Question

One ton of refrigeration (TR) can be expressed as :

• A. 1 TR = 311 kJ/min = 5.5167 kW
• B. 1 TR = 111 kJ/min = 4.5167 kW
• C. 1 TR = 411 kJ/min = 2.5167 kW
• D. 1 TR = 211 kJ/min = 3.5167 kW

Hint:

Remember these standard conversion constants for 1 TR:
- Imperial units: \(200\ \text{Btu/min}\) or \(12000\ \text{Btu/hr}\).
- Metric units: \(50\ \text{kcal/min}\) or \(3000\ \text{kcal/hr}\).
- SI units: \(210\ \text{kJ/min}\) (or 211) or \(3.5167\ \text{kW}\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
One Ton of Refrigeration (TR) is a traditional unit of cooling capacity.
It is defined as the rate of heat transfer required to freeze one short ton (2000 lbs) of pure water at 0°C into ice at 0°C in exactly 24 hours.
Key Formula or Approach:
To convert 1 TR into standard metric units of energy and power:
- Latent heat of fusion of ice \(\approx 144\ \text{Btu/lb}\) (or \(333.55\ \text{kJ/kg}\)).
- Mass of 1 short ton \(= 2000\ \text{lbs}\) (or \(907.185\ \text{kg}\)).
- Time interval \(= 24\ \text{hours} = 1440\ \text{minutes} = 86400\ \text{seconds}\).

Step 2: Detailed Explanation:
Let us calculate the heat transfer rate in SI units:
- Total heat absorbed during the phase change:
\[ Q = m \times L_f \]
Using metric values:
\[ Q = 907.185\ \text{kg} \times 333.55\ \text{kJ/kg} \approx 302591\ \text{kJ} \]
- Rate of heat transfer per minute:
\[ \text{Rate}_{\text{min}} = \frac{302591\ \text{kJ}}{1440\ \text{min}} \approx 210.13\ \text{kJ/min} \]
Using engineering approximations, this is standardly rounded to 211 kJ/min (or 210 kJ/min).
- Rate of heat transfer per second (Power in kW):
\[ \text{Power} = \frac{302591\ \text{kJ}}{86400\ \text{s}} \approx 3.502\ \text{kW} \]
Using exact thermochemical values, 1 TR is internationally defined as:
\[ 1\ \text{TR} = 3.5167\ \text{kW} = 3.5167\ \text{kJ/s} \]
- Converting this exact kW value back to kJ/min:
\[ \text{Rate}_{\text{min}} = 3.5167\ \text{kJ/s} \times 60\ \text{s/min} \approx 211\ \text{kJ/min} \]
This matches Option (D) perfectly.

Step 3: Final Answer:
One ton of refrigeration (TR) is equivalent to 211 kJ/min or 3.5167 kW.