Subtopic: Kinetics of microbial death – pasteurization and sterilization of milk and other liquid foods
Question Statement:
Bacillus stearothermophilus has a z value of 10.20 °C at a reference temperature of 121 °C. The activation energy for the destruction of Bacillus stearothermophilus is
Options:
(A) 327.56 MJ kg mole⁻¹
(B) 298.95 MJ kg mole⁻¹
(C) 208.35 MJ kg mole⁻¹
(D) 75.62 MJ kg mole⁻¹
Official Answer Key:
B
Step-by-Step Solution & Explanation
The z-value relates to activation energy through the thermal-death-time (Arrhenius-based) relationship: z = 2.303·R·T_ref²/E_a ⟹ E_a = 2.303·R·T_ref²/z. R=8.314 J/mol·K, T_ref = 121+273=394 K. E_a = 2.303×8.314×394² / 10.20 = 2.303×8.314×155,236/10.20 = ≈291.4 MJ/kg-mole, closest to option (B) 298.95. A small (~2–3%) discrepancy from option B is noted — likely arising from a slightly different rounding of T_ref (394 vs 394.15 K) or R in the source solution; using T_ref=394.15 K narrows the gap further but does not fully close it.
Verification note: Independent verification gives ≈291.4 MJ/kg-mole vs. the closest listed option of 298.95 (B) — flagged per the verification protocol as a minor (≈2.5%) discrepancy, most likely from rounding of absolute temperature in the source solution.
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