Understanding One Ton of Refrigeration

The term "ton of refrigeration" is a unit of power used primarily to describe the heat extraction rate of refrigeration and air conditioning systems. It is based on the rate at which heat must be removed to melt one short ton (2,000 pounds) of ice in 24 hours.

Historically, this unit was defined based on the latent heat of fusion of ice. The latent heat of fusion of ice is approximately 334 kilojoules per kilogram (kJ/kg).

Let's calculate the energy involved in melting one short ton of ice:

• One short ton is equal to 2,000 pounds.
• To convert pounds to kilograms, we use the conversion factor: 1 pound \(\approx\) 0.453592 kg.
• So, 1 short ton \(\approx\) 2000 pounds \(\times\) 0.453592 kg/pound \(\approx\) 907.184 kg.
• The total heat required to melt this amount of ice is the mass multiplied by the latent heat of fusion: \(907.184 \text{ kg} \times 334 \text{ kJ/kg} \approx 302900 \text{ kJ}\).

This amount of heat removal happens over a period of 24 hours.

To find the rate in kilojoules per minute (kJ/min), we need to divide the total heat by the total time in minutes:

• Time in minutes = 24 hours \(\times\) 60 minutes/hour = 1440 minutes.
• Rate of heat removal = \(\frac{\text{Total Heat}}{\text{Total Time}} = \frac{302900 \text{ kJ}}{1440 \text{ min}}\).
• Calculating this value: \(\frac{302900}{1440} \text{ kJ/min} \approx 210.35 \text{ kJ/min}\).

The standard value for one ton of refrigeration is commonly rounded and defined as 210 kJ/min.

Comparing this calculated value to the given options:

• Option 1: 2100 KJ/min
• Option 2: 105 KJ/min
• Option 3: 210 KJ/min
• Option 4: 21 KJ/min

The calculated value of approximately 210 kJ/min matches Option 3.

Therefore, one ton of refrigeration is equal to 210 KJ/min.