EGEE 102
Energy Conservation and Environmental Protection

Power

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What is Power?

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Power vs. Energy
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What is Power?

Two cyclists compete in a 10 mile race. Cyclist A finishes the race in 30 minutes and burns 218 calories. Cyclist B finishes the race in 60 minutes and also burns 218 calories.

1) Which cyclist did the most work?

  • Cyclist A
  • Cyclist B
  • Both

2) Which cyclist had the most energy?

  • Cyclist A
  • Cyclist B
  • Both

3) Which cyclist had more power?

  • Cyclist A
  • Cyclist B
  • Both

Answers:

  • 1.  Both
  • 2.  Both
  • 3. Cyclist A

 

Power vs. Energy

Both cyclists did the same amount of work (they both pedaled 10 miles), and used the same amount of energy (218 calories). The blue cyclist, however, demonstrated the most power, because he did the equivalent amount of work as the red cyclist, but in a faster time.

Power is the rate at which we do work.

Energy is the capacity to do work.

Work is the amount done.

Measuring Power

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

Examples of Units of Power include:

  • Watt (W) = 1 joule of energy per second or 1 J/S
  • BTU per hour (BTUs/h) = 1,055J
  • Horsepower (hp) = 550 foot-pounds per second or 550 ft lb/S
  • Calories per second (cal/sec)
  • Kilowatt (kW) = 1000 watts

Calculating Power

Power can be determined by the following formula:

Power = Energy (or work) / Time

or

Energy = Power x Duration of Usage (Time)

Example

On a winter day, a home needs 1 x 106 or 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?

Power(Watts)=( 1× 10 6 Btus/24h ) =1,000,000Btus/24h Power(J/s)= ( 1,000,000Btus×1,055J/s ) ( 24h×3,600s ) =12,200(roundednumber)

If 1 J/s = 1 Watt, and 1000 Watt = 1kW, then 12,200 J/s = 12,200 Watts = 12.2 kW

To solve this problem, you must realize the following: You know the Power (1,000,000 BTUs/24 hours) and the time (24 hours), so you need to solve for Energy. The measurements must be consistent, so the BTUs should be converted to a consistent measure, such as Joules:

1 Watt = 1 J/s and 1 BTU = 1,055 J

If using Joules per second instead of watts, you must convert 24 hours into seconds or divide it by the number of seconds in an hour (3600).

Power & Cost of Energy

We can also use a version of the Power formula to determine Cost of Energy:

Energy Use = Power x Time of Power Use

Cost of the Energy = Energy Used x Cost of the Unit of Energy

Example

If a 100 W light bulb is accidentally left on overnight (8 hours), how much energy does it consume?

Energy Use = Power x Time of Power Use

Energy Use = 100W x 8h = 800Wh or 0.8kWh

How much energy does this cost, if electricity costs 10 cents per Kilowatt?

Cost of Energy = Energy Used x Cost of the Unit of Energy

Cost of Energy = .8kWh x 10 cents = $0.08