Energy and Power

Most people can name two units of power, few can name even one unit of energy.

And yet, "power" just means "energy flow per unit time". We all know the "Watt" is a unit of power consumption and have an idea how quickly a 1500 Watt kettle boils water. The unit of energy is the "Joule" - a Watt is just a flow of one Joule per second.

The other popular unit of power is the "horsepower". The conversion is that one horsepower = 756 Watts. A 100-HP car would be able to turn a 75,600 - Watt electrical generator, or 75.6 kilowatts.

So anybody who does talk about energy, rarely speaks in Joules. We instead multiply power back by time again and have the unit, the kilowatt-hour. A kilowatt, a thousand Joules/second, times 3600 seconds in an hour, is 3,600,000 Joules - 3.6 megaJoules (MJ).

You often see a neat division by a thousand in articles about power stations. A 400 megawatt (400,000 kilowatt) power station is said to be "enough to power 400,000 homes". That's because, nationwide, the average home consumer buys about 9800 kilowatt-hours ( 36 gigajoules (GJ). They don't buy it at a steady kilowatt day-round, year-round, of course.

A few machinery engineers do speak of the horsepower-hour. 756 Watts times 3600 is 2.7MJ.

The largest power unit used in discussion is the gigawatt, a thousand megawatts. The largest power plants can exceed one gigawatt by a bit - one GJ per second, 3.6 terajoules (TJ) per hour.

Units of Power

Going over watts in "SI" units:
  1. kilowatt - 1000 watts - largest industrial lightbulb - 1.3 Horsepower

  2. megawatt - 1 million watts - enough to play a night game at a stadium - 1300 horsepower - smallest locomotive

  3. gigawatt - 1 billion watts - only a few power plants are larger - enough to power a major city most days

  4. terawatt - 1 trillion watts - all the power plants in the US on full at the same time might reach one terawatt. Yearly average US consumtion is only 0.47 terawatts (469 GW).
The next SI prefix is "peta" - one thousand trillion - (also, that classic unit for children, "a million billion") and that will never come up in terms of watts. Joules, however, are often discussed in "terajoules" (TJ) and even "petajoules", (PJ).

Units of Energy

  1. kilojoule (kJ) - a small 13 watt compact-flourescent bulb uses up 1 kJ in 1000/13 = 76 seconds

  2. megajoule (MJ) - one kilowatt-hour (kWh) is 3.6 MJ. Or, four 75W floodlights in track-lighting use up 1 MJ per hour

  3. gigajoule (GJ) - now-popular unit of natural gas, about the same as "1 cubic foot" in the old days.
    For electricity, 1 GJ = (1000 MJ/3.6 MJ/kWh) = 277 kWh. Your monthly electrical bill (700-1000 kWh in winter) is probably about 2-3 GJ.
    Your gas bill in winter is likely 15-20 GJ.

  4. terajoule (TJ) - 8 years of home natural gas consumption; 30 years of electrical (or, all the electricity used on your block this year, including streetlights).

  5. petajoule (PJ) - joules - 31.5 PJ is the electrical output of one of those big gigawatt power plants for a year; 1 PJ is enough to run Calgary's electrical needs for about 3 weeks.

Power, Energy, and Work - Especially Construction Work

A huge D-10 bulldozer can push with 700 HP, or 529 kilowatts. If it could somehow go all-out for a 16-hour double shift at 700 HP the whole time, it would burn 529,000 x 3600 x 16 = 30 billion J, that is 30 GJ.

But here we must make a clear difference between thermal energy and output energy. For a good rule of thumb, turning heat into work - the output of an engine or generator - you have to put in three times as much heat as the work you get out. That's why car engines run so hot they need a radiator. That's why power plants need to be on rivers to dump the heat into cold water, or must build those big cooling towers.

In the meantime, some new power plants are being constructed to make use of the waste heat: Calgary's new downtown power plant will heat "up to 10 million square feet of buildings".

So while an efficient furnace burns 1 GJ worth of natural gas and actually puts 1 GJ of heat into your house (bad furnaces lose a little heat up the stack), 1 GJ of electrical energy (277 kilowatt-hours, about ten day's home electricity) actually took about 3 GJ of heat to make, whether you got the heat from uranium, coal, gas, or wood. It's the same with your car or the D-10 bulldozer: that 700 HP, or 529 kW output, took nearly 1600 kW of heat generation from burning diesel to make, with the bulldozer engine throwing two-thirds of it away in the radiator.

However, "529 kW" is actually a pretty conservative average heat output for that D-10. Power plant generators may run at the same speed all the time, they are designed for it. Vehicle motors are never at their maximum output for a more than a minute or so at a time, while your car is pedal-to-the-metal accelerating, or the bulldozer doing a big push after spending a minute getting into position. Your 200-HP car is really putting out only 20-or-so horsepower most of the time, and even industrial equipment like the bulldozer, has the engine at maximum revs perhaps a third of the time, at best. So using the 700 HP, 529 kW maximum "output power" of such an engine is probably conservative for the original "thermal energy" use of the engine per hour of work.

Assuming, then, that a bulldozer at best might use up 30 GJ of diesel in that 16-hour double-shift. If they only took alternate Sundays off, it wuld still take a year to use up 10 TJ. A massive construction site with 100 such bulldozers or their equivalent would take a year to burn 1 PJ of diesel. Running a more believable 12-hour-day, 5-day-week with statutory holidays, the 100-machine crew would need nearly two work-years to burn 1 PJ.