In an ideal Otto cycle, the system executing the cycle undergoes a series of four internally reversible processes: two isentropic (reversible adiabatic) processes alternated with two isochoric processes:
- Isentropic compression (compression stroke) – The gas (fuel-air mixture) is compressed adiabatically from state 1 to state 2, as the piston moves from bottom dead center to top dead center. The surroundings do work on the gas, increasing its internal energy (temperature) and compressing it. On the other hand, the entropy remains unchanged. The volume changes, and the ratio (V1 / V2) is known as the compression ratio.
- Isochoric compression (ignition phase) – In this phase (between state 2 and state 3), there is a constant volume (the piston is at rest ) heat transfer to the air from an external source while the piston is at rest at the top dead center. This process is intended to represent the ignition of the fuel-air mixture injected into the chamber and the subsequent rapid burning. The pressure rises, and the ratio (P3 / P2) is known as the “explosion ratio”.
- Isentropic expansion (power stroke) – The gas expands adiabatically from state 3 to state 4, as the piston moves from top dead center to bottom dead center. The gas works on the surroundings (piston) and loses an amount of internal energy equal to the work that leaves the system. Again the entropy remains unchanged. The volume ratio (V4 / V3) is known as the isentropic expansion ratio, but it is equal to the compression ratio for the Otto cycle.
- Isochoric decompression (exhaust stroke) – In this phase, the cycle completes by a constant-volume process in which heat is rejected from the air while the piston is at the bottom dead center. The working gas pressure drops instantaneously from point 4 to point 1. The exhaust valve opens at point 4. The exhaust stroke is directly after this decompression. As the piston moves from the bottom dead center (point 1) to the top dead center (point 0) with the exhaust valve opened, the gaseous mixture is vented to the atmosphere, and the process starts anew.
During the Otto cycle, the piston works on the gas between states 1 and 2 (isentropic compression). Work is done by the gas on the piston between stages 3 and 4 (isentropic expansion). The difference between the work done by the gas and the work done on the gas is the network produced by the cycle, and it corresponds to the area enclosed by the cycle curve. The work produced by the cycle times the rate of the cycle (cycles per second) is equal to the power produced by the Otto engine.
Isentropic Process
An isentropic process is a thermodynamic process in which the entropy of the fluid or gas remains constant. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. It is a reversible adiabatic process. The assumption of no heat transfer is very important since we can use the adiabatic approximation only in very rapid processes.
Isentropic Process and the First Law
For a closed system, we can write the first law of thermodynamics in terms of enthalpy:
dH = dQ + Vdp
or
dH = TdS + Vdp
Isentropic process (dQ = 0):
dH = Vdp → W = H2 – H1 → H2 – H1 = Cp (T2 – T1) (for ideal gas)
Isentropic Process of the Ideal Gas
The isentropic process (a special case of the adiabatic process) can be expressed with the ideal gas law as:
pVκ = constant
or
p1V1κ = p2V2κ
in which κ = cp/cv is the ratio of the specific heats (or heat capacities) for the gas. One for constant pressure (cp) and one for constant volume (cv). Note that, this ratio κ = cp/cv is a factor in determining the speed of sound in a gas and other adiabatic processes.
Isochoric Process
An isochoric process is a thermodynamic process in which the volume of the closed system remains constant (V = const). It describes the behavior of gas inside the container that cannot be deformed. Since the volume remains constant, the heat transfer into or out of the system does not the p∆V work but only changes the system’s internal energy (the temperature).
Isochoric Process and the First Law
The classical form of the first law of thermodynamics is the following equation:
dU = dQ – dW
In this equation, dW is equal to dW = pdV and is known as the boundary work. Then:
dU = dQ – pdV
An isochoric process and the ideal gas, all of the heat added to the system, will increase the internal energy.
Isochoric process (pdV = 0):
dU = dQ (for ideal gas)
dU = 0 = Q – W → W = Q (for ideal gas)
Isochoric Process of the Ideal Gas
The isochoric process can be expressed with the ideal gas law as:
or
On a p-V diagram, the process occurs along a horizontal line with the equation V = constant.
See also: Guy-Lussac’s Law.
