Consider the ordinary differential equation 2 2( , ) 2dy f x y x ydx .
If (1) 1y , the value(s) of (1.5)y , using the Euler's implicit method
[yାଵ = y + ℎf(xାଵ, yାଵ)] with a step size of h = 0.5, is (are)
Options:
(A) Effectiveness factor is ratio of the reaction rate with diffusion-limitation to the
reaction rate without diffusion-limitation
(B) Internal diffusion is rate-limiting at low values of Thiele modulus
(C) Effectiveness factor increases with decrease in Thiele modulus
(D) Internal diffusion-limitation can be reduced by decreasing the size of the
particle
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2022 Q.47)**
**1. Governing Concept & Domain**:
This question evaluates **Engineering Mathematics** under *Section 1: Engineering Mathematics* (2 Marks, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Engineering Mathematics.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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