Question Dual cycle's four processess in t-s DIAGRAM, explanation, equations, efficiency derivation, advantages and disadvantages

Step 1The T-S diagram of the Dual cycle is as follows:Step 2Process 1-2: Reversible adiabatic (Isentropic) compression processProcess 2-3: Constant volume heat addition processProcess 3-4: Constant pressure heat addition processProcess 4-5: Reversible adiabatic (Isentropic) expansion processProcess 5-1: Constant volume heat rejection processFor the process 1-2, Reversible adiabatic compression process is as follows:T2T1=V1V2γ-1T2=rγ-1T1⋯⋯⋯(1)Here,r=V1V2 is the Compression ratioStep 3For the process 2-3, Constant volume heat addition process is as follows:T3T2=P3P2Here, α=P3P2 is the pressure ratioT3=αT2T3=α·rγ-1T1⋯⋯⋯(2)For the process 3-4, Constant pressure heat addition process is as follows:T4T3=V4V3Here,ρ=V4V3 is the cutoff ratioT4=ρT3T4=ρ·α·rγ-1T1⋯⋯⋯⋯(3)Step 4For the process 4-5 , Reversible adiabatic expansion process is as follows:T5T4=V4V5γ-1T5T4=V4V3×V3V5γ-1T5T4=V4V3×V2V1γ-1T5=T4ρrγ-1T5=ρ·α·rγ-1·ρrγ-1·T1T5=ργ·α·T1⋯⋯⋯⋯⋯4Step 5Efficiency derivation:The efficiency of the Dual cycle is as follows:η=1-Heat rejection at constant volumeHeat addition at constant volume+Heat addition at constant pressureNow, substitute all the values in the above equation as follows:η=1-mCvT5-T1mCvT3-T2+mCPT4-T3η=1-T5-T1T3-T2+γ(T4-T3)η=1-ργ·α·T1-T1αrγ-1T1-rγ-1T1+γραrγ-1T1-αry-1T1η=1-ργ·α-1rγ-1α-1+γαry-1γ-1η=1-1rγ-1αργ-1α-1+γαγ-1Step 6Advantages of the Dual cycle:The advantages of the Dual cycle is as follows:1. In the Dual cycle, there is more time available to burn the fuel completely due to its two heating cycles.2. For the same compression ratio, there is more efficiency obtain than the diesel cycle.Disadvantages of the Dual cycle:The disadvantages of the Dual cycle is as follows:1. The heat rejected zone in the Dual cycle is greater than the Otto cycle.2. The efficiency is less compared to the Otto cycle for the same compression ratio. ...