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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

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

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

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 1 orange/day = 40.97 calories/minute (take a moment to calculate this).

So why do people have a problem with watts

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? $4 bulbs \times \frac{25W}{bulb} = 100 W$ $E = P\times t \Rightarrow t = \frac{E}{P} \Rightarrow \frac{1 kWh}{100W} = \frac{1kWh}{.1kW} = 10 hours$

Kilowatt hour aka kWh

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? $60 W \times 100 hours = 6,000 watt hours$

and $6,000 watthours \times \frac{1 kilowatt}{1000 watts} = 6 kilowatthours = 6 kWh$

Electric energy consumption is usually metered and billed in kWh.

Analogies

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

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

Hall of Shame

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