Thermodynamics
Otto cycle
The petrol-engine cycle: two adiabats + two isochors.
Cycle through the four strokes of an Otto gasoline engine on a PV diagram. Compare work output, heat input, and thermal efficiency.
Otto cycle
The petrol-engine cycle: two adiabats + two isochors.
The Otto cycle models a spark-ignition engine: rapid combustion at nearly constant volume raises pressure, followed by adiabatic expansion doing work, then exhaust at constant volume. It is less efficient than Carnot at the same temperature extremes because heat is added at varying temperature.
- η ≈ 1 − (V₂/V₁)^(γ−1)
- Petrol engine
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
The Otto cycle (adiabatic compression, isochoric heating, adiabatic expansion, isochoric cooling) models a gasoline engine. Unlike the Carnot cycle, two of its legs are at constant volume rather than constant temperature. During those constant-volume legs, does the gas do any work?
Predictions to weigh
- Work is still done because pressure changes during those legs.
- The constant-volume legs do negative work.
- No work is done during the constant-volume legs, since W = PΔV and ΔV = 0.
Variable roles
What you set:
- Leg number
What you measure:
- Leg's target volume V (m³)
- Work done by gas this leg (J)
How the investigation runs
- Open the otto-cycle preset and press Reset. 1 mol of nitrogen (f = 5) compresses from 0.04 m³ to 0.01 m³, then heats at constant volume to 900 K.
- Enable the per-leg work and heat readouts.
- For each leg of the cycle (1 through 4), read off the leg's target volume and the work done by the gas during that leg.
Governing equation
Otto-Cycle Efficiency — η = W / Qin
For an idealized Otto cycle, efficiency depends only on the compression ratio r = V₁/V₂ and the gas's heat-capacity ratio γ: η = 1 − 1/r^(γ−1). Higher compression ratios give higher efficiency.
What the printable worksheet asks students to work out
- Confirm legs 2 and 4 (the isochoric legs) show W = 0 in your table, while legs 1 and 3 (adiabatic) show nonzero work. Compute the compression ratio r = V₁/V₂ = 4 and the cycle efficiency η = 1 − 1/r^(γ−1) using γ = 1.4.
- This cycle's net work is positive even though half its legs do zero work. Explain how the two adiabatic legs alone can produce a net positive work output.
Where this shows up beyond the lab
- Real gasoline engines are limited to compression ratios around 10-12 (higher ratios cause pre-ignition/knocking). Using η = 1 − 1/r^(γ−1), explain why engine designers push for higher compression ratios when possible.
- A Diesel engine uses a different cycle (isobaric heating instead of isochoric) but a similar adiabatic-compression idea. Both rely on adiabatic legs to convert compression work into higher temperatures. Why is minimizing heat loss during compression important for both designs?
- AP Physics 2 — Unit 9: Thermodynamics
- IB Physics — B.4 Thermodynamics
- General High School Physics — Heat, temperature & gas laws
- NGSS High School Physics — Thermal energy transfer
- Welcome to Otto Cycle
- Select the chamber
- Press Play
- Petrol-engine cycle
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.
Heat Engines & Carnot Efficiency