Tons of Refrigeration (RT) to Foot-pounds per second (ft-lb/s) conversion

What is the Ton of Refrigeration?

The ton of refrigeration (RT) is a unit of power that measures the rate of heat removal in cooling and air-conditioning systems. It is widely used in the HVAC industry to rate chillers, air conditioners, and industrial refrigeration equipment.

Definition

One ton of refrigeration is the rate of heat transfer needed to freeze 2,000 pounds (one short ton) of water at 0 °C into ice at 0 °C over 24 hours. Using the latent heat of fusion of water, this equals exactly 12,000 Btu/h, which is:

$$1\ \text{RT} = 3516.85\ \text{W}$$

Equivalently, $1\ \text{RT} = 12{,}000\ \text{Btu/h} = 3.51685\ \text{kW}$. It is a power (heat-flow) unit, not a unit of mass or energy; the NIST Guide to the SI (SP 811) lists the ton of refrigeration (12 000 Btu(IT)/h) as 3.516 853 × 10³ W.

Origin and History

The unit dates to the 19th century, when mechanical refrigeration competed directly with the natural-ice trade. Cooling capacity was rated by how much ice a machine could effectively replace, so one "ton" of refrigeration described equipment capable of melting one ton of ice per day. The measure stuck even as ice harvesting disappeared.

Law and Notable Facts

The ton of refrigeration is not an SI unit; the SI unit of power is the watt. It remains an industry standard in North America, where residential air conditioners are commonly sized in tons (for example, a "3-ton" central AC unit). Note that the "ton" here refers to heat-removal rate, not the weight of the equipment. A closely related metric variant, the frigorie-based commercial ton, is defined slightly differently in some regions, but the U.S. value of exactly 12,000 Btu/h is the most common.

Real-World Examples and Conversions

• A typical residential central air conditioner rated at 3 RT removes about 36,000 Btu/h, or roughly 10,551 W of heat.
• A single ton of refrigeration (3516.85 W) is comparable to the cooling output of a large window AC unit sized for a big room.
• Large commercial chillers are often rated in the hundreds or thousands of tons; a 500 RT chiller handles about 1.758 MW of heat load.
• To convert tons to kilowatts of cooling, multiply by 3.51685: a 2 RT mini-split delivers about 7.03 kW of cooling.

What is the foot-pound per second?

Foot-pounds per second is a unit of power, commonly used in mechanical engineering and physics, especially in the United States. It represents the amount of work done (in foot-pounds) per unit of time (in seconds). Let's break it down.

Definition of Foot-Pounds per Second

Foot-pounds per second (ft⋅lb/s) is a unit of power that expresses the rate at which work is performed. One foot-pound is the amount of energy required to raise a one-pound object a distance of one foot against gravity. Therefore, foot-pounds per second tell you how quickly that work is being done.

Understanding the Components

• Foot-pound (ft⋅lb): This is a unit of energy or work. It's calculated as the force in pounds multiplied by the distance in feet.

  $$\text{Work (ft⋅lb)} = \text{Force (lb)} \times \text{Distance (ft)}$$

• Second (s): This is the unit of time.

Combining these gives you:

$$\text{Power (ft⋅lb/s)} = \frac{\text{Work (ft⋅lb)}}{\text{Time (s)}}$$

Conversion to Other Units

Foot-pounds per second can be converted to other common units of power:

• Watts (W): The standard SI unit of power.

  $$1 \text{ ft⋅lb/s} \approx 1.35582 \text{ W}$$

• Horsepower (hp): A common unit of power, especially for engines.

  $$1 \text{ hp} = 550 \text{ ft⋅lb/s}$$

  Therefore:

  $$1 \text{ ft⋅lb/s} \approx 0.001818 \text{ hp}$$

Historical Context

While there isn't a specific "law" tied directly to foot-pounds per second, the concept of power and its measurement is closely related to the work of James Watt. He improved the steam engine, and horsepower was originally defined to compare the power of steam engines to that of horses. While horsepower is more commonly associated with Watt, foot-pounds per second provides a more granular and fundamental way to express power.

Real-World Examples

• Lifting Objects: A motor lifting a 100-pound object 5 feet in 2 seconds is doing work at a rate of:

  $$\text{Power} = \frac{100 \text{ lb} \times 5 \text{ ft}}{2 \text{ s}} = 250 \text{ ft⋅lb/s}$$

• Pumping Water: A pump lifting water 20 feet at a rate of 10 pounds per second is performing work at a rate of:

  $$\text{Power} = 10 \text{ lb/s} \times 20 \text{ ft} = 200 \text{ ft⋅lb/s}$$

• Small Electric Motors: Many small electric motors are rated in terms of horsepower or watts, but you can convert those ratings to foot-pounds per second to understand the rate at which they can perform work. For example, a motor rated at 1/4 horsepower is approximately 137.5 ft⋅lb/s.

Importance

Foot-pounds per second are valuable for calculating the rate at which machines perform work, enabling engineers to design and analyze mechanical systems. Understanding this unit provides a fundamental grasp of power and its relationship to work and time.