Question

One ton of litchi was cooled from 35$^\circ$C to 5$^\circ$C using a 5 ton refrigeration system in 3 hours. The amount of heat removed by the refrigeration system will be (given specific heat of litchi = 0.5 kcal/kg.$^\circ$C)

• A. 15000 kcal
• B. 30000 kcal
• C. 15 kcal
• D. 3000 kcal

Hint:

Always read the unit requirements of the final answer.
Since the options are in kilocalories (kcal) and the specific heat is provided in \( \text{kcal/kg}\cdot^\circ\text{C} \), you can perform the calculation directly without converting units to Joules.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Sensible heat transfer is the energy exchanged by a body that results in a temperature change without any change in phase.
The total amount of thermal energy removed during a cooling process depends on the mass of the commodity, its specific heat capacity, and the temperature difference.
Key Formula or Approach:
The formula for the total sensible heat removed (\( Q \)) is:
\[ Q = m \cdot C_p \cdot \Delta T \]
where:
- \( m \) is the mass of the commodity in kg.
- \( C_p \) is the specific heat capacity in \( \text{kcal/kg}\cdot^\circ\text{C} \).
- \( \Delta T \) is the change in temperature (\( T_{\text{initial}} - T_{\text{final}} \)) in \( ^\circ\text{C} \).

Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
1. Identify and extract the given values:
- Mass of litchi, \( m = 1 \text{ ton} = 1000 \text{ kg} \).
- Initial temperature, \( T_1 = 35^\circ\text{C} \).
- Final temperature, \( T_2 = 5^\circ\text{C} \).
- Specific heat of litchi, \( C_p = 0.5 \text{ kcal/kg}\cdot^\circ\text{C} \).
- Note that the capacity of the refrigeration system (\( 5 \text{ tons} \)) and the time duration (\( 3 \text{ hours} \)) are given in the problem statement but are not required to find the total heat removed, as we only need the total energy quantity rather than the rate of heat transfer.
2. Calculate the temperature difference (\( \Delta T \)):
\[ \Delta T = T_1 - T_2 = 35^\circ\text{C} - 5^\circ\text{C} = 30^\circ\text{C} \]
3. Substitute the values into the sensible heat formula:
\[ Q = 1000 \text{ kg} \times 0.5 \text{ kcal/kg}\cdot^\circ\text{C} \times 30^\circ\text{C} \]
4. Simplify the expression:
\[ Q = 500 \times 30 = 15,000 \text{ kcal} \]
Therefore, the total amount of heat removed from the litchi during the cooling process is \( 15,000 \text{ kcal} \).

Step 3: Final Answer:
The total heat removed by the refrigeration system is 15000 kcal.