Question

Calculate the regeneration efficiency if the milk is heated from an initial temperature of 4\(^\circ\)C to 67\(^\circ\)C in a regenerator and pasteurization was done at 74\(^\circ\)C.

• A. 80%
• B. 75%
• C. 90%
• D. 85%

Hint:

To quickly find regeneration efficiency, use the ratio of the achieved temperature rise to the total required temperature rise:
\[ \frac{\text{achieved rise}}{\text{total rise}} = \frac{63}{70} = \frac{9}{10} = 90\% \]

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Regeneration is a heat recovery process used in pasteurizers (specifically High-Temperature Short-Time or HTST plate heat exchangers).
Cold raw milk entering the pasteurized section is preheated by hot pasteurized milk flowing in the opposite direction.
This saves significant heating and cooling energy.
Key Formula or Approach:
The regeneration efficiency (\(\eta_{\text{reg}}\)) is defined as the ratio of the temperature increase achieved by regeneration to the total temperature increase required for pasteurization:
\[ \eta_{\text{reg}} = \frac{T_{\text{reg}} - T_{\text{initial}}}{T_{\text{past}} - T_{\text{initial}}} \times 100 \]
Where:
- \(T_{\text{initial}}\) is the inlet temperature of the cold raw milk.
- \(T_{\text{reg}}\) is the temperature of the milk after passing through the regenerator section.
- \(T_{\text{past}}\) is the final pasteurization temperature of the milk.

Step 2: Detailed Explanation:
Let us identify the given values:
- Initial temperature of raw milk, \(T_{\text{initial}} = 4\ ^\circ\text{C}\)
- Temperature after regeneration, \(T_{\text{reg}} = 67\ ^\circ\text{C}\)
- Pasteurization temperature, \(T_{\text{past}} = 74\ ^\circ\text{C}\)
Now, calculate the temperature increase achieved through regeneration:
\[ \Delta T_{\text{achieved}} = 67\ ^\circ\text{C} - 4\ ^\circ\text{C} = 63\ ^\circ\text{C} \]
Calculate the total temperature increase required for pasteurization:
\[ \Delta T_{\text{total}} = 74\ ^\circ\text{C} - 4\ ^\circ\text{C} = 70\ ^\circ\text{C} \]
Now, calculate the regeneration efficiency:
\[ \eta_{\text{reg}} = \frac{63\ ^\circ\text{C}}{70\ ^\circ\text{C}} \times 100 \]
\[ \eta_{\text{reg}} = 0.9 \times 100 = 90\% \]

Step 3: Final Answer:
The regeneration efficiency of the system is 90%. Hence, the correct option is (C).