### What is Power?

Click the "play" button below and observe what happens.

### 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:

$$\begin{array}{l}\text{Power}=\text{Energy}\left(\text{orwork}\right)\text{}/\text{Time}\\ \text{or}\\ \text{Energy}=\text{Power}x\text{DurationofUsage}\left(\text{Time}\right)\end{array}$$#### Example

**On a winter day, a home needs 1 x 10 ^{6} 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?**

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:

$$1\text{}Watt\text{}=\text{}1\text{}J/s\text{}and\text{}1\text{}BTU\text{}=\text{}1,055\text{}J$$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).

Image Credit: © Penn State University, is licensed under CC BY-NX-SA 4.0

### Power & Cost of Energy

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

$$\begin{array}{l}\text{EnergyUse}=\text{Power}\times \text{TimeofPowerUse}\\ \text{CostofEnergy}=\text{EnergyUsed}\times \text{CostoftheUnitofEnergy}\end{array}$$**Example**

**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?**