Q.3 N and N0 represent the number of viable cells at time ‘t’ during sterilization and at the start of
sterilization (t=0), respectively. Assuming that cell death follows first order kinetics and that k is
the death rate constant, which of the following relationship(s) is/are correct?
(A) N = N0 ekt (B) െln (N/N0 ) = k t (C) N = N0 k t 2 (D) N – N0 = k t
First-order kinetics governs microbial death during sterilization, where the rate of viable cell reduction is proportional to the current number of cells. The correct relationships are derived from the differential equation -dN/dt = kN, leading to specific integrated forms. Options (A) and (B) are correct, while (C) and (D) are not.
Core Equation
Microbial death in sterilization follows first-order kinetics, expressed as dN/dt = -kN, where N is viable cells at time t, N₀ is initial cells (t=0), and k is the death rate constant (positive). Integrating yields N = N₀ e^{-kt}, showing exponential decay.
Option Analysis
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(A) N = N₀ e^{kt}: Incorrect. The exponent is positive, implying growth, not death; correct form is N = N₀ e^{-kt}.
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(B) -ln(N/N₀) = kt: Correct. Taking ln of N = N₀ e^{-kt} gives ln(N/N₀) = -kt, or -ln(N/N₀) = kt.
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(C) N = N₀ kt²: Incorrect. This resembles second-order kinetics or unrelated physics; lacks exponential decay.
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(D) N – N₀ = kt: Incorrect. This is zero-order (constant rate), not proportional to N.
In sterilization processes for bioprocessing and microbiology, first order kinetics cell death describes how viable cells (N) decline from initial count (N₀) over time (t) at death rate constant (k). This model, vital for CSIR NET Life Sciences, ensures microbial safety in fermenters via exponential decay: N = N₀ e^{-kt}.
Key Equation Derivation
The rate law -dN/dt = kN integrates to ln(N/N₀) = -kt or -ln(N/N₀) = kt, plotting linearly as log(N/N₀) vs t. Del factor (∇ = ln(N₀/N)) quantifies sterility, e.g., ∇=12 for 10^{-3} risk from 10^9 cells/cm³.
MCQ Solution Breakdown
For the query: N and N₀ are viable cells at t and t=0 in first order kinetics cell death sterilization. Correct: (A) wrong (growth form); (B) right (-ln(N/N₀)=kt); (C)/(D) wrong (not first-order).
| Option | Equation | Kinetics Type | Correct? |
|---|---|---|---|
| (A) | N = N₀ e^{kt} | Growth (wrong sign) | No |
| (B) | -ln(N/N₀) = kt | First-order log form | Yes |
| (C) | N = N₀ k t² | Quadratic (unrelated) | No |
| (D) | N – N₀ = k t | Zero-order | No |
CSIR NET Applications
Use for batch sterilization: calculate t for target N from k (species/temperature-dependent via Arrhenius). Practice plots confirm straight line on semi-log scale.
