Question

The gasoline internal combustion engine [petrol engine] operates in a cycle that consists of six operations, out of which four are called strokes. Although processes of the cycle are actually irreversible, and friction and heat losses are present, we may assume the entire cycle as an idealised quasi-static cycle, as shown in the figure.
This cycle is known as the “Air-standard Otto cycle”. Throughout this idealized cycle the working substance is treated as if it were an ideal gas of adiabatic exponent $\gamma = 1.4$alone, ignoring the fuel vapours and combustion products.
I. “Isobaric intake stroke” in which the volume increases from zero to ${V_a}$ at atmospheric pressure into the cylinder.
II. Adiabatic compression stroke: The inlet valve is closed and the gasoline-air mixture is compressed adiabatically from ${V_a}$ to ${V_b}$. Here, $r = \dfrac{{{V_a}}}{{{V_b}}}$ is known as the compression ratio of engine $\left[ {r = 6} \right]$. If $r > 7$then the temperature ${T_b}$ that is reached at the end is sufficiently high to ignite the fuel mixture before the occurrence of spark. Such pre-ignition causes “knocking” and loss of power.
III. Constant volume ignition : A spark is produced and a mixture of air-gasoline vapour is ignited.
IV. Adiabatic expansion or power stroke: The heated air and combustion products expand against and drive the piston. This is the stroke that delivers power to the crankshaft.
V. Constant volume exhaust: At the end of power stroke the exhaust valve is opened; this causes a sudden partial escape of cylinder gases. No piston motion takes place in this part of the cycle.
VI. Isobaric exhaust stroke: The moving piston drives out the residual cylinder gases to restore the initial condition of the engine.
The adiabatic power stroke is-

Answer 1

Hint: There are six different types of operations that take place in the Otto cycle. Four of these operations are strokes. They are the isobaric intake stroke, Adiabatic compression stroke, Adiabatic expansion stroke and isobaric exhaust stroke. We need to point out the adiabatic power stroke in the cycle abcd.

Complete step by step answer:
In the question, we are provided with the details of all the six operations, in order to solve the question we need to relate all the operations with the P-V diagram.
I. Isobaric intake stroke: Isobaric refers to constant pressure, and during intake the volume increases to ${V_a}$. The highlighted line corresponds to the isobaric intake stroke.

II. Adiabatic compression stroke: P-V plot for an adiabatic stroke is a curve of ${V^\gamma }$, if the stroke is compressive, volume must decrease. Therefore, process ab represents the adiabatic compressive stroke.

III. Constant volume ignition: Volume is constant, thus it should be a vertical line. During pressure increases very rapidly, therefore, process bc represents the constant volume ignition.

IV. Adiabatic expansion (power stroke) : Since the process is adiabatic, thus the plot will be a curve of ${V^\gamma }$also the volume will increase as the process is “expansion”. This is represented by the process cd. This is the required process.

V. Constant volume exhaust: This process involves exhaust of gas which means reduction of pressure and constant volume points to process da.

VI. Isobaric exhaust stroke: The volume decreases at a constant pressure as the process is isobaric. This is represented by the highlighted process.

Therefore, the stroke cd represents the adiabatic power stroke and is the correct answer.

Note: It is to be noted that during the isobaric process, the plot of the P-V diagram remains horizontal. During the constant volume process, the plot is vertical. During adiabatic process, the graph is a curve with the slope $- \dfrac{{\gamma P}}{V}$. Volume increases during expansion and decreases during compression.