Question

For the same temperature difference between first and last effect of multiple effect evaporator, the possibility of greater number of effects could be achieved by

• A. Shorter size calandria
• B. Taller size calandria
• C. Increased steam pressure
• D. Increased vacuum

Hint:

Evaporator Design Optimization: To fit a GREATER NUMBER OF EFFECTS without burning milk in effect 1, apply INCREASED VACUUM to depress the final effect boiling temperature ($40^\circ\text{C}$).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Multiple effect evaporator operating span thermodynamics: total available temperature driving force ($\sum \Delta T = T_{ ext{steam, 1st effect}} - T_{ ext{boiling, last effect}}$) is maximized by increasing vacuum in the final condenser, which depresses the last-effect boiling temperature to allow more individual thermal stages ($\Delta T = \sum \Delta T / N$).
Key Formula or Approach:
\[ \sum \Delta T_{\text{available}} = T_{\text{steam}} - \mathbf{T_{\text{last effect}} (\downarrow \text{ with Increased Vacuum})} \implies \mathbf{Number \text{ } of \text{ } Effects \text{ } (N) \uparrow} \]

Step 2: Detailed Explanation:
In multiple effect evaporator thermodynamics:
- In a multiple effect evaporator of $N$ effects, each effect requires a minimum temperature driving force (typically $\Delta T_i \ge 3^\circ - 5^\circ ext{C}$) to drive boiling heat transfer.
- The total available temperature driving span across the system is:
\[ \sum \Delta T = T_{\text{steam supply to 1st effect}} - T_{\text{boiling in final effect}} \]
1. The maximum permissible temperature in the first effect is strictly limited to $70^\circ - 75^\circ ext{C}$ to prevent whey protein thermal denaturation and burn-on fouling.
2. Therefore, to expand the total temperature span and accommodate a greater number of effects ($N$), the operating boiling temperature of the final effect must be pushed as low as possible ($40^\circ - 45^\circ ext{C}$).
3. This is achieved by Increasing the Vacuum (D) (deeper vacuum $\approx 85 - 90\text{ kPa}$) in the surface/barometric condenser.

Step 3: Final Answer:
Hence, greater number of effects is achieved by Increased vacuum, matching option (D).