thermal efficiency and compression ratiocalculate

Question

Thermal efficiency and compression ratio:

Calculate thermal efficiency and compression ratio for automobile working on otto cycle. If energy generated per cycle is thrice which of rejected during the exhaust. Consider fluid as an ideal gas with = 1.4       

Sol.: Since we have

Where

W_otto = (Q₁  - Q₂)/Q₁

Q₁ = Heat supplied

Q₂ = Heat rejected

Given that     Q₁ = 3Q₂

otto = (3Q₂  - Q₂)/3Q₂  = 2/3 = 66.6%                                                   ...(i)

We also have;

Q_otto = 1 - 1/(r)  ^{- 1}

0.667 = 1/(r)1.4 ^{- 1}

r = (3^)1/0.4  = 15.59