Question

Given below are two statements:
Statement (I): For the same compression ratio and same heat input, Diesel cycle is more efficient than Otto cycle.
Statement (II): The peak pressure in the cylinder of diesel engine are much higher than in a spark ignition engine.
In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both Statement (I) and Statement (II) are true.
• B. Both Statement (I) and Statement (II) are false.
• C. Statement (I) is true but Statement (II) is false.
• D. Statement (I) is false but Statement (II) is true.

Hint:

Remember the order of efficiency under different conditions:
1. Same compression ratio and heat rejection: $\eta_{\text{Otto}} > \eta_{\text{Dual}} > \eta_{\text{Diesel}}$.
2. Same maximum pressure and temperature: $\eta_{\text{Diesel}} > \eta_{\text{Dual}} > \eta_{\text{Otto}}$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Internal combustion engines operate on idealized thermodynamic cycles: the Otto cycle for gasoline (SI) engines and the Diesel cycle for diesel (CI) engines.
The thermal efficiency of these cycles depends on parameters like the compression ratio, the cut-off ratio, and the specific heat ratio.

Step 2: Detailed Explanation:
Let us analyze Statement (I).
For the same compression ratio ($r$) and the same heat input, the Otto cycle is more efficient than the Diesel cycle.
The thermal efficiency of the Otto cycle is:
\[ \eta_{\text{Otto}} = 1 - \frac{1}{r^{\gamma-1}} \] The thermal efficiency of the Diesel cycle is:
\[ \eta_{\text{Diesel}} = 1 - \frac{1}{r^{\gamma-1}} \left[ \frac{\rho^{\gamma} - 1}{\gamma (\rho - 1)} \right] \] where $\rho > 1$ is the cut-off ratio.
Since the term in the brackets is always greater than $1$, the Diesel cycle is less efficient under these conditions.
Hence, Statement (I) is false.
Now let us analyze Statement (II).
Diesel engines operate on much higher compression ratios ($14:1$ to $22:1$) compared to spark ignition engines ($8:1$ to $12:1$).
The higher compression ratio combined with compression ignition results in peak pressures inside a diesel cylinder (typically $60$ to $120\text{ bar}$) that are significantly higher than those in a spark-ignition engine (typically $40$ to $60\text{ bar}$).
Hence, Statement (II) is true.

Step 3: Final Answer:
Statement (I) is false because the Otto cycle is more efficient than the Diesel cycle for the same compression ratio and heat input, while Statement (II) is true because diesel engines operate at much higher compression ratios and peak pressures.