Define the expansion ratio in steam/IC engines The expansion ratio is defined as the ratio of which two cylinder volumes with respect to the cut-off point during the power stroke?

Introduction:
In reciprocating steam engines (and by analogy in some IC engine analyses), the expansion ratio quantifies how much the working fluid expands after steam admission is cut off. It is a key parameter affecting efficiency and indicated work because it determines how fully pressure energy is utilized during expansion.

Given Data / Assumptions:

• Cut-off occurs during the forward power stroke.
• Volumes are measured in-cylinder, typically referenced from inner dead centre.
• Clearance volume is present at all times, but the definition involves total cylinder volumes at specific crank positions.

Concept / Approach:
Let V_c be clearance volume, V_cut be the cylinder volume at the cut-off crank position, and V_e be the total cylinder volume at the end of the stroke. The expansion ratio r_exp expresses the extent of volumetric expansion after cut-off and is defined by r_exp = V_e / V_cut. This definition captures the thermodynamic leverage obtained by allowing the working fluid to expand over a larger volume before exhaust or release.

Step-by-Step Solution:

Verification / Alternative check:
Indicator diagrams show steam admission up to cut-off followed by expansion; the horizontal (volume) spread from V_cut to V_e corresponds to the expansion process, confirming the ratio definition.

Why Other Options Are Wrong:

• Clearance-to-cut-off or swept-to-clearance: not the standard definition; these ratios have other uses.
• Cut-off to end-of-stroke: inverse of the correct expansion ratio.
• Swept-to-cut-off: ignores the unavoidable clearance volume component contained in both volumes.

Common Pitfalls:
Forgetting to include clearance volume in total cylinder volumes; confusing expansion ratio with compression ratio in IC engines; using stroke length directly instead of actual volumes defined by geometry.

Final Answer: