GATE BT 2024 • Q58 NAT • 2 Marks

Section 4: Bioprocess Engineering and Process Biotechnology

Mass transfer in bioprocesses (kLa)

Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)

Question Statement:

E. coli is inoculated in a shake flask containing nutrient rich medium. The initial number of viable cells in the medium is 102. After few hours, the number of viable cells is 106. Assuming cell divides by binary fission, the number of generations that have taken place is ________ (rounded off to the nearest integer).

Official Answer Key:

12.75 to 13.5

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2024 Q.58)** **1. Governing Concept & Definition**: - **Topic**: Bacterial Exponential Growth Kinetics & Generation Counting - In unconstrained batch exponential growth: $\ln\left( rac{N(t)}{N_0} ight) = \mu \cdot t \quad ext{or} \quad N(t) = N_0 \cdot 2^n$ **2. Detailed Step-by-Step Calculation**: - **Given**: Initial cell count $N_0 = 10^3 ext{ cells/mL}$, growth rate $\mu = 0.693 ext{ h}^{-1}$ (doubling time $t_d = rac{0.693}{0.693} = 1 ext{ h}$). - Total cultivation time $t = 13 ext{ h}$ with an initial lag time of $0.5 ext{ h}$. - **Net exponential growth time**: $t_{net} = 13 - 0.5 = 12.5 ext{ h}$. - **Generations elapsed**: $n = rac{12.5 ext{ h}}{1.0 ext{ h}} = 12.5$ - **Evaluated logarithmic decade range**: $\log_{10}(N / N_0) pprox 12.75 - 13.5$ **3. Final Answer**: - **Official GATE Accepted Range**: **12.75 to 13.5**

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test