Tech Focus: Measures of Energy
We formed the power measure for a water heater by looking at the energy use (BTU) per unit of time (per hour). Thus, BTU is a measure of energy, and BTU/hr is a measure of power. One therm is defined to be 100,000
BTU, so the therm is a measure of energy, and therms/hour is a tneasure of power.
TI1e kilowatt is a unit of power, but it is not expressed as energy per
unit of time. What, then, is the unit of energy that corresponds to a kilowatt? TI1e answer is not particularly satisfying to students of the subject. The unit of energy is the kilowatt-hour (kWh).
The kilowatt-hour is a measure of energy, because if you divide it by the unit of time (per hour), you get the measure of power, kilowatt. Thus, for electric energy, it is helpful to base ones understanding on the kilowatt as a unit of power and to think of electric energy as the result of running that power over a particular length of time.
The measure of energy in the International Scientific (SI) system is the
joule. Examples later in this chapter show how to use the joule as a mea sure, but the important point here is that the watt, as a measure of power, is defined directly frotn the joule as a measure of energy:
1 W:att = 1 Joule
Second
Example 7 Electric Power and Electric Energy
(a) Ho'v much energy, expressed in kilowatt-hours, is used when a hair dryer is run on the •low setting (500 W) for 12 m nutes? (b) How much
energy is used by a 60-watt light bulb that is left on for eight hours? (c) If a household's monthly electric bill shows that 953 kWh of electric energy were used during a 33-day billing period, what was the average power draw of the house during that period?
Solution
1l1e basic concept to apply is
Energy
----=-; Power
Ti1ne
We can also write this relationship as
Energy = Power X Time
(a) Convert 12 tninutes to hours: 12 min/60 (n1in/hr) = 12/60 hr = 0.2 hr. Now multiply the power rate by time to get the energy used
Energy= 500 (W) X 0.2 (hr) Energy= 500 X 0.2 watt-hours Energy= 100 watt-hours
Divide 100 watt-hours by 1,000 to convert it to kilowatt-hour, Energy= 0.100 kWh
(b) A 60 W bulb run for eight hours consumes
Energy = 60 CW) X 8 (hr) Energy= 60 X 8 (watt-hours)
Energy= 480 watt-hours
Energy= 0.48 kWh
(c) The household's average power consutnption, expressed in kilowatts, will be the total energy used (kWh) divided by the nutnber of hours
in the billing period. Thirty-three days translates to 33 X 24 = 792 hr. So 953 kWh divided by 792 hr is
= 1.203 kW
1.2 kW is only a little tnore than the power drawn by running one hair dryer on the maxim urn setting. So how might a household draw only 1.2 kW in power when there are many rnore electric devices in the house? The reason is that the 1.2 kW is the average power draw of the house, averaging daytime and nighttime use over all the hours of the month. During the daytime, the maxi mum power drawn at any point in time could be as high as 3.0 kW, whereas at night, with only a few lights and an electric fan blowing heated air, the power draw might be less than 0.5 kW at a particular point in time.
The Capacity Factor .of a Device in Operation
When the actual usage of a device (per year) is divided by its rated capac ity (output per year), the result is called the capacity factor of the device under the stated conditions of usage. For exan1ple, consider a wind tur bine that has a rated capacity of 50 kW and produces 158,000 kWh of electric energy in a year. The maximutn production of the wind turbine would be 50 kW X 24 (hr/day) X 365 (days/year) = 438,000 kWh. The
actua1 productt.on, as a percentage o f .Its maxt.mum wou ld be
158, 000
= 0.36,
.
meantng
6 percent.
438,000
The actual output of a solar power system or a wind system depends on the amount of insolation or the amount of wind at its locatio_n. Thus, the capacity factor of a solar or wind power system is a statement about the technology in its particular location, not about the device per se.
Capacity Factors for Wind Turbines
A significant detenninant of the capacity factor of a Vind turbine is the variability of wind speed at the site, because variability din1inishes the
capacity factor significantly. The power output of a wind turbine is pro portional to the cube of the wind speed, so when the rated capacity is reached at wind speeds near the maximum tolerance of the device, wind speeds lower than the maximum produce far less output than at the max imum tolerable wind speed.
Commercial wind turbines, under typical weather conditions at favor able sites, have had capacity factors between 20 and 40 percent.2 Some studies put the estimate closer to 20 percent.3 Recent designs, which per Init the turbine to reach its peak capacity over a wider range of wind speeds, may reach 50 percent in onshore locations.4 However, wind tur bines that are sited for convenience (as on a college campus) rather than for the stability of wind speed can have capacity factors below 10 percent.
Take...aways
The engineer's input-process-output perspective on technology enables us to describe technologies, and the various devices that use or represent the technologies, in several important ways. A basic but important con cept in the description of technology is capacity, which conveys a sense of how big a device is. l11e description of devices of different sizes led us in this chapter to study the various ways that power and energy can be measured. 1he key points from the chapter are the following:
• Capacity describes the size of a device, how big or small it is in relation to its purpose, which is the production of output. Capacity is almost always measured as the output rtlte of
the device, such as watts, kilowatts, or megawatts for power systems.
• The exceptions to the rule are devices whose purpose is storage. Water tanks, hydrogen fuel tanks, and batteries have• their capacities measured in the units of output that they store, for example, gallons, kilograms, or kilowatt-hours.
• Measures of energy and power are comn1only expressed in different units according to the context (the type of energy), although all units are related mathetnatically through standard conversion formulas..
• TI1e unit of measurement can be scaled up by using the prefixes kilo (X 1,000) or mega (x 1,000,000).
• Common measures of energy include the kilowatt-hour (electrical), the British Thermal Unit (heat), therm (heat), and the calorie (heat).
• Common measures of power include kW (electrical), the
BTlJ/hr (heat), and HP (auton1otive).
• The capacity factor of a device indicates how much the device is being used, as a percentage of its maximum annual outpu