Question

One ton of refrigeration is equal to

• A. 50 kcal/minute
• B. 50 kcal/h
• C. 50 kcal/s
• D. 50 cal/minute

Hint:

Equivalences for 1 TR:
$1\text{ TR} = 50\text{ kcal/min} = 3000\text{ kcal/h} = 3.517\text{ kW} = 210\text{ kJ/min} = 12,000\text{ BTU/h}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
One Ton of Refrigeration (1 TR) is the rate of heat extraction required to freeze 1 short ton (2000 lb or 907.18 kg) of pure water at \(0^\circ\text{C}\) into ice at \(0^\circ\text{C}\) in 24 hours.
Key Formula or Approach:
\[ 1\text{ TR} = \frac{1000\text{ kg} \times 80\text{ kcal/kg}}{24\text{ h}} = \frac{80,000\text{ kcal}}{24 \times 60\text{ min}} \approx 50\text{ kcal/minute} \]

Step 2: Detailed Explanation:
Using standard metric refrigeration units:
Latent heat of fusion of ice \(\approx 80\text{ kcal/kg}\) (or \(334.9\text{ kJ/kg}\)).
For 1 metric ton (1000 kg) in 24 hours:
\[ \text{Cooling Capacity} = \frac{1000\text{ kg} \times 80\text{ kcal/kg}}{24\text{ hours}} = 3333.33\text{ kcal/h} \]
In standard American engineering units (2000 lb ton, latent heat = 144 BTU/lb):
\[ 1\text{ TR} = 12,000\text{ BTU/h} = 3024\text{ kcal/h} \]
Converting to kcal per minute:
\[ 1\text{ TR} = \frac{3000\text{ kcal/h}}{60\text{ minutes}} = 50\text{ kcal/minute} \]
In SI units: \(1\text{ TR} = 3.5168\text{ kW} = 211\text{ kJ/min}\).

Step 3: Final Answer:
Thus, one ton of refrigeration equals 50 kcal/minute, matching option (A).