`eta = 1-(1/r^(gamma-1))`

Enter a value for all fields

The Maximum Thermal Efficiency of an Otto Cycle calculator computes the ideal thermal efficiency of a gasoline engine.

INSTRUCTIONS: Enter the following:

• (r) Compression Ratio
• (γ) Ratio of Specific Heats

Maximum Thermal Efficiency of an Otto Cycle (η): The results are returned as a real number.

The Math / Science

The Maximum Thermal Efficiency of an Otto Cycle is the thermal efficiency of an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is thermodynamic cycle most commonly found in automobile engines. It is a description of what happens to a mass of gas as it is subjected to changes of pressure, temperature, volume, addition of heat, and removal of heat.

The following formula is used to calculate the thermal efficiency:

`eta=1-(1/r^(gamma-1))`

where:

• `r` = compression ratio
• `gamma` = specific heat ratio

The Otto cycle is an model of a gasoline engine in ideal operations, consisting of:

1. Isentropic compression
2. Constant-volume combustion
3. Isentropic expansion (power)
4. Constant-volume heat rejection

The Four Processes of the Otto Cycle

The ideal Otto cycle consists of four internally reversible processes: two isentropic (adiabatic) and two constant-volume processes.

1. Isentropic Compression (Process 1 → 2)
   • The piston moves upward.
   • The air-fuel mixture is compressed.
   • No heat is exchanged with surroundings.
   • Temperature and pressure rise significantly.
2. Constant-Volume Heat Addition (Process 2 → 3)
   • This represents the ignition (spark plug fires).
   • The combustion is modeled as heat being added at constant volume.
   • Pressure and temperature increase sharply.
3. Isentropic Expansion (Power Stroke) (Process 3 → 4)
   • High-pressure gas pushes the piston downward.
   • This is where useful work output occurs.
   • Again, no heat transfer.
4. Constant-Volume Heat Rejection (Process 4 → 1)
   • Exhaust valve opens.
   • Heat leaves the system at constant volume (idealized representation of exhaust).

Then the cycle repeats.

References

Wikipedia (https://en.wikipedia.org/wiki/Otto_cycle)