Diesel (air-standard) cycle — effect of cut-off ratio on efficiency Consider the ideal Diesel cycle at a fixed compression ratio and fixed specific heat ratio. How does the thermal efficiency vary as the cut-off ratio increases?

Introduction / Context:
The Diesel cycle differs from the Otto cycle by adding heat at (approximately) constant pressure over a finite cut-off. The cut-off ratio (rc) is the ratio of cylinder volumes at the end and start of heat addition. Understanding how rc affects efficiency is essential in engine thermodynamics.

Given Data / Assumptions:

• Air-standard Diesel cycle with ideal gas and constant specific heats.
• Compression ratio r is fixed.
• No pumping, friction, or heat losses in the ideal model.

Concept / Approach:
Diesel efficiency can be written in terms of r, k, and rc. For fixed r and k, increasing rc prolongs heat addition at higher specific volumes, lowering the mean effective temperature of heat addition relative to the isentropic temperature rise. This reduces thermal efficiency compared with smaller rc, approaching Otto behavior only as rc → 1.

Step-by-Step Solution:
Recognize: as rc increases (longer constant-pressure heat addition), expansion begins later at higher volume.The average temperature at which heat is supplied decreases relative to the temperature rise achievable with earlier expansion.Consequently, the cycle’s efficiency decreases with increasing rc for constant r and k.

Verification / Alternative check:
Plot η_Diesel vs rc for a fixed r (e.g., r = 16, k = 1.4). Curves show monotonic decrease in η as rc increases above 1.

Why Other Options Are Wrong:
Option A contradicts standard Diesel analysis; option C ignores rc’s role; option D has no basis in the ideal model; option E is true only in the limiting case rc → 1.

Common Pitfalls:
Confusing the practical increase of real Diesel efficiency due to higher r (compared with SI engines) with the theoretical effect of rc when r is held fixed.

Final Answer:
Efficiency decreases with increasing cut-off ratio