Steam Engine Terminology — Definition of Expansion Ratio In a reciprocating steam engine, the expansion ratio is defined as the ratio of which two volumes (neglecting clearance for a basic definition)?

Introduction / Context:
Expansion ratio is a key parameter linking cut-off to the thermodynamic expansion of steam in the cylinder. It strongly influences efficiency, work output, and the shape of the indicator diagram.

Given Data / Assumptions:

• Simple definition that neglects clearance volume to illustrate the concept.
• Cut-off occurs when admission ceases and steam expands to the end of the stroke.
• Uniform cross-section cylinder so volume is proportional to piston travel.

Concept / Approach:
If the fraction of stroke completed at cut-off is f (0 < f < 1), then the remaining part of the stroke allows expansion. Expansion ratio r is commonly taken as total swept volume divided by the volume admitted at cut-off, giving r = 1 / f in the no-clearance idealization. This directly relates valve setting (cut-off) to expansion.

Step-by-Step Solution:
Define swept volume V_s proportional to full stroke.Define volume at cut-off V_c proportional to piston travel at cut-off.Expansion ratio r = V_s / V_c (neglecting clearance), i.e., “swept volume to the volume at cut-off”.If cut-off is, for example, 25% of stroke (f = 0.25), then r = 1 / 0.25 = 4.

Verification / Alternative check:
More exact definitions include clearance: r_exact = (V_clearing + V_end) / (V_clearing + V_cutoff). For teaching purposes, the simplified ratio captures the primary dependency on cut-off.

Why Other Options Are Wrong:

• Volume at cut-off to swept volume: inverse of the standard simplified definition.
• Ratios including clearance or unrelated volumes: do not represent the intended simple concept.

Common Pitfalls:
Forgetting that real cylinders have clearance, which reduces the effective expansion ratio slightly compared with the simple 1/f rule; always state the assumption when precision matters.

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