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An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.[1]

The Otto cycle 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 mass of gas that is subjected to those changes is called the system. The system, in this case, is defined to be the fluid (gas) within the cylinder. By describing the changes that take place within the system, it will also describe in inverse, the system's effect on the environment. In the case of the Otto cycle, the effect will be to produce enough net work from the system so as to propel an automobile and its occupants in the environment.

The Otto cycle is constructed from:

Top and bottom of the loop: a pair of quasi-parallel and isentropic processes (frictionless, adiabatic reversible).
Left and right sides of the loop: a pair of parallel isochoric processes (constant volume).

The isentropic process of compression or expansion implies that there will be no inefficiency (loss of mechanical energy), and there be no transfer of heat into or out of the system during that process. The cylinder and piston are assumed to be impermeable to heat during that time. Work is performed on the system during the lower isentropic compression process. Heat flows into the Otto cycle through the left pressurizing process and some of it flows back out through the right depressurizing process. The summation of the work added to the system plus the heat added minus the heat removed yields the net mechanical work generated by the system.

## Processes

The processes are described by:[2][page needed]

• Process 0–1 a mass of air is drawn into piston/cylinder arrangement at constant pressure.
• Process 1–2 is an adiabatic (isentropic) compression of the charge as the piston moves from bottom dead center (BDC) to top dead center (TDC).
• Process 2–3 is a constant-volume heat transfer to the working gas from an external source while the piston is at top dead center. This process is intended to represent the ignition of the fuel-air mixture and the subsequent rapid burning.
• Process 3–4 is an adiabatic (isentropic) expansion (power stroke).
• Process 4–1 completes the cycle by a constant-volume process in which heat is rejected from the air while the piston is at bottom dead center.
• Process 1–0 the mass of air is released to the atmosphere in a constant pressure process.

The Otto cycle consists of isentropic compression, heat addition at constant volume, isentropic expansion, and rejection of heat at constant volume. In the case of a four-stroke Otto cycle, technically there are two additional processes: one for the exhaust of waste heat and combustion products at constant pressure (isobaric), and one for the intake of cool oxygen-rich air also at constant pressure; however, these are often omitted in a simplified analysis. Even though those two processes are critical to the functioning of a real engine, wherein the details of heat transfer and combustion chemistry are relevant, for the simplified analysis of the thermodynamic cycle, it is more convenient to assume that all of the waste-heat is removed during a single volume change.

## History

The four-stroke engine was first patented by Alphonse Beau de Rochas in 1861.[3] Before, in about 1854–57, two Italians (Eugenio Barsanti and Felice Matteucci) invented an engine that was rumored to be very similar, but the patent was lost.

The first person to build a working four-stroke engine, a stationary engine using a coal gas-air mixture for fuel (a gas engine), was German engineer Nicolaus Otto.[4] This is why the four-stroke principle today is commonly known as the Otto cycle and four-stroke engines using spark plugs often are called Otto engines.

## Processes

The system is defined to be the mass of air that's drawn from the atmosphere into the cylinder, compressed by the piston, heated by the spark ignition of the added fuel, allowed to expand as it pushes on the piston, and finally exhausted back into the atmosphere. The mass of air is followed as its volume, pressure and temperature change during the various thermodynamic steps. As the piston is capable of moving along the cylinder, the volume of the air changes with its position in the cylinder. The compression and expansion processes induced on the gas by the movement of the piston are idealised as reversible, i.e., no useful work is lost through turbulence or friction and no heat is transferred to or from the gas during those two processes. Energy is added to the air by the combustion of fuel. Useful work is extracted by the expansion of the gas in the cylinder. After the expansion is completed in the cylinder, the remaining heat is extracted and finally the gas is exhausted to the environment. Useful mechanical work is produced during the expansion process and some of that used to compress the air mass of the next cycle. The useful mechanical work produced minus that used for the compression process is the net work gained and that can be used for propulsion or for driving other machines. Alternatively the useful work gained is the difference between the heat added and the heat removed.

### Process 0–1 intake stroke (Blue Shade)

A mass of air (working fluid) is drawn into the cylinder, from 0 to 1, at atmospheric pressure (constant pressure) through the open intake valve, while the exhaust valve is closed during this process. The intake valve closes at point 1.

### Process 1–2 compression stroke (B on diagrams)

Piston moves from crank end (BDC, bottom dead centre and maximum volume) to cylinder head end (TDC, top dead centre and minimum volume) as the working gas with initial state 1 is compressed isentropically to state point 2, through compression ratio (V1/V2). Mechanically this is the isentropic compression of the air/fuel mixture in the cylinder, also known as the compression stroke. This isentropic process assumes that no mechanical energy is lost due to friction and no heat is transferred to or from the gas, hence the process is reversible. The compression process requires that mechanical work be added to the working gas. Generally the compression ratio is around 9–10:1 (V1:V2) for a typical engine.[5]

### Process 2–3 ignition phase (C on diagrams)

The piston is momentarily at rest at TDC. During this instant, which is known as the ignition phase, the air/fuel mixture remains in a small volume at the top of the compression stroke. Heat is added to the working fluid by the combustion of the injected fuel, with the volume essentially being held constant. The pressure rises and the ratio ${\displaystyle (P_{3}/P_{2})}$ is called the "explosion ratio".

### Process 3–4 expansion stroke (D on diagrams)

The increased high pressure exerts a force on the piston and pushes it towards the BDC. Expansion of working fluid takes place isentropically and work is done by the system on the piston. The volume ratio ${\displaystyle V_{4}/V_{3}}$ is called the "isentropic expansion ratio". (For the Otto cycle is the same as the compression ratio ${\displaystyle V_{1}/V_{2}}$). Mechanically this is the expansion of the hot gaseous mixture in the cylinder known as expansion (power) stroke.

### Process 4–1 idealized heat rejection (A on diagrams)

The piston is momentarily at rest at BDC. The working gas pressure drops instantaneously from point 4 to point 1 during a constant volume process as heat is removed to an idealized external sink that is brought into contact with the cylinder head. In modern internal combustion engines, the heat-sink may be surrounding air (for low powered engines), or a circulating fluid, such as coolant. The gas has returned to state 1.

### Process 1–0 exhaust stroke

The exhaust valve opens at point 1. As the piston moves from "BDC" (point 1) to "TDC" (point 0) with the exhaust valve opened, the gaseous mixture is vented to the atmosphere and the process starts anew.

## Cycle analysis

In the process 1–2 the piston does work on the gas and in process 3–4 the gas does work on the piston during those isentropic compression and expansion processes, respectively. Processes 2–3 and 4–1 are isochoric processes; heat is transferred into the system from 2—3 and out of the system from 4—1 but no work is done on the system or extracted from the system during those processes. No work is done during an isochoric (constant volume) process because addition or removal of work from a system requires the movement of the boundaries of the system; hence, as the cylinder volume does not change, no shaft work is added to or removed from the system.

Four different equations are used to describe those four processes. A simplification is made by assuming changes of the kinetic and potential energy that take place in the system (mass of gas) can be neglected and then applying the first law of thermodynamics (energy conservation) to the mass of gas as it changes state as characterized by the gas's temperature, pressure, and volume.[2][page needed][6][page needed]

During a complete cycle, the gas returns to its original state of temperature, pressure and volume, hence the net internal energy change of the system (gas) is zero. As a result, the energy (heat or work) added to the system must be offset by energy (heat or work) that leaves the system. In the analysis of thermodynamic systems, the convention is to account energy that enters the system as positive and energy that leaves the system is accounted as negative.

Equation 1a.

During a complete cycle, the net change of energy of the system is zero:

${\displaystyle \Delta E=E_{\text{in}}-E_{\text{out}}=0}$

The above states that the system (the mass of gas) returns to the original thermodynamic state it was in at the start of the cycle.

Where ${\displaystyle E_{\text{in}}}$is energy added to the system from 1–2–3 and ${\displaystyle E_{\text{out}}}$ is energy removed from the system from 3–4–1. In terms of work and heat added to the system

Equation 1b:

${\displaystyle W_{1-2}+Q_{2-3}+W_{3-4}+Q_{4-1}=0}$

Each term of the equation can be expressed in terms of the internal energy of the gas at each point in the process:

${\displaystyle W_{1-2}=U_{2}-U_{1}}$
${\displaystyle Q_{2-3}=U_{3}-U_{2}}$
${\displaystyle W_{3-4}=U_{4}-U_{3}}$
${\displaystyle Q_{4-1}=U_{1}-U_{4}}$

The energy balance Equation 1b becomes

${\displaystyle W_{1-2}+Q_{2-3}+W_{3-4}+Q_{4-1}=\left(U_{2}-U_{1}\right)+\left(U_{3}-U_{2}\right)+\left(U_{4}-U_{3}\right)+\left(U_{1}-U_{4}\right)=0}$

To illustrate the example we choose some values to the points in the illustration:

${\displaystyle U_{1}=1}$
${\displaystyle U_{2}=5}$
${\displaystyle U_{3}=9}$
${\displaystyle U_{4}=4}$

These values are arbitrarily but rationally selected. The work and heat terms can then be calculated.

The energy added to the system as work during the compression from 1 to 2 is

${\displaystyle \left(U_{2}-U_{1}\right)=\left(5-1\right)=4}$

The energy added to the system as heat from point 2 to 3 is

${\displaystyle \left({U_{3}-U_{2}}\right)=\left(9-5\right)=4}$

The energy removed from the system as work during the expansion from 3 to 4 is

${\displaystyle \left(U_{4}-U_{3}\right)=\left(4-9\right)=-5}$

The energy removed from the system as heat from point 4 to 1 is

${\displaystyle \left(U_{1}-U_{4}\right)=\left(1-4\right)=-3}$

The energy balance is

The Otto cycle 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 mass of gas that is subjected to those changes is called the system. The system, in this case, is defined to be the fluid (gas) within the cylinder. By describing the changes that take place within the system, it will also describe in inverse, the system's effect on the environment. In the case of the Otto cycle, the effect will be to produce enough net work from the system so as to propel an automobile and its occupants in the environment.

The Otto cycle is constructed from:

The isentropic process of compression or expansion implies that there will be no inefficiency (loss of mechanical energy), and there be no transfer of heat into or out of the system during that process. The cylinder and piston are assumed to be impermeable to heat during that time. Work is performed on the system during the lower isentropic compression process. Heat flows into the Otto cycle through the left pressurizing process and some of it flows back out through the right depressurizing process. The summation of the work added to the system plus the heat added minus the heat removed yields the net mechanical work generated by the system.