Energy and Power

Most of you reading this column consider yourselves heating professionals. As such, you deal with units such as Btu/hr., kilowatts, therms and tons on a daily basis. For the most part, you use valid units to describe physical quantities. For example, you know that flow rate is measured in gallons per minute (gpm) and not gallons. You also know that temperature is expressed in ºF or ºC and not in therms.

But when it comes to the difference between energy and power, our industry tends to get sloppy with its terminology. For example, we might tell a potential customer how a new geothermal heat pump could reduce his “power bill.” We also might describe the choice between two boilers as the 75,000 Btu model vs. a 100,000 Btu model.

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 miles per hour 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 have units of distance (e.g., 90 miles). For that matter, it would be technically valid to tell someone it’s about 475,200 ft. or even about 14,484,096 cm. 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 convey only 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-lb. weight 3 ft. above where it was resting, you would have imparted 3 ft. x 20 lb. = 60 ft•lb of mechanical energy to that object. Thus, a ft•lb (pronounced 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 ft•lb = 1 Btu

The unit of ft•lb is most commonly associated with mechanical energy, whereas the 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 nanometer, 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 ft•lb is concealed in the definition of “head.” We commonly state the head produced by a circulator in units of feet. This comes from the following ratio: (see Formula 2).

Since the unit of pound appears in the top and bottom of the fraction, 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 ft•lb of mechanical energy added to each pound of fluid that passes through the circulator.

Powerful Thoughts

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 Btu/hr., 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 kW gas-fired boiler is just as common as a U.S. installer asking his supplier for a 72,000 Btu/hr. 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 Btu/hr.

The conversion factor between kilowatts and Btu/hr. is used so commonly that it’s worth memorizing:

1 kW = 3,413 Btu/hr.

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 for energy and power.

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

Energy = 1 kW x 1 hr. = 1 kWhr

The unit kWhr is sometimes abbreviated as kWh, as seen in Figure 1.

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

Energy = 250 w x 3 hr = 750 whr = 0.75 kWhr

Thus, a kWhr is a unit of energy and, as such, can be converted to any other unit of energy.

The vast majority of us buy electrical energy from a utility and we are charged based on the number of kWhr of energy we have used in that billing period (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 (e.g., Megawatt•hours). It also had a scale indicating “Temp Diff” (e.g., temperature differential) in ºC. 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 (megawatt•hours), 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 times 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.

Be a Pro

Over the years I’ve seen technical publications, product literature and advertisements that have described energy, or energy savings, using terms such as kilowatts or kilowatts per hour. 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 and use the right terminology and the right units when dealing with energy or power. I’ll appreciate it and so would my old physics professor.