Question

What four processes make up the ideal Otto cycle?

Short answer

Question: Identify and briefly explain the four processes that make up the ideal Otto cycle. Answer: The four processes that make up the ideal Otto cycle are: 1. Isentropic Compression - The working fluid is compressed without any heat transfer, resulting in increased temperature and pressure. 2. Constant Volume Heat Addition - Fuel is injected and ignited, causing rapid heating of the working fluid and a significant pressure increase inside the cylinder. 3. Isentropic Expansion - The high-pressure, high-temperature fluid expands, producing mechanical work and power output while decreasing fluid's pressure and temperature. 4. Constant Volume Heat Rejection - The remaining heat is rejected, and exhaust gases are expelled, resetting the working fluid's temperature and pressure before the cycle repeats.

Step-by-step solution

Process 1 - Isentropic Compression

In this process, the working fluid (air or air-fuel mixture) inside the cylinder is compressed isentropically, i.e., without any heat transfer, by the piston moving from bottom dead center (BDC) to top dead center (TDC). Since the process is isentropic, entropy remains constant during this compression, and the temperature and pressure of the fluid increase.

Process 2 - Constant Volume Heat Addition

After the isentropic compression is completed (piston at TDC), the working fluid is heated at constant volume by injecting fuel and generating a spark for ignition. This process results in a rapid temperature rise and a significant pressure increase inside the cylinder. This phase represents the power or "combustion" stroke in a spark-ignition engine.

Process 3 - Isentropic Expansion

In the third process, the high-pressure and high-temperature working fluid expand isentropically, causing the piston to move from TDC back towards BDC. This expansion process does work on the piston, producing mechanical work and power output. Since this process is isentropic, the entropy remains constant, and the fluid's pressure and temperature decrease.

Process 4 - Constant Volume Heat Rejection

In the final process of the Otto cycle, the working fluid's remaining heat is rejected at constant volume as the piston reaches BDC, and the exhaust valve opens. This heat rejection process resets the working fluid's temperature and pressure to their initial values, as the exhaust gases are expelled from the cylinder. Once the heat rejection process is completed, the cycle begins again with isentropic compression.

Key concepts

Isentropic Compression

Imagine squeezing a spring in your hand; as you apply pressure, the spring's tension increases, but its shape remains unchanged. Isentropic compression in the Otto cycle is akin to this process but with air or a fuel-air mixture. It occurs when the piston in an engine compresses the mixture in the cylinder from the bottom dead center to the top dead center (BDC to TDC) without any heat entering or leaving the system. The name 'isentropic' derives from this idea — 'iso' meaning equal, and 'entropic' relating to entropy, which remains constant during the compression.

Due to this compression, both the temperature and pressure of the mixture significantly increase. This step is crucial because it prepares the mixture for ignition. The more compressed the mixture is, the greater the explosive force will be during the ignition phase, which will subsequently lead to more power being produced during the expansion phase. To visualize the increase in temperature and pressure mathematically, we use the relation \(PV^\gamma = \text{constant}\), where \(P\) is the pressure, \(V\) is the volume, and \(\gamma\) is the specific heat ratio of the gas.

Constant Volume Heat Addition

Next in the Otto cycle, immediately following isentropic compression, comes the explosive moment: constant volume heat addition. This is the dramatic phase where fuel is ignited. At this point, the piston is at its highest point, known as the top dead center, and the volume of the air-fuel mixture does not change; hence, 'constant volume'.

When the spark plug ignites the compressed mixture, there's a rapid increase in temperature, causing the pressure inside the cylinder to skyrocket. This process is the heart of an engine's power generation, as it's where the chemical energy from the fuel is converted into the thermal energy that pushes the piston back down. The auto cycle curve for this phase would show a straight line going up on a Pressure-Volume \(P-V\) diagram since the volume is constant but the pressure increases.

Isentropic Expansion

The blissful moment for an engine occurs in the isentropic expansion phase, where the work to drive the vehicle is generated. To picture this, imagine the release of the spring held in your hand; it pushes back, returning to its original shape. Similarly, the heated and highly pressurized air-fuel mixture, now expanded, forces the piston down from the top dead center to the bottom dead center(TDC to BDC).

Again, as in isentropic compression, the expansion in this step is adiabatic, meaning no heat is transferred into or out of the system, and it's also reversible. The gas does work on the piston as it expands, which is how engines produce motion. The pressure and temperature drop, but entropy stays steady — hence 'isentropic'. It's essentially the reverse process of isentropic compression, with the mathematical description also following \(PV^\gamma = \text{constant}\).

Constant Volume Heat Rejection

After the engine has harnessed energy from the fuel, it must release the waste; this is where constant volume heat rejection steps in. Picture your car's exhaust puffing out smoke — that's part of the finale of the Otto cycle. As the piston reaches the bottom dead center, the now-cooled gases at a lower pressure must be expelled to make room for the next cycle.

In this phase, even though the volume of gas doesn't change, the heat is removed from the system when the exhaust valve opens. The temperature and pressure fall back to their initial states, much like letting out a breath of air to relax after exerting effort. The engine is now ready to begin the same cycle again with fresh air-fuel mixture. This constant volume process on a \(P-V\) diagram would manifest as a line descending straight down, as the volume remains unchanged while pressure decreases due to heat rejection.