For gases other than monoatomic species, what is the typical molal heat capacity at constant volume (Cv, in kcal per kg-mol per K)?

Introduction / Context:
Heat capacities of gases determine energy requirements for heating, cooling, and reacting streams. An order-of-magnitude grasp helps check calculations and select appropriate correlations without constantly consulting tables.

Given Data / Assumptions:

• Gas molar heat capacity at constant volume for a monatomic ideal gas: Cv = (3/2)R.
• Gas constant R ≈ 1.987 kcal per kg-mol per K.
• Polyatomic gases have additional degrees of freedom (rotational and vibrational) that increase Cv above monatomic values at ordinary temperatures.

Concept / Approach:
For monatomic gases, Cv ≈ 1.5R ≈ 2.98 kcal per kg-mol per K (often rounded to about 3). Diatomic and polyatomic gases possess rotational (and at higher T, vibrational) modes, leading to Cv values exceeding ~3 kcal per kg-mol per K at ambient to moderate temperatures. Hence, for all but monatomic gases, Cv is typically greater than 3 on this unit basis.

Step-by-Step Solution:
Compute monatomic benchmark: 1.5 * 1.987 ≈ 2.98 ≈ 3.Recognize added degrees of freedom for non-monoatomic gases raise Cv.Conclude: for “all except monatomic,” Cv > 3 kcal per kg-mol per K.Select option “> 3.”

Verification / Alternative check:
Reference data: at room temperature, N2 and O2 have Cv near 5/2 R ≈ 4.97 kcal per kg-mol per K; CO2 and other polyatomics are typically higher, consistent with “> 3.”

Why Other Options Are Wrong:
3 is approximately the monatomic value; non-monoatomic commonly exceed it.“< 3” or “< 1” contradict well-established degrees of freedom arguments and data.

Common Pitfalls:
Mixing mass-based (per kg) with molar (per kg-mol) bases; forgetting temperature dependence of vibrational contributions at high T.

Final Answer:
> 3