.A.3

License options

$17 Individual

One student or one household.

You may:

  • Use, print, and modify the files for your own builds and experiments
  • Share photos and videos of your finished project

You may not:

  • Use the pack as curriculum for a class, club, camp, or co-op (see Homeschool / Co-op and Classroom)
  • Redistribute, resell, or publish the pack files
$39 Homeschool / Co-op

One homeschool family, or one co-op group of up to 10 learners with its facilitator(s).

You may:

  • Print guides and lab sheets for the learners in that family or co-op group
  • Use the facilitator notes, rubric, and pacing guide with that group

You may not:

  • Use it for a co-op group larger than 10 learners, or for a school class (see Classroom)
  • Redistribute, resell, or publish the pack files
$59 Classroom

One teacher with up to 30 students in a single class or cohort.

You may:

  • Print or project materials for those students
  • Copy code and cut files to student machines for that class

You may not:

  • Share files with other teachers or schools, or post them publicly
  • Use it as a whole-school or multi-year site license, or for more than 30 students, without contacting us

All licenses: digital files only (hardware not included). Keep Laue Labs attribution on printed handouts. After checkout you get an instant download on the thanks page. License questions, more learners, or site licenses: lance.haney@gmail.com.

Safety & legal notes

  • Hot water scalds: use water no hotter than the engine maker specifies (typically well below boiling), a stable heat-resistant container, and adult supervision.
  • No open flames or alcohol burners in this pack.
  • Keep fingers clear of the flywheel and crank.
  • Students should work with adult supervision for tools, soldering, batteries, and anything flagged in the BOM.