Heat capacity ratio question: The ratio γ = cp/cv (specific heats at constant pressure and constant volume) is always __________ one for a gas.

Introduction / Context:
The heat capacity ratio γ = cp/cv is a key parameter in isentropic flow, speed of sound, and adiabatic relations. Understanding its magnitude relative to unity is essential for predicting expansion/compression behavior and wave propagation in gases.

Given Data / Assumptions:

• Ideal or calorically perfect gas for conceptual reasoning.
• Definitions: cp is heat per unit mass per degree at constant pressure; cv at constant volume.
• For a gas, cp = cv + R where R is the specific gas constant.

Concept / Approach:
Because cp = cv + R and R is positive for any gas, cp must exceed cv, hence γ = cp/cv > 1. Typical values are around 1.4 for diatomic gases (air at moderate temperatures) and around 1.67 for monatomic gases. Values decrease slightly with increasing temperature as vibrational modes become active in real gases, but remain greater than one.

Step-by-Step Solution:

Verification / Alternative check:
For air at room temperature: cp ≈ 1.004 kJ/kg·K, cv ≈ 0.718 kJ/kg·K ⇒ γ ≈ 1.4 > 1, matching common textbook values.

Why Other Options Are Wrong:

• Equal to one: Would imply R = 0 which is impossible for a gas.
• Less than one: Contradicts cp − cv = R > 0.

Common Pitfalls:
Confusing γ with polytropic index n; γ is a property ratio, whereas n depends on process path.

Final Answer:
greater than