Question

For the same compression ratio, show that the efficiency of Otto cycle is greater than that of Diesel cycle.

Answer 1

We know that

As the compression ratio is same,

If \(\cfrac{V_4}{V_3}\) = r₁ then cut-off ratio, ρ = \(\cfrac{V_3}{V_2}\) = \(\cfrac rr_1\)

Putting the value of ρ in η_Diesel, we get

From above equation, we observe

\(\cfrac rr_1\) > 1

Let r₁ = r – δ, where δ is a small quantity.

The ratio inside the bracket is greater than 1 since the co-efficients of terms δ²/r² is greater than 1 in the numerator. Its means that something more is subtracted in case of diesel cycle than in Otto cycle. 

Hence, for same compression ratio η η_otto > η_diesel .