Identify the correct 1.987-value for the universal gas constant R by unit system.

Introduction / Context:
The universal gas constant R has the same physical value expressed in different unit systems. Remembering the common numeric representations avoids unit mistakes in thermodynamic equations of state and energy balances.

Given Data / Assumptions:

• The numeric value 1.987 is associated with R in certain units.
• 1 kcal = 1000 cal; 1 kg-mole (kmol) = 1000 moles; 1 Btu is the British thermal unit.

Concept / Approach:
The most familiar is R = 1.987 cal/mol·K. Multiplying numerator and denominator by 1000 gives R = 1.987 kcal/kg-mole·K. In English units, R ≈ 1.986–1.987 Btu/lb-mole·°R. Thus, the 1.987 figure corresponds to both kcal/kg-mole·K and Btu/lb-mole·°R.

Step-by-Step Solution:
From cal/mol·K to kcal/kg-mole·K: (1.987 cal/mol·K) × (1 kcal/1000 cal) × (1000 mol/kg-mole) = 1.987 kcal/kg-mole·K.Standard English-units value: R ≈ 1.9869 Btu/lb-mole·°R.Therefore, both (b) and (c) are valid for the 1.987 numeral.

Verification / Alternative check:
Other common forms: R = 8.314 kJ/kmol·K and R = 10.731 psia·ft^3/(lb-mole·°R) corroborate consistency after unit conversions.

Why Other Options Are Wrong:
(a) uses °C instead of K; while Δ°C equals ΔK, R is conventionally tabulated per K. (e) with kJ has numeric 8.314, not 1.987.

Common Pitfalls:
Forgetting that kg-mole is kmol; mixing absolute units (K, °R) with relative scales (°C, °F).

Final Answer:
both (b) & (c)