While I’m sure these statements each convey a valid point, they are both incorrect from a technical point. They are using invalid units for the physical quantities being discussed.

For example, suppose I told you that it’s 90 minutes between where I live and Albany, N.Y. I’m using a unit of time to describe a distance. It might take 90 minutes at an average speed of 60 mph to drive the distance of 90 miles from my house to Albany. However, it also might take 98 minutes if I average 55 mph, or 77 minutes if I average 70 mph. The speed I drive doesn’t change the distance.

So, if someone wants to know how far it is from my house to Albany, a valid answer would be expressed in units of distance (e.g., 90 miles). For that matter, it would be technically valid to tell someone it’s about 475,200 feet or even about 14,484,096 centimeters from my house to Albany. Granted, very few people would have any feel for that distance when expressed in either of these units but, nevertheless, both units are valid for describing distance.

Terminologist

Back in the 1970s, I had a physics professor who was as methodical as a computer and not the least bit tolerant of improper usage of physics terminology. He revered the precise mathematic definitions used to define physical quantities. He was very careful in using words that, at times, could only convey partial meaning to physical quantities such as velocity, acceleration, frequency, weight, and temperature.

The precision he used made a deep impression on me. It also clarified these concepts in my mind and removed the apprehension that most Americans seem to have over almost anything associated with physics.

He burned this respect for proper terminology and units into my brain. So much so that I can still remember his lectures from 38 years ago.

Two of the most important principles in physics are energy and power. They also are two of the most widely used (and misused) concepts in the HVAC industry.

Most physics textbooks define energy as the ability to do work. At first, this sounds like a pretty loose definition. After all, following a good night’s rest, and hearty breakfast, most of us think we have the ability to do work. The key is in that last word — work. In physics, work is mathematically defined as the multiplication of a force times the distance over which the force acts.

For example, if you lifted a 20 pound weight 3 feet above where it was resting, you would have imparted 3 feet x 20 pounds equaling 60 foot-pounds of mechanical energy to that object. Thus, a foot-pound is a unit of energy (albeit a fairly small amount). As such, it can be converted to any other unit of energy. For example, 778.2 foot-pounds equals 1 Btu.

The foot-pound unit is most commonly associated with mechanical energy, whereas the unit Btu is usually associated with thermal energy. However, mechanical energy can be converted to an equivalent amount of thermal energy. It’s like comparing the unit of mile, commonly used to express distances that we drive or bike, to nanometers, a unit of distance often used to describe the width of conductor paths in microprocessors. Both are units of distance and each happens to be more commonly used for certain types of distance measurements.

In hydronics, the unit of foot-pounds is concealed in the definition of “head.” We commonly state the head produced by a circulator in units of feet. This comes from the ratio explained in Formula 1.

Since the unit of pound appears in the top and bottom of the fraction in Formula 1, it mathematically cancels out, and we can just state pump head in units of feet. However, I still contend that the best understanding of head comes when it’s thought of as the number of foot-pounds of mechanical energy added to each pound of fluid that passes through the circulator.

Defining Power

In physics, power is defined as the instantaneous rate of energy transfer. Although the word “energy” is in the definition of power, the word “rate” makes the concept of power as different from energy as speed is from distance.

In the HVAC trade we are usually concerned with rates of energy flow, rather than a quantity of energy. The thermal output of a boiler is a rate. So is the output from a heat emitter and the heat loss of a building. Some of the most common units for power in our trade are: Btuh, watt, and kilowatt.

In North America, the units of watt and kilowatt are most often associated with electrical power. However, they are just as valid for describing the rate of heat output from a boiler and are commonly used for such in Europe. Thus, a European installer asking his wholesaler for a 21-kWh gas-fired boiler is just as common as a U.S. installer asking his supplier for a 72,000-Btuh boiler. Just have a look at the thermal ratings of boilers, heat pumps, or heat emitters shown on the websites of European manufacturers. North America is about the only place that lists thermal ratings in units of Btuh.

The conversion factor between kW and Btuh is used so commonly that it’s worth memorizing:

1 kW = 3,413 Btuh

Different but Related

The relationship between energy and power is pretty simple:

Energy = Power x Time

It’s analogous to the relationship:

Distance = Speed x Time

Distance and speed are related, but they’re not the same thing. Same philosophy applies to energy and power.

If a device supplies power at 1 kW and maintains that power for one hour, it will have supplied:

Energy = 1 kW x 1 hour = 1 kWh

If a heat emitter dissipated heat at a rate of 250 W for three hours, it will have supplied the following amount of energy to the room:

Energy = 250 W x three hours =

750 watt-hours = 0.75 kWh.

Thus, a kWh is a unit of energy and, as such, can be converted to any other unit of energy. For example, 1 kWh = 3,413 Btu.

The vast majority of us buy electrical energy from a utility and we are charged based on the number of kWh of energy we have used in that billing period. For example, see Figure 1, thus, the term “power bill” is not correct. It’s an energy bill we receive.

Figure It Out

Recognizing the relationship between units and the physical quantities they represent can be helpful. For example, take a look at Figure 2. I took this photo in the mechanical room of a hotel in Cologne, Germany. This device was connected to a pipe and had an odometer-like totalizer that gave a reading in MWh. It also had a scale indicating “Temp Diff,” or temperature differential, in °C. Inside the glass cover was an assortment of springs, gears, shafts, and linkages that would make a clockmaker proud. So what do you think it is?

Well, it gives a readout of MWh, which is a large unit of energy, so it must be an energy meter. The connection to the pipe measured flow rate and the multiplication of flow rate x temperature differential is directly proportional to energy.

The system’s caretaker confirmed my suspicion. He told me that this thermal energy meter has been in place and operational since the 1960s. No wires, no batteries, no microprocessors, just an elegant mechanical integrator mechanism. Someday, I hope that energy meter will be displayed in a heating museum.

Act Like a Professional

Over the years, I’ve seen technical publications, product literature, and advertisements that have described energy, or energy savings, using terms such as kW or kWh. The former is a unit of power and the latter is undefined. Sadly, few Americans would recognize these errors or even care. You know, “potAto, potOto,” whatever ...

But caring about details, even when it’s a seemingly small difference, is what makes a professional different from the average Joe Wrenchturner. So be a pro. Use the right terminology and the right units when dealing with energy or power. I’ll appreciate it, as would my old physics professor.

Publication date: 7/8/2013 

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