Which combination of the following statements is CORRECT for cyanobacteria?
P. They can perform oxygenic photosynthesis
Q. Usually filamentous forms are involved in nitrogen fixation
R. Nitrogen fixation occurs in heterocysts
S. They cannot grow in a mineral medium exposed to light and air
(A) P, Q and R (B) P, S and R (C) Q, R and S (D) P, Q and S
Options:
(A) P, Q and R
(B) P, S and R
(C) Q, R and S
(D) P, Q and S
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.26)**
**1. Governing Concept & Question Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (1 Mark)
- **Topic**: Bioprocess Engineering / Transport Phenomena (Dimensionless Numbers: Prandtl Number)
**2. Detailed Step-by-Step Derivation**:
- In heat and momentum transport phenomena, the **Prandtl number ($Pr$)** is a fundamental dimensionless number named after Ludwig Prandtl.
- It is mathematically defined as the ratio of **momentum diffusivity** (kinematic viscosity, $\nu$) to **thermal diffusivity** ($\alpha$):
$Pr = \frac{\nu}{\alpha} = \frac{\mu / \rho}{k / (\rho C_p)} = \frac{C_p \mu}{k}$
where:
- $\nu = \frac{\mu}{\rho}$ is the momentum diffusivity ($\text{m}^2/\text{s}$).
- $\alpha = \frac{k}{\rho C_p}$ is the thermal diffusivity ($\text{m}^2/\text{s}$).
- $\mu$ is dynamic viscosity, $\rho$ is density, $C_p$ is specific heat capacity, and $k$ is thermal conductivity.
- The Prandtl number compares the relative thickness of the hydrodynamic (momentum) boundary layer to the thermal boundary layer.
- Therefore, $Pr$ is explicitly the **ratio of momentum diffusivity to thermal diffusivity**.
- **Option-by-Option Evaluation**:
- **Option (A) [INCORRECT]**: Thermal diffusivity to momentum diffusivity is the inverse, $1/Pr$.
- **Option (B) [INCORRECT]**: Kinematic viscosity to mass diffusivity is the Schmidt number ($Sc = \nu / D$).
- **Option (C) [CORRECT]**: Prandtl number is the ratio of momentum diffusivity to thermal diffusivity ($Pr = \nu / \alpha$).
- **Option (D) [INCORRECT]**: Thermal diffusivity to mass diffusivity is the Lewis number ($Le = \alpha / D$).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **C**
- **Scoring Criteria**: +1.0 Mark (Negative marking: -0.33 marks).
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