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=CurrentPressure (P=QH)	Power=CurrentVoltage (P=IV)	kg•m²/s³
Energy	E	The ability to do work	Energy=PowerTime (E=Pt)	Energy=PowerTime (E=Pt)	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?

$4bulbs\times {\frac {25W}{bulb}}=100W$

$E=P\times t\Rightarrow t={\frac {E}{P}}\Rightarrow {\frac {1kWh}{100W}}={\frac {1kWh}{.1kW}}=10hours$

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?

$60W\times 100hours=6,000watthours$

and

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

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

There is no such thing as kilowatts per hour

Hall of Shame

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