Definition – Expansion Ratio in a Thermodynamic Process If v1 is the volume at the beginning of expansion and v2 is the volume at the end of expansion, then the expansion ratio r is defined as r = v2 / v1.

Introduction / Context:
Ratios of volumes are used to characterize compression and expansion in ideal cycles and real engines. Knowing the correct definition avoids confusion when switching between compression ratio and expansion ratio in p–v analyses.

Given Data / Assumptions:

• Single expansion from initial volume v1 to final volume v2.
• No restriction on the path (polytropic, isentropic, etc.).
• Positive volumes and monotonic increase during expansion (v2 > v1).

Concept / Approach:

By convention, compression ratio r_c = v_max / v_min. Analogously, the expansion ratio compares the end volume to the start volume during the expansion leg. Hence r = v2 / v1 > 1 for an expansion. This aids in writing temperature and pressure relations for specific process models (e.g., isentropic relations involving volume ratios raised to powers of gamma − 1).

Step-by-Step Solution:

Verification / Alternative check:

In an isentropic ideal gas process, T2/T1 = (v1/v2)^(gamma−1); writing v2/v1 = r ensures consistent exponents for expansions (T drops when r > 1).

Why Other Options Are Wrong:

v1/v2 corresponds to a compression ratio. Arithmetic mean or product have no standard thermodynamic meaning here. (v2 − v1)/v1 is a fractional change, not the expansion ratio by definition.

Common Pitfalls:

Mixing up start/end labels; assuming r must be the same as the engine geometric compression ratio (not necessarily, depending on cycle).

Final Answer:

r = v2 / v1