# 7.7 Power  (Page 3/8)

 Page 3 / 8
$E=\text{Pt.}$

Electricity bills state the energy used in units of kilowatt-hours $\left(\text{kW}\cdot h\right),$ which is the product of power in kilowatts and time in hours. This unit is convenient because electrical power consumption at the kilowatt level for hours at a time is typical.

## Calculating energy costs

What is the cost of running a 0.200-kW computer 6.00 h per day for 30.0 d if the cost of electricity is \$0.120 per $\text{kW}\cdot h$ ?

Strategy

Cost is based on energy consumed; thus, we must find $E$ from $E=\text{Pt}$ and then calculate the cost. Because electrical energy is expressed in $\text{kW}\cdot h$ , at the start of a problem such as this it is convenient to convert the units into $\text{kW}$ and hours.

Solution

The energy consumed in $\text{kW}\cdot \text{h}$ is

$\begin{array}{lll}E& =& \text{Pt}=\left(0\text{.}\text{200}\phantom{\rule{0.20em}{0ex}}\text{kW}\right)\left(6\text{.}\text{00}\phantom{\rule{0.20em}{0ex}}\text{h/d}\right)\left(\text{30}\text{.}0\phantom{\rule{0.20em}{0ex}}\text{d}\right)\\ & =& \text{}\text{36}\text{.}\text{0 kW}\cdot \text{h,}\end{array}$

and the cost is simply given by

$\text{cost}=\left(\text{36.0 kW}\cdot h\right)\left(0.120 per kW\cdot h\right)=4.32 per month.$

Discussion

The cost of using the computer in this example is neither exorbitant nor negligible. It is clear that the cost is a combination of power and time. When both are high, such as for an air conditioner in the summer, the cost is high.

The motivation to save energy has become more compelling with its ever-increasing price. Armed with the knowledge that energy consumed is the product of power and time, you can estimate costs for yourself and make the necessary value judgments about where to save energy. Either power or time must be reduced. It is most cost-effective to limit the use of high-power devices that normally operate for long periods of time, such as water heaters and air conditioners. This would not include relatively high power devices like toasters, because they are on only a few minutes per day. It would also not include electric clocks, in spite of their 24-hour-per-day usage, because they are very low power devices. It is sometimes possible to use devices that have greater efficiencies—that is, devices that consume less power to accomplish the same task. One example is the compact fluorescent light bulb, which produces over four times more light per watt of power consumed than its incandescent cousin.

Modern civilization depends on energy, but current levels of energy consumption and production are not sustainable. The likelihood of a link between global warming and fossil fuel use (with its concomitant production of carbon dioxide), has made reduction in energy use as well as a shift to non-fossil fuels of the utmost importance. Even though energy in an isolated system is a conserved quantity, the final result of most energy transformations is waste heat transfer to the environment, which is no longer useful for doing work. As we will discuss in more detail in Thermodynamics , the potential for energy to produce useful work has been “degraded” in the energy transformation.

## Section summary

• Power is the rate at which work is done, or in equation form, for the average power $P$ for work $W$ done over a time $t$ , $P=W/t$ .
• The SI unit for power is the watt (W), where $\text{1 W}=\text{1 J/s}$ .
• The power of many devices such as electric motors is also often expressed in horsepower (hp), where $\text{1 hp}=\text{746 W}$ .

#### Questions & Answers

how can I read physics...am finding it difficult to understand...pls help
rerry Reply
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju
I have a exam on 12 february
David Reply
what is velocity
Jiti
the speed of something in a given direction.
Ju
what is a magnitude in physics
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Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
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u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
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if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
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define variable velocity
Ali Reply
displacement in easy way.
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binding energy per nucleon
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why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
why god made humenity
Ali
and he to multiply
Owofemi
stuff happens
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God plays dice
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Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
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when we face electric shock these elements work as a conductor that's why we got this shock
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