Air-standard Diesel cycle parameter: The cut-off ratio r_c is defined using cylinder volumes at the start and end of the constant-pressure heat addition. Select the correct definition below.

Introduction:
In the Diesel cycle, heat addition occurs at approximately constant pressure from the end of compression (top dead centre) to the cut-off point during the expansion. The ratio of volumes at these two instants is called the cut-off ratio, a key parameter that governs efficiency and work output.

Given Data / Assumptions:

• Ideal air-standard Diesel cycle.
• State 2: end of compression at top dead centre (volume V_2).
• State 3: end of heat addition at cut-off (volume V_3).

Concept / Approach:
By definition, r_c = V_3 / V_2. At the end of compression, the piston is at TDC and the cylinder volume equals the clearance volume V_c. Therefore, V_2 = V_c. Hence, r_c = V_3 / V_c. Recognizing this identity resolves many confusions between swept volume, clearance volume, and instantaneous volumes during the combustion process in Diesel engines.

Step-by-Step Solution:
1) Identify the two states spanning constant-pressure heat addition: start at V_2, end at V_3.2) At TDC, V_2 equals the clearance volume V_c.3) Write r_c = V_3 / V_2 = V_3 / V_c.4) Match with the option that states “volume at cut-off to the clearance volume”.

Verification / Alternative check:
Other cycle relations: compression ratio r = V_1 / V_2; expansion ratio relates to V_4 / V_3; these are distinct from r_c.

Why Other Options Are Wrong:
Using swept volume is incorrect because swept volume does not equal V_2 or V_3 at the instants of interest.

Clearance to cut-off (inverse) is not the standard definition.

Start-of-compression volume is V_1, not V_2; r_c uses V_2 at TDC.

Common Pitfalls:
Mixing up compression ratio r with cut-off ratio r_c; forgetting that V_2 equals the clearance volume at TDC.

Final Answer:
volume at cut-off to the clearance volume