Power and efficiency

A phone battery is labeled 20 Wh. Its charger is labeled 20 W. The numbers look almost the same, but they measure completely different things, and mixing them up is the most common mistake on an electricity bill. One is a total. The other is a speed.

You already have energy: the ledger that is never destroyed, only moved. This lesson adds two everyday questions the ledger cannot answer on its own. First, how fast is energy being moved? A sprinter and a slow walker can climb the same staircase, spending the same energy, but the sprinter does it in a tenth of the time. Second, of the energy you pour in, how much actually does the job you wanted, and where does the rest go?

First, predict

Two things that draw power very differently. Which one uses more electricity over a whole day?

If that surprised you, it is because the label on a device is its power, the rate, but the bill charges you for energy, the total. Big rate, tiny time, can lose to small rate, long time.

Play with the energy budget first

Pick a device and set how hard it is working with the load slider. The incoming stream of watts splits into the part that does the useful job and the part that leaves as heat, and the band widths are the actual split. Below, the same watts run forward into energy per day and a yearly cost. Compare the incandescent bulb to the LED, and notice how little of the old bulb becomes light.

Every device turns nearly all its input into heat in the end, but the useful fraction is what you are paying for. That fraction has a name, and so does the rate.

Power: energy per second

power is energy per unit time (STATED). Its unit, the watt, is just one joule per second.

Turn that around and energy is power multiplied by time, $E=Pt$. That is where the bill's unit comes from. A kilowatt-hour is one kilowatt sustained for one hour, which works out to 3.6 million joules.^[1] A watt-hour, like the 20 Wh on a battery, is the same idea a thousand times smaller. These are units of energy, the total, even though a rate hides in the name.

Efficiency: the tax reality takes

No device turns all of its input into the output you want. efficiency is the useful output divided by the total input, a bare fraction with no units.

An old incandescent bulb runs at about 5 percent: almost all of its 60 watts becomes heat, and only a sliver becomes light.^[1] An LED reaches roughly 40 percent, which is why a 9 watt LED can out-shine it while sipping a seventh of the power. A car engine is about 25 percent. Whatever is not the useful fraction is not lost from the universe, it is the heat band in the widget, obeying the same conservation as the skate park.

The 65 watt CPU that is really a 65 watt heater

Here is the case that matters most for a programmer. A CPU rated at 65 watts, run flat out, draws 65 joules of electrical energy every second. It does an astonishing amount of computation with that energy, but the computation itself stores almost nothing: essentially all 65 joules per second come straight back out as heat.^[2] A 65 watt chip is, thermally, a 65 watt heater glued to your circuit board.

power_watts = 65          # what the CPU pulls at full load
heat_per_second = power_watts   # ~all of it leaves as heat -> 65 J/s

# over a 10-minute compile:
joules = power_watts * (10 * 60)   # 39,000 J to get rid of
kwh = joules / 3.6e6               # about 0.011 kWh of energy, all now heat

Check yourself