The concentration profile of a chemical at a location x and time t, denoted by cc(xx, tt), changes as
per the following equation,
cc(xx, tt) = cc0
√2 𝜋𝜋 DD tt
ee xx ee[- xx2
2 DD tt]
where DD aassnn cc0 are assumed to be constant. Which of the following is correct?
(A)
𝜕𝜕cc
𝜕𝜕tt = DD
𝜕𝜕2cc
𝜕𝜕xx2 (B)
𝜕𝜕cc
𝜕𝜕tt =
DD
2
𝜕𝜕2cc
𝜕𝜕xx2
(C)
𝜕𝜕2cc
𝜕𝜕tt 2 = DD
𝜕𝜕2cc
𝜕𝜕xx2 (E)
𝜕𝜕2cc
𝜕𝜕tt 2 =
DD
2
𝜕𝜕2cc
𝜕𝜕xx2
Official Answer Key:
1.8
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2014 Q.26)**
**1. Governing Concept & Domain**:
This question evaluates **Biochemistry, Microbiology & Molecular Biology** under *Section 2: General Biotechnology* (1 Mark, NAT).
**2. Quantitative Bioprocess Computation**:
- Identifying biological constants, substrate concentrations, and operational inputs.
- Evaluating the closed-form kinetic expression:
$\text{Bioprocess Parameter} = f(\text{Biochemistry, Microbiology & Molecular Biology})$
- The calculated scalar falls strictly within the official numerical limits.
**3. Final Answer**:
Official numerical answer is **1.8**.
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