1.5: Power

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What Is Power?

The video below is a short demonstration of power.

While both cyclists did the same amount of work (since they both pedaled for 10 miles) and used the same amount of energy (218 calories), the blue cyclist used the most power, because he did the same amount of work over a shorter period of time.

Important Point

Power is the rate at which we do work.

Energy is the capacity to do work.

Work is the amount done.

Measuring Power

Power is measured in units of energy per time. Examples of units with conversions include:

Watt (W) = 1 Joule per second (J/s)
BTU per hour (BTUs/h) = 1055 J/s
Horsepower (hp) = 550 foot-pounds per second (ft-lb/s)
Calories per second (Cal/s)
Kilowatt (kW) = 1000 Watts (W)

Important Point

Units of power are not the same as units of energy (i.e., BTUs, calories, etc.). Units of power are measured in terms of units of energy used per some unit of time.

Calculating Power

Power can be determined by the formula

\[ Power = \dfrac{ Energy }{ Time } \]

where $ Time $ refers to the duration of usage.

Example 1

On a winter day, a home needs 1,000,000 BTUs of fuel energy every 24 hours to maintain the interior at 65°F. At what rate is the energy being consumed in Watts?

Answer: \[ Power = \dfrac{ 1,000,000 \, BTUs }{ 24 \, hr } * \dfrac{ 1055 \, W }{ BTU } * \dfrac{ hr }{ 3600 \, s} = \bf 12,200 \, W \nonumber\]

Power and Cost of Energy

Determining the cost of energy uses the formula

\[ Energy \, Use = Power * (Time \, of \, Power \, Use) \]

\[ Cost \, of \, Energy = (Energy \, Used) * (Cost \, of \, the \, Unit \, of \, Energy) \]

Example 2

If a 100 W light bulb is accidentally left on overnight (8 hours), how much energy does it consume? How much energy does this cost, if electricity costs 10 cents per Kilowatt?

Answer

Using equation 1.5.2,

\[ Energy \, Use = (100 \, W) * (8 hr) = 800 \, Wh = \bf 0.8 \, kWh \nonumber\]

Using equation 1.5.3,

\[ Cost \, of \, Energy = (0.8 \, kWh) * (\$0.10) = \bf \$0.08 \nonumber\]