1.6: Energy Use of Home Appliances
- Page ID
- 47155
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Calculating Energy Use
The previous section introduced the formula to calculate power as
\[ Power = \dfrac{ Energy }{ Time } \]
and therefore
\[ Energy = Power * Time \]
where time is the duration of usage. This formula can be slightly modified to give a formula for energy consumption per day, i.e.,
\[ \dfrac{ Energy \, Consumption }{ day } = (Power \, Consumption) * \dfrac{ Hours \, Used }{day} \]
where
- Energy consumption has units of kWh (like on utility bills)
- Power consumption has units of W
- Hours used per day is the number of hours that the appliance is used
Since we want to measure energy consumption in kWh, we must change the way power consumption is measured from watts to kilowatts. We know that \( 1 kWh = 1,000 Wh \), so we can adjust equation 1.6.3 to
\[ \dfrac{ Energy \, Consumption \, (kWh) }{ day } \, = Power \, Consumption \, (W) * \dfrac{ kW }{1000 \, W} * \dfrac{Hours \, Used}{day} \]
Example 1
If you use a ceiling fan (200 watts) for four hours per day, and for 120 days per year, what would be the annual energy consumption?
- Answer
-
Using equation 1.6.4,
\[ \dfrac{Energy \, Consumption}{day} = \dfrac{200}{1000} * \dfrac{4 \, hrs}{day} = \dfrac{0.8 \, kWh}{day} \nonumber\]
The energy used for 120 days is
\[ Energy \, Consumption = \dfrac{0.8 \, kWh}{day} * 120 \, days = \bf 96 \, kWh \nonumber\]
Example 2
Using the results from Example 1, if the price per kWh for electricity is $.0845, what is the annual cost to operate the ceiling fan?
- Answer
-
\[ Annual \, Cost = 96 \, kWh * \dfrac{\$0.0845}{kWh} = \bf \$8.12 \nonumber\]
Example 3
If you use a personal computer (120 Watts) and monitor (150 Watts) for four hours per day, and for 365 days per year, what would be the annual energy consumption and cost?
- Answer
-
\[ \dfrac{Energy \, Consumption}{day} = \dfrac{120 + 150}{1000} * \dfrac{4 \, hr}{day} = 1.08 \dfrac{kWh}{day} \nonumber\]
\[ Annual \, Energy \, Consumption = 1.08 \dfrac{kWh}{day} * 365 \, days = \bf 394.2 \, kWh \nonumber\]
\[ Cost = 394.2 \, kWh * \dfrac{\$0.0845}{kWh} = \bf \$33.30 \nonumber\]
Locating Wattage
Most appliances will have their wattage stamped on the bottom or back or on the "nameplate". This wattage denotes the maximum power drawn by the appliance. Since many appliances have a range of settings (for example, the volume on speakers), the actual amount of power consumed depends on the setting used at any one time.
A refrigerator, although turned "on" the entire time while being used, actually cycles on and off at a rate that depends on numerous factors, such as how well it is insulated, what the ambient and freezer temperatures are, how often the door is opened, if the coils are clean, if it is defrosted regularly, and how well the door seals function.
Table 1.6.1 shows the power consumption of some typical home appliances.
Table 1.6.1. Power consumption
| Appliance | Wattage (range) |
|---|---|
| Clock radio | 10 |
| Coffee maker | 900 - 1200 |
| Clothes dryer | 350 - 500 |
| Dishwasher | 1200 - 2400 |
| Hair dryer | 1200 - 1875 |
| Microwave oven | 750 - 1100 |
| Laptop | 50 |
| Refrigerator | 725 |
| 36'' TV | 133 |
| Toaster | 800 - 1400 |
| Water heater | 4500 - 5500 |
Amperes and Voltage
If the current instead of the wattage is listed on an appliance, one can estimate the wattage by multiplying the current (in amperes) drawn by the voltage used by the appliance. Most appliances in the U.S. use 120 volts. Larger appliances, including clothes dryers and electric cooktops, use 240 volts.
If neither the current nor wattage is listed, an ammeter can be used to find the current flowing through the appliance. Stores that sell electronics usually have ammeters. Use the ammeter while the appliance is running to obtain the current in that instance.
Phantom Loads
Many appliances will continue to draw a small amount of power even when they are switched "off" and increase the appliance's energy consumption by a few watts per hour. This occurs in most appliances that use electricity, such as TVs, VCRs, stereos, computers, and kitchen appliances.
Phantom loads can be avoided by unplugging the appliance or plugging the appliance into a power strip and cutting off all power to the appliance with the power strip switch.