# Joules, Watts and Kilowatthours

When we talk about energy, we often mean really power = energy / time. Let's first see what the basic units are, how they can be expressed and how they are connected. The links take you to the modules of the Hyperscript "Einführung in die Materialwissenschaft I", where more details can be found
Units for Energy, Power, and Electricity
Quantity Name Symbol Units Relations
In basic units In secondary units
Energy Joule J m2 kg s–2
N · m 1 kWh = 3.6 · 106 J
W · s
1 kcal = 4,1868 kJ = 1,163 kWh
1 to SKE = 8 140 kWh
Power Watt W J/s m2 kg s–3 1 kW = 3.15 · 1010 J/yr
1 kW = 3.6 · 106 J/hr
1 kW = 106 J/s
V · A
Electric potential,
voltage
Volt V W/A m2 kg s-3 A–1
Time Second s s s 1 yr = 1 a = 3.15 · 107 s
1 d = 86 400 s
There are a few points to note:
• The time unit is the second or "s". Then we have the minute = "m", the hour = "h" and the day = "d" as officially (allowed) SI units. There is no official abbreviation for year; here we use either "yr" or "a" (for annum).
• Terms like energy consumption do not mean (of course!) that energy is really consumed, but that it is just transformed (to heat in the end). There is such a thing as the energy conservation law, after all!
• In case of doubt, when just the term "energy" is used, what is meant is often energy per year - formally this is power. However, it is not always sensible to refer to formal "power" as power: If your gas tank contains x liters of gasoline, it contains some equivalent of pure energy. If your consumption of gasoline is 2 000 l per year, you talk about the energy per year that you have consumed (about 20 000 kWh)! You could express that as an average consumption of 2 000/3,15 · 107 l/s = 6,5 · 10–5 l/s in SI units - but that doesn't make much sense.
• There is primary energy and secondary energy. If your personal consumption of electrical energy is, for example, 2 000 kWh (per year; a good number for an average German), then this is what your power company charges your for. In this case you are charged for your use of secondary (electrical) energy. The primary energy needed for producing that amount of secondary energy (per year!), is roughly three times larger, because the efficiency of our fuel-burning power plants is around 35 %. This means that in terms of the energy contained in coal, oil or gas - whatever was burnt to produce your personal 2 000 kWh (per year), you actually consumed around 6 000 kWh (per year).
• Your direct consumption of these secondary 2 000 kWh, that you paid for directly, is not all the electrical energy that you personally consumed (per year; last time!). You also consumed electrical energy in the form of light at the place you work, products you buy (that somebody made somewhere, using electrical energy), and so on. Your indirect (secondary) electrical energy consumption is probably much higher than your direct consumption - about a factor of 2,5.
• Besides electrical energy, you, personally, consumed energy in the form of heat (including hot water for showers), gasoline (for driving your car and for riding a bus and so on) eating and drinking (somebody had to ride a tractor to harvest the hops, transport your beer, and so on); your grand total of primary energy consumption is around 50 000 kWh (per year) - if you are a German or EU citizen. If you are an American, it's 2,5 times more; it's far less if you are, e.g., from Ghana or Peru
We have now defined the quality of energy and power; next let's get a feeling for the quantities involved.
We will not care about precise numbers. If humankind right now consumes 13 TW, 12,8 TW or already 14,783 TW, is just as irrelevant in this context, as the question if the 50 W of power produced by the slave mentioned below includes his sleeping time, or only the time he actually works.
Typical examples for energy and power
Example Formula
Energy E Potential energy Epot if
I climb h = 1.000 m
(For you it might
be a little less)
Epot   = m · g · h
= 100 kg · 9,81 m/s2 · 1000 m
= 9,81 · 105 J
= 0,273 kWh
1 kWh corresponds to: 367 t lifted to 1 m
9,5 l water à 10oC bring to boil
2 km - 10 km car driving
1 kWh is stored in: Large (85 Ah) truck batterie
0,1 l gasoline / Diesel
0,25 kg dry wood
0,12 m3 natural gas
0,28 m3 H2
7,3 t H2O in a reservoir with 50 m height difference
Power P What I can sustain for »
1 hr on a bicycle
175 W
Hard working slave
on average
50 W
Power consumed by a light. » 50 W
Power consumed by a toaster. » 1 kW
Energy consumed by a toaster in 3 minutes 50 Whr
Time your slave has to work to power your toaster for 3 min. 1 hr
Power consumed by your car » 20 kW - 100 kW
Power consumed by a (small) jet engine » 1 000 kW
Output of "standard" power plant. » 1 000 000 kW = 1 GW
Global secondary electrical power demand. 1 000 GW = 1012 W = 1 TW
1 "Terawatt" = 1 trillion Watt (USA)
= 1 Billion Watt (Europe)
Total primary global power produced (2001)
Oil: 4,66 TW
Gas 2,89 TW
Coal 2,98
Nuclear 0,92 TW
Rest: 1,81 TW
13 TW
USA (303 Mill. people) 3,2 TW
Rest (6.331 Mill. people) 9,8 TW
Total energy produced (= consumed) per year in 2001
(EJ = Exa Joule = 1018 J)
13 TW · 3,15 · 107 s = 4 · 1020 J/yr = 400 EJ/yr
Total energy produced (= consumed) per year and capita
USA: 350 GJ/yr = 97 200 kWh/yr
Australia: 240 GJ/yr = 66 600 kWh/yr
Japan; EU; S.-Korea: 150 GJ/yr = 41 700 kWh/yr
Brazil: 40 GJ/yr = 11 100 kWh/yr
China: 30 GJ/yr = 8 330 kWh/yr
India: 15 GJ/yr = 4 170 kWh/yr
60 GJ/yr · capita = 16 660 kWh/yr · capita
Time it takes if we built 1 renewable standard 1 GW power
plant per day on Terra to replace all
"carbon emission" power plants
11 TW / 1 GW = 11 000 days

= 30 years
Total energy needed (per year) in 2050 Who knows?
Extrapolation: All like EU:
33 TW
Additional power plant building rate needed to
account for the expected increase.
22 TW / 1 GW · 50 yr = 1.2 power plants / day
Present (2007) rate of 1 GW solar cell
power plants built per day
3 · 10–4 power plants / day

Conclusion: You, the young student, are in trouble!
(I, the old professor, will get by)
What you find in this table you may call the "The Terawatt Challenge", and it has been called this way. Read more about it in the article Future Global Energy Prosperity: The Terawatt Challenge of Nobel prize winner Richard Smalley published in the MRS Bulletin 30, 2005, and in the article "Powering the Planet" of Nathan S. Lewis in the MRS Bulletin 32, 2007

This looks like somebody should do something. Right. This somebody is you - and you, over there in the USA, too!
While the shear magnitude of the numbers may induce a feeling of hopelessness, fixing the problem within the next 50 years or so is not impossible. Let's look at the bright side:
Building power plants: Build one big 1 GW power plant per day?? Impossible! Wrong - that's exactly what we have been doing for many years! The energy - time curve in the past had the same slope we used for the extrapolation, roughly 1 GW/day. So it can be done, and if we really want to do it (and pay the higher price!) we can do it with renewable energy plants, too, in the not-so-distant future.
Reducing energy consumption: You (and I) don't really need 50 000 kWh/year or even more to experience a high quality of life. The average quality of life in the USA is certainly not higher than in the EU, but energy consumption is more than 2 times larger. In 1970 I, personally, had a pretty good life, too - but consumed far less energy than I do now. So let's reduce energy consumption without compromising the quality of life - it can be done!
Renewable energy is too expensive: Bullshit! It is nominally more expensive than my, the old Professor's, present kWh price - yes! But I'm not paying the full bill; it does not include, for example, the cost of climate change or the destruction of the environment, the costs of the wars for resources etc. -Either you, the young student, will have to pay for this later, or all of us pay somewhat more soon.
Slave labor: A slave could give you 50 W · 24 · 365 hr = 438 kWh/year if you worked him really hard (your female slave may give you things not always measured in W). You European thus command 114 slaves working all the time for you; even more if you let them go to the bath room on occasion. You have this much power at your fingertips only because you have access to technology. Think a moment about this! It is the only reason why you, personally, are doing so well in modern society! In good old-fashioned society, only one out of 114 or more could command that much power, so chances are > 114 : 1 that he was your Lord and you one of his slaves / serfs / indebted servants, or whatever you like to call it.
Exponential growth: Nobody has a feeling for exponential growth - you must sit down and calculate. OK. Here is the exercise:
(Look at least at the solution!)
 Exercise b8_1_1 Exponential growth

8.1.1 Basic Solar Cell Topics

Frequently Asked Questions Concerning Solar Cells

Solution to Exercise 8.1-1: Exponential Growth

Exercise Basic 8.1-1

© H. Föll (Semiconductor Technology - Script)