## Comparing Various Kinds of Energy

By W. Clawpaws on Sunday 18 April 2010, 19:09 - Permalink

I was thinking about various ways in which I consume energy and trying to relate them to one another, and after spending some time poking around gathering numbers, I figured I'd share what I'd learned.

My partner and I drive a “clean diesel” Golf TDI; we use natural gas to cook and heat water and the house; we use various electrical appliances (lights, refrigerator/freezer, computers, television, clothes washer and dryer, hair dryer, electric kettle, etc.); we have a variety of things that use replaceable batteries (flashlights, remote controls, clocks, electric toothbrushes, etc.); and, of course, we ourselves eat food.

One interesting thing about trying to compare all these different energy sources is discovering that electricity is sold by the kilowatt hour, gas by the therm, diesel by the gallon, and so on. To compare them, we need a single unit for energy. The two most common scientific units are kilowatt hours (kWh) and joules (J). Because 1 kW = 1 kJ/s, it's easy to convert between them; 1 kWh = 3600 kJ = 3.6 MJ. I'm going to use joules as my main unit, mostly speaking about megajoules (MJ). To convert MJ to kWh, divide by 3.6.

Gas for hot water and cooking (including running pilot lights on our 1950s stove) uses 0.69 therms a day; that's about 72.75 MJ. Last summer, we paid about $1.02 per therm, so that works out at 0.97 cents (yes, that's $0.0097) per MJ. Heating the house in winter demands a lot more energy (especially given how poorly insulated our 1949 house is; something we should really fix). Looking at our gas bill for this February/March, we used an average of 4 therms (421.9 MJ) a day, which cost us 0.93 cents per MJ. Natural gas is by far the cheapest energy we use; it could triple in price and still be the cheapest, which is just as well when you're burning through 12.75 GJ per month!

Outside of the summer, when we have to run our air conditioning, our house uses 15 kWh of electricity per day, or, because 1 kWh = 3.6 MJ, 54 MJ. (FWIW, the national average is about double that, at about 30 kWh per day.) Based on our last bill, we paid $0.14 per kWh or 3.89 cents per megajoule, which is more than natural gas, but not too bad. (I'm somewhat surprised that ignoring winter/summer heating/cooling costs we use more energy from natural gas than we do electricity.)

As I mentioned, a number of things we use have AAA and AA batteries, so let's next consider how much energy is in a battery. Batteries are usually quoted according to their mAh, but you can use the average discharge voltage to convert from mAh to joules. Alkaline long-life batteries have an average voltage during discharge of 1.225 volts, and rechargeable nickel-metal hydride (NiMH) batteries have an average discharge voltage of 1.2 volts. From those figures, we can determine that alkaline AAA batteries rated at 1200 mAh store 5.29 kJ and good NiMH cells rated at 1000 mAh store about 4.3 kJ. Similarly, for AA batteries, 2700 mAh alkaline cells store 11.9 kJ and good NiMH cells are about the same. C-cell batteries store 32.25 kJ, and D cells store about 52.92 kJ.

A reasonable deal on alkaline AAA batteries is 20 for $10, or $0.50 each, or $94.51 per MJ. Or, put another way, buying your electricity in AAA battery form is about 2430 times more expensive than buying it from the grid! We'd also need to have about 10,200 AAA batteries weighing 127.2 kg delivered every day just to cover our daily use.

Now let's look at diesel. Diesel has an energy density (aka “net heating value”) of 36.24 MJ/l, or 137.18 MJ/gal (US). Thus our daily electricity use is the same as the amount of raw energy in 1.5 litres of diesel. My local price for diesel is about $3.20/gal right now, or 2.33 cents per MJ, making it cheaper per joule than electricity but not cheaper than natural gas. (Obviously, if I were to turn the diesel into electricity, there would be some serious inefficiencies in generation, so I'm better off paying the electric company for power, and, likewise, diesel engines aren't nearly as efficient as electric ones, so an electric car might still be more economical, but not by as huge a margin as you might think.)

I have a relatively short commute to work, 5.5 miles, so on work days I travel at least 11 miles, and let's say I do those miles at 33 mpg, meaning I use a third of a gallon of diesel. My commute then costs me $1.07, but it also means that I use 45.72 MJ of energy, which is close to what the entire house uses. I only have to add a side trip for lunch or the grocery store, and our car will easily use more energy that day than every electrical appliance in our house.

It's also worth thinking about the power output of our car's diesel engine. It's rated at 140 hp / 103 kW, which we can also write as 103 kJ/s. You can see that peak energy output in a couple of ways: It's equal to almost 20 fully charged AAA batteries every second. It is equivalent to 936.4 amperes at 110 volts, which certainly sounds like a lot. It doesn't seem quite as massive if you say that it outputs an hour's worth of power for our house in 22 seconds.

Finally, let's talk about the kind of energy I use to fuel my body. The kinds of calories we talk about in food are actually kilocalories, which are defined (according to the IUNS) as 1 kcal = 4.182 kJ. Thus, just one food calorie is about 80% of the amount of energy in a AAA battery. A tablespoon of butter is about 100 kcal, or 410 kJ -- that's about 8 D-cell batteries or 79 AAAs. One pound of butter costs $2.50 at Trader Joes, and provides 3250 kcal, or 13.59 MJ. That's 18.4 cents per MJ, not as cheap as diesel or electricity, but a much better energy deal than batteries (and is much nicer on toast too!). I buy more expensive free-range organic eggs, where a carton of a dozen eggs costs $4.00 and provides about 900 kcal or 3.76 MJ, or about $1.06 per MJ. You can buy (crueler) eggs for about half that, but eggs are still much a pricier energy source than butter (fat is, after all, more energy dense than protein and carbohydrates).

Continuing our exploration of food energy, Belgian chocolate costs $2 for 90 g, providing 500 kcal, or 2.1 MJ, making it cost 95 cents per MJ. A Niman Ranch ham steak costs $5.49 per lb, and the ham has 594 kcal (or 2.48 MJ) per lb. That makes that ham $2.21 per MJ; a pretty pricey (if tasty) way to get energy. At the other end of the spectrum, a much cheaper energy source would be a 24 fl oz bottle of corn oil on sale for $2 (or $10.66 a gallon) at Albertsons; that's 5781 kcal or 24.2 MJ, or 8.23 cents per MJ, but that would hardly be very good for you. But the best deal comes from my local Henry's Farmer's Market store, which has 10 lb. bags of potatoes on sale for $0.98; that's 3583 kcal or 15 MJ, working out to 6.33 cents per MJ — still not as cheap as diesel, but it's close. And because the potato is almost nutritionally complete, it's not a bad choice for cheap human energy.

I guess I should be glad I don't run on batteries. I need about 2000 kcal per day, which is 8.36 MJ, and that's 158 D-cell batteries every day. Put another way, on average I use 96.8 watts, so if I had to be plugged in, I'd draw an average of 0.88 amps at 110 volts. If I had rechargeable batteries and could be charged at an average current of 10 amps from the wall socket with no inefficiencies, it would take me over two hours to charge — as I don't spend that long putting food in my mouth, eating food is a pretty efficient way to recharge. On the other hand, if I met my energy needs from diesel, I'd only need to down just under a cup of diesel and I'd be good to go. (In theory, I actually could also meet my energy needs with just over a cup of cooking oil, but I'm not about to go there. Yuck.)

And on that bizarre note, we seem to have reached a good stopping point. Hopefully you've learned something. I did.

## Comments

Well, I got to hand it to you for completeness. What's interesting is even with a fairly efficient car, a small saving in miles driven is a saving in energy or cost or co2 (however you measure it) that would have a huge impact if you did it in the home. And to save energy at home heating uses about 3/4 of all energy, so insulation should do more than (say) turning lights off.

To illustrate the impact of a car you can give people a yard stick of "A human being runs on the equivalent of a cup of diesel or Petrol for a whole day - how many times your body's consumption does your commute use" or

"Express your car engines power as a multiple of what your home uses on average over a day"