The Otto Cycle: A Gasoline Engine's Idealized Model

1 · Predict

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?

• 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.

2 · Set Up

1. Open the otto-cycle preset and press Reset. 1 mol of nitrogen (f = 5) compresses from 40 L to 10 L, then heats at constant volume to 900 K.
2. Enable the per-leg work and heat readouts.
3. 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.

3 · Collect Data

Sketch the P-V diagram for all 4 legs. Mark which legs are the constant-volume (vertical) segments and confirm your work readings are 0 there.

4 · Analyze

1. 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.
2. 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.

5 · Extend

1. 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.
2. 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?

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