## Introduction

I get some strange phone calls. I recently received one from a customer who wanted to know how many “tons of air conditioning” he needed to cool some equipment he had purchased from my company. After I assisted this customer with his problem, he asked me if I knew where this strange unit came from. Here is the story I told him.

## Background

This unit of air conditioning is a real fossil. It goes back to the first days of the air conditioning/refrigeration industry. The ton came into use by the refrigeration industry because early refrigerators were used to make ice. The ton represents the amount of cooling capacity needed to make 1 ton of ice per day. In the US, home air conditioners are usually rated in BTUs/hour, and commercial refrigeration units are usually rated in terms of tons of ice frozen per day.

The temperature of liquid water reduces by roughly 1 °C for every calorie per gram. When liquid water is at 0 °C and you continue to extract heat, water begins to undergo a phase transition from liquid to ice. The energy required to make this transition is referred to as heat of fusion (symbol ΔH°m). The heat of fusion for water is 79.72 cal/g.

We can compute the energy required for one ton of water to transition from liquid to ice as shown in Equation 1.

 Eq. 1 $E=\left( \frac{1\text{ ton}}{\text{day}} \right)\cdot \left( \frac{2000\text{ lb}}{1\text{ ton}} \right)\cdot \left( \frac{1000\text{ g}}{2.20\text{ lb}} \right)\cdot \left( \frac{79.72\text{ cal}}{\text{g}} \right)=3.03\text{E8 }\frac{\text{J}}{\text{day}}\text{ = 287000 }\frac{\text{BTU}}{\text{day}}$

We usually say that 12000 BTUs per hour equals on 1 ton of refrigeration per day. Equation 2 illustrates this calculation.

 Eq. 2 $\frac{1\text{ ton}}{\text{day}}\text{=287000}\frac{\text{BTU}}{\text{day}}\cdot \frac{1\text{ day}}{24\text{ hour}}=11958\frac{\text{BTU}}{\text{hr}}$

## Conclusion

I must admit that I find the units of measure used in the US confusing. I wish things were different, but I am a realist. All I can do is try to shed some light on the subject.