Energy & Power

Most HPAC readers deal with units such as Btu/hr, kilowatts, °C and many others 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 gallon per minute (gpm), and not gallons. You also know that temperature is expressed in °C or °F, and not in therms. However, when it comes to the difference between energy and power, our industry tends to get sloppy with its terminology. For example, some of us might tell a potential customer how a new geothermal heat pump system could reduce their “power bill.” We might also describe the choice between a couple of boilers as the 75 000 Btu model versus a 100 000 Btu model.

While I am sure that 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 “it is 5.5 hours between where I live and Toronto.”  I am using a unit of time to describe a distance. It might take 5.5 hours at an average speed of 60 miles per hour to drive the distance of 330 miles from my house to Toronto. However, it might also take six hours if I average 55 mph, or 4.7 hours if I average 70 mph (and manage not to get pulled over for speeding). The speed I drive does not change the distance. So, if someone wants to know how far it is from my house to Toronto, ON a valid answer would have units of distance (330 miles). For that matter, it would also be technically valid to tell someone it is about 1 742 400 feet, or even about 53 108 352 centimeters from my house to Toronto. 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 also 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 and removed the apprehension that many people seem to have over almost anything associated with physics.

Two of the most important principles in all of physics are energy and power. They are also 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 that 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, three feet 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 unit Btu is usually associated with thermal energy. However, mechanical energy can be converted to an equivalent amount of thermal energy. It is like comparing the unit of kilometer, which is 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 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:

ƒt•lb⁄lb=ƒt

Since the unit of lb 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 is thought of as the number of ft•lbs of mechanical energy added to each lb. 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, as 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 as such in Europe. Thus, a European installer asking his wholesaler for a 21 kW gas-fired boiler is just as common as an installer in North America asking their 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 on earth that lists thermal ratings in units of Btu/hr.

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

                  1 kW = 3413 Btu/hr

They are not the same thing. The relationship between energy and power is pretty simple:

                  Energy = power x time

It is analogous to the relationship: Distance = speed x time. Distance and speed are related, but they are not the same thing and the same applies to energy and power.

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

                  Energy = 1 kW x 1 hr = 1 kWhr

The unit kwhr is also sometimes abbreviated as kWh.

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

A kWhr is a unit of energy, and as such, can be converted to any other unit of energy. For example 1 kWhr = 3413 Btu

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. The term “power bill” is not correct. It is in fac
t an energy bill that 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 1. 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 °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 (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 also 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. 

BE A PRO

Over the years I have seen technical publications, product literature, advertisements and even materials issued by ASHRAE, that have described energy, or energy savings, using terms like kilowatts, or kilowatts per hour. The former is a unit of power and the latter is undefined. Sadly, few North Americans would recognize these errors, or even care.

But caring about details, even when it is 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 will appreciate it, and so would my old physics professor. <>