Universal gas constant (molar basis): Select the correct SI value and unit for the universal gas constant R_u.

Introduction / Context:
The universal gas constant R_u links macroscopic thermodynamic variables on a molar basis via pV = n R_u T. Correct numerical value and units are essential for accurate conversions between molar and mass-based formulations.

Given Data / Assumptions:

• Molar basis: per kmol (engineering) or per mol (scientific).
• Common engineering unit: J/(kmol·K).
• R_u ≈ 8.314 J/(mol·K) = 8314 J/(kmol·K).

Concept / Approach:
Because 1 kmol = 1000 mol, multiply the molar value by 1000 to convert: 8.314 J/(mol·K) × 1000 = 8314 J/(kmol·K). Many textbooks denote kmol as “kgmole” in older notation, hence 8314 J/kgmole·K. The specific gas constant for a particular gas is R = R_u / M, where M is molar mass (kg/kmol).

Step-by-Step Solution:

Verification / Alternative check:
Using R = R_u/M for air with M ≈ 28.97 kg/kmol gives R ≈ 287 J/(kg·K), a widely known value, confirming consistency.

Why Other Options Are Wrong:

• 8.314 J/kgmole-K, 83.14, 831.4: Off by factors of 10^3, 10^2, and 10, respectively.

Common Pitfalls:
Mixing molar and mass-specific constants; missing the 1000 factor when switching mol→kmol.

Final Answer:
8314 J/kgmole-K