Understanding Ton of Refrigeration and Horsepower

The question asks us to convert a cooling capacity unit, the Ton of Refrigeration (TR), into a power unit, metric horsepower (HP). This type of conversion is common in HVAC (Heating, Ventilation, and Air Conditioning) and mechanical engineering to relate cooling effect to the power required to achieve it.

What is a Ton of Refrigeration (TR)?

A Ton of Refrigeration is a unit of power used to describe the heat removal rate of refrigeration and air conditioning systems. Historically, it was defined as the rate of heat removal required to freeze one short ton (2000 pounds) of water at 0°C (32°F) into ice at 0°C over a 24-hour period.

• The commonly accepted value for 1 Ton of Refrigeration is equivalent to 12,000 BTU per hour (BTU/hr).
• It can also be expressed in Watts: \(1 \text{ TR} \approx 3517.15 \text{ Watts (W)}\).

What is Metric Horsepower (HP)?

Horsepower is a unit of power, commonly used to measure the output of engines or the power required to drive machinery. There are several definitions of horsepower, but the question specifically asks for metric horsepower.

• Metric horsepower (often abbreviated as PS, hp(M), or cv) is defined as 75 kilogram-force metres per second.
• In terms of Watts, \(1 \text{ metric HP} \approx 735.49875 \text{ Watts (W)}\).

Converting 2 Ton Refrigeration to Metric Horsepower

To convert from Ton of Refrigeration to metric horsepower, we can use Watts as an intermediate unit.

We know the following conversion factors:

• \(1 \text{ TR} \approx 3517.15 \text{ W}\)
• \(1 \text{ metric HP} \approx 735.49875 \text{ W}\)

From the second factor, we can determine how many metric horsepower are in one Watt:

\(1 \text{ W} \approx \frac{1}{735.49875} \text{ metric HP}\)

Now, we can convert 1 TR to metric HP:

\(1 \text{ TR} \approx 3517.15 \text{ W} \times \frac{1}{735.49875} \frac{\text{metric HP}}{\text{W}}\)

Calculating the value:

\(1 \text{ TR} \approx \frac{3517.15}{735.49875} \text{ metric HP}\)

\(1 \text{ TR} \approx 4.7818 \text{ metric HP}\) (approximately)

The question asks for the conversion of 2 Ton Refrigeration to metric horsepower. So, we multiply the value for 1 TR by 2:

\(2 \text{ TR} = 2 \times (1 \text{ TR})\)

\(2 \text{ TR} \approx 2 \times 4.7818 \text{ metric HP}\)

\(2 \text{ TR} \approx 9.5636 \text{ metric HP}\)

Comparing this calculated value to the given options:

• Option 1: 9.56
• Option 2: 7.46
• Option 3: 8.97
• Option 4: 6.47

The calculated value of approximately 9.5636 metric HP is very close to Option 1 (9.56).

Calculation Summary

Here’s a summary of the conversion process:

Conversion steps:

1. Convert TR to Watts: \(2 \text{ TR} = 2 \times 3517.15 \text{ W} = 7034.3 \text{ W}\)
2. Convert Watts to Metric HP: \(7034.3 \text{ W} \times \frac{1 \text{ metric HP}}{735.49875 \text{ W}}\)
3. Calculate: \(\frac{7034.3}{735.49875} \approx 9.564 \text{ metric HP}\)

Rounding to two decimal places, this is 9.56 metric HP.

Revision Table: Refrigeration and Power Units

Additional Information: Why Convert TR to HP?

Understanding the conversion between Ton of Refrigeration and Horsepower is useful in HVAC and related fields for several reasons:

• System Sizing: Engineers need to determine the power input required to achieve a certain cooling capacity. Converting TR to HP helps specify the motor size for compressors.
• Energy Efficiency: By comparing the cooling output (TR) to the power input (HP or kW), one can assess the efficiency of a refrigeration system (often expressed as EER or COP).
• Comparative Analysis: Different components or systems might be rated in different units, requiring conversion for direct comparison.

It's important to note whether 'horsepower' refers to metric horsepower (~735.5 W) or mechanical/imperial horsepower (~745.7 W), as this affects the conversion value.