Question

Statement I: Efficiency of an Otto cycle increases as the compression ratio decreases.
Statement II: As the fuel-cutoff approaches zero, the efficiency of diesel cycle approaches that of Otto cycle for same compression ratio.
In light of the above statements, choose the correct 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:

Otto cycle efficiency: \(\eta = 1 - 1/r^{\gamma-1}\).
Higher compression ratio means higher efficiency.
Diesel cycle efficiency approaches Otto cycle as cutoff ratio approaches 1.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We need to evaluate the statements about Otto and diesel cycle efficiencies.

Step 2: Key Formula or Approach:
Efficiency of Otto cycle: \(\eta = 1 - 1/r^{\gamma-1}\).
Efficiency of diesel cycle: \(\eta = 1 - \frac{1}{r^{\gamma-1}} \frac{r_c^\gamma - 1}{\gamma (r_c - 1)}\).

Step 3: Detailed Explanation:
For Otto cycle, efficiency increases as the compression ratio increases.
So, Statement I is false.
For diesel cycle, as the fuel-cutoff ratio approaches 1 (cutoff approaches zero), the efficiency approaches that of the Otto cycle.
This is a known fact.
So, Statement II is true.

Step 4: Final Answer:
Statement I is false, but Statement II is true.
Hence, the correct option is (D).