Q.32 Decimal reduction time of a bacterial strain is 20 min. Specific death rate constant
in min^-1 (rounded off to two decimal places) is _________.

Decimal reduction time (D-value) of 20 minutes means the specific death rate constant (k) is 0.11 min^-1, calculated from the formula relating first-order microbial inactivation kinetics.

Understanding D-Value

Decimal reduction time, or D-value, represents the time required at a specific temperature to reduce a microbial population by 90% (one log cycle), following first-order kinetics. For a bacterial strain with D = 20 min, this indicates 90% inactivation occurs every 20 minutes under defined conditions like heat sterilization. The relationship derives from survivor curve equations where log₁₀(N/N₀) = -t/D, linking D directly to the rate constant.

Formula and Calculation

Microbial death follows first-order kinetics: dN/dt = -kN, where k is the specific death rate constant in min^-1. The D-value connects via D = ln(10)/k ≈ 2.3026/k, so k = 2.3026/D. Substituting D = 20 min yields k = 2.3026/20 = 0.11513 min^-1, rounded to 0.11 min^-1 as specified.

Step-by-Step Derivation

• Start with integrated rate law: ln(N/N₀) = -kt, or log₁₀(N/N₀) = -t/(2.3026D) since D = 2.3026/k.
• For 90% reduction, N/N₀ = 0.1, so t = D when log₁₀(0.1) = -1.
• Solve k = ln(10)/D = 2.302585/20 = 0.115129 min^-1 → 0.11 (two decimals).

Exam Relevance

This concept appears in GATE BT for sterilization validation, where lower D-values indicate higher heat resistance susceptibility. No options are provided in the query, but common distractors include k=1/D=0.05 (ignoring ln(10)) or k=1/20=0.050 without log base adjustment. Always verify units match min^-1 for consistency.