# Power and energy basics

Energy is a property of physics that can be a little hard to describe completely. The most common definition is one that will work well for us. Energy is the ability to do work.

Power is just a rate of that work being done. Specifically, power is rate of energy per time (e.g. power generation, power consumption, etc.).

## Energy = Power x Time[edit | edit source]

Energy equals power times time, i.e. ` E=P*t`.
Where:

- Energy is the ability to do work.
- Power is the rate at which work is performed.

Symbol | Description | In Water | In Electricity | Base Units | |
---|---|---|---|---|---|

Power | P | Rate at which work is performed | Power=Current*Pressure (P=Q*H) | Power=Current*Voltage (P=I*V) | kg•m²/s³ |

Energy | E | The ability to do work | Energy=Power*Time (E=P*t) | Energy=Power*Time (E=P*t) | kg•m²/s² |

## Common units of Energy and Power[edit | edit source]

Common Units of Energy and Power | |
---|---|

Energy | Power |

joule | joule/sec |

calorie | calorie/min |

Btu | Btu/hour |

orange* | orange/day |

watt-hour | watt |

kilowatt-hour | kilowatt |

### *Oranges[edit | edit source]

Okay so oranges are a made up unit of energy. But it could be a unit of energy. According to the USDA, one medium sized, 2-5/8" diameter orange, weighing 121g, has 59 Calories. And, because people in the USA do not want to think they are eating thousands of calories per serving, a Calorie is actually a kilocalorie, so one medium sized orange has 59,000 calories. So ` 1 orange = 59,000 calories` and

`(take a moment to calculate this).`

**1 orange/day = 40.97 calories/minute**### So why do people have a problem with watts[edit | edit source]

Watts are a rate. One watt is equal to one joule per second, i.e. ` 1 W = 1 J/s`, but there is no unit of time in the name. Likewise one kilowatt-hour is a quantity with no explicit time. In fact, one kilowatt-hour equals 3,600,000 joules

*(take a moment to calculate this)*. One kWh could be an appliance drawing:

- 1 kW for 1 hour
- 2 kW for .5 hours
- 1 W for 1000 hours (remember that the little k signifies kilo and means 1000x)

Example:

If you turn on 4 light bulbs, each rated at 25 W, how long can they be on before you reach 1 kWh?

[math]4 bulbs \times \frac{25W}{bulb} = 100 W [/math]

[math]E = P\times t \Rightarrow t = \frac{E}{P} \Rightarrow \frac{1 kWh}{100W} = \frac{1kWh}{.1kW} = 10 hours [/math]

### Kilowatt hour aka kWh[edit | edit source]

A kilowatt is just 1000 watts (kilo means 1000x). A kWh is 1000 watt hours.

Example:

How many kilowatt hours would be needed to run one 60W incandescent bulb for 100 hours?

[math] 60 W \times 100 hours = 6,000 watt hours [/math]

and

[math] 6,000 watthours \times \frac{1 kilowatt}{1000 watts} = 6 kilowatthours = 6 kWh [/math]

Electric energy consumption is usually metered and billed in kWh.

### Analogies[edit | edit source]

Energy is a measurable quantity like distance. Power is a rate like speed.

Units | Analog | Units | |
---|---|---|---|

Energy | kWh | Distance | miles |

Power | W | Speed | MPH |

### Conversions[edit | edit source]

joule | calorie | Btu | watt-hour | |
---|---|---|---|---|

1 joule | 1 | ~0.239 | ~9.478 x 10^-4 | ~2.778 x 10^-4 |

1 calorie | ~4.184 | 1 | ~3.966 x 10^-3 | ~1.163 x 10^-3 |

1 Btu | ~1,055.056 | ~252.164 | 1 | ~0.293 |

1 watt-hour | 3,600 | ~860.42 | ~3.412 | 1 |

## There is no such thing as kilowatts per hour[edit | edit source]

## Hall of Shame[edit | edit source]

Please see the Hall of Shame for a short list of violators.