Otto Cycle – Definition, PV Diagram and TS Diagram:

It is an idealized cycle for the spark ignition internal combustion engines. It is the thermodynamic cycle most commonly found in automobile engine. Otto Cycle was conceived by Nikolaws Otto. It is the standard of comparison for internal combustion engine and a description of what happens to a mass of gas when it is subjected to changes like pressure, temperature, volume, addition of heat, removal of heat.

Fig. 2.1 shows the theoretical P-V diagram and T- s diagrams of this cycle.

The otto cycle consists of four processes 1 – 2 – 3 – 4

Refer the P-V diagram and T- s diagram.

Process 1-2: Reversible adiabatic compression of air:

In this process, the piston moves from BDC to TDC position. Air undergoes reversible adiabatic compression. Hence the volume of the air decreases from V₁ to V₂ and the pressure increases from P₁ to P₂. Temperature increases from T₁ to T₂ as it is an isentropic process and the entropy remains constant S₁ = S₂.

Process 2-3: Heat addition at constant volume:

It is a isochoric (constant volume) heat addition process. Here the piston remains at TDC for a moment. Heat is added at constant volume V₂ = V₃ from an external heat source. Temperature increases from T₂ to T₃, pressure increases from P₂ to P₃ and entropy increases from S₂ to S₃.

In this process

Where

• m = mass
• C_v = Specific heat at constant volume

Process 3-4: Reversible adiabatic expansion of air:

In this process, air undergoes isentropic (reversible adiabatic) expansion of air. The piston is pushed from TDC to BDC position. The pressure decreases from P₃ to P₄, volume rises from V₃ to V₄, temperature decreases from T₃ to T₄ and the entropy remains constant (S₃ = S₄).

Process 4-1: Heat rejection at constant volume:

In this process, the piston remains at BDC for a moment and heat is rejected at constant volume (V₄ = V₁). The pressure falls from P₄ to P₁. The temperature decreases from T₄ to T₁ and entropy falls from S₄ to S₁.

In this process

The compression ratio (r) in the ratio of total volume to the clearance volume.

Expression for air-standard efficiency of otto cycle.

To derive η_otto, we must first derive T₂ and T₃ from the process 1-2 and process 3-4 respectively.

Process 1-2:

It is an isentropic process, therefore the relation between T and V is as follows.

Process 3-4:

It is also an isentropic process, therefore the relation between T and V is similar to process 1-2.

Substituting the values of equation 4 and 5 in equation 3.

The above expression shows that efficiency increases with the increase of compression ratio.