Last time, we discussed the way we measure energy, and how we measure the rate at which we use it. Keeping with this idea, let’s think about what it means in terms of energy sources. There will be a little math this time. Not much, I promise. This is by far the most calculation we will need to do to compare energy sources.

Recall that we said that Joules are used to measure energy. Energy is defined as the ability to do work, which makes sense, but it doesn’t say anything about how fast. That’s where we use Watts.

So what is a Joule? It is the quantity of work represented by moving 1 Kg for 1 meter, so that it accelerates at 1 meter per second. I feel obliged to tell you this formal definition, which I know isn\’t clear or helpful, but which Wikipedia covers nicely. But it is also the case that energy and heat are equivalent, so we will think in terms of heat. This will be far more illuminating, I think.

How much energy does it take to heat up a cup of water? Of course, it depends on the cup, so we do have to get specific to know. If you have a measuring cup filled to the 1 cup line, this is 240 milliliters. With water, the math is easy, because the mass of the water is then 240 grams.

About 4.2 Joules will heat one gram of water 1 degree C. Let’s suppose you want to heat a cup of water from room temperature to 45 C (113 F) to make some tea. Room temperature varies, of course, but let’s assume it is 22 C (72F). We have to add 45 minus 22 or 23 degrees to the temperature. At 4.2 Joules each, we need about 97 Joules for each gram. Let’s round to 100 J, and we should recognize that we are also neglecting the losses that inevitably happen. So 100 J/gram x 240 grams=24000J is necessary to heat our cup of water.

Thinking back to power usage, if we are going to do this in 30 seconds, we need 24000J/30s or almost 0.8 kiloWatts. We need the same energy, no matter what the rate, so Joules are a good way to measure it. By comparison, this would be 0.007 kiloWatt-hour. Not such an inconvenient measure, in this case, but I still prefer thinking in terms of the energy in traditional energy units, because when we start to think about how much fuel this will take, it will simplify things. (I don’t mean to suggest that your microwave will only use 24 kJ- there are a lot of things going on that require much more power than that. But if we had a perfect way to use the energy to heat the water, 24 kJ would do it, so I will stick to this to do comparisons.)

A lot of work has been done figuring out the energy in a quantity of fuel. The exact same sort of thing is done for food, but instead of Joules, we use Calories. I won’t go there, because it isn’t relevant, and Calories used for food are not calories used by chemists and engineers, but just want you to recognize that the quantity of energy in a substance is being measured, whether for lumps of coal or corn flakes. (Because someone will wonder, 1 food Calorie is 1000 calories an engineer would measure).

One gallon of gasoline is about 6.25 pounds. It contains about 100 million J of energy. For our cup of water, we need, then, about 6.25/100000000*24000= (after some conversions) about 1 microgram of gasoline!

Let’s compare this to coal. Coal contains about 50 million Joules per pound, so 6.25 pounds of it contains 312.5 million joules. We could go through a similar calculation as before, but the ratio of the energy per an amount of weight will tell us how much coal we need. 100MJ/312MJ*2.8 micrograms= 0.9 microgram of coal. Since both coal and gasoline are largely hydrocarbons, the amount of CO_{2} produced would scale similarly. Neglecting all the other stuff each one belches out, about 2/3 less CO_{2} is produced by the coal. (I admit that this surprised me when I saw it).

Now, let’s consider lithium batteries. These are sort of the gold standard for power density. 6.2 pounds of batteries, among the best ones available, contains about 5000J. We then need 100MJ/5KJ x 1microgram or 200 milligrams of batteries to heat the same water. 20000 times the mass of the gasoline we need. This calculation clearly has implications for electric vehicles, too.

This comparison neglects a lot- I am not knocking electric cars or suggesting coal-fired station wagons would be our best bet. But this exercise brings into stark relief what the differences in energy density mean. Don’t read too much into the numbers yet; right now, all we have considered is how dense the sources are. We will return to things like what it takes to make the energy, and eventually talk about losses and pollution.

Next time, we will consider the energy available from run-of-the-mill power plants, solar installations, and wind farms, and see how they compare. We’ll look at nuclear power, too, only with an eye to comparison, not as advocacy.