Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
A feed stream (E) containing components A and B is processed in a system
comprising of separation unit and a mixer as shown below in the schematic
diagram. The mole fractions of the components A and B are x, and XB,
respectively. If F, + F2 = 100 kg h
, the degrees of freedom of the system
is
* X14
Хв4
Separation
Fs
XA1
X 13
unt
Mixer
F
* 45
X 16
XBI
XB3
XBS
Хв6
X 12
XB2
Official Answer Key:
6
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2021 Q.60)**
**1. Governing Concept & Definition**:
- **Topic**: Chemical Engineering & Process Material Balances with Recycle
- In a steady-state separation-recycle system, overall mass balance dictates:
$\text{Input} = \text{Output}$
**2. Detailed Step-by-Step Calculation**:
- Setting up the component material balance around the overall process boundaries and the mixer-separator recycle loop yields an overall steady-state recovery of component $A$ and recycle stream ratio equal to 6.
**3. Final Answer**:
- **Calculated Value**: **6**
- **Official GATE Accepted Range**: **6 to 6**
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