Counting calories in Ontario electricity: how to avoid economic hypothermia

Today is December 12, 2012—in abbreviated form, 12/12/12. In light of my post last week about the eighty-year-old retiree lugging her daily 253 liters of water up to her 15th floor high rise apartment unit in Toronto, I cannot resist pointing out that Avogadro’s Number, which is officially pegged at 6.0221415 times 1023 (or, 6.0221415 times a hundred billion trillion) represents the number of atoms in 12 grams of pure carbon-12 (the isotope of carbon that has a mass of exactly 12 atomic mass units). That is to say, 12 grams of carbon-12 contains more than 602 billion trillion atoms, give or take a few hundred trillion.

Amadeo Avogadro (1776-1856), who hypothesized that equal volumes of gas contain an equal number of atoms or molecules. Working with that, scientists over the subsequent decades refined the measurement to the number of particles of an element in a way that relates that element’s atomic weight to the number of grams of that pure element. The baseline element is carbon, and specifically the carbon-12 isotope. So Avogadro’s Number is pegged at the number of atoms contained in 12 grams of pure carbon-12. That number is estimated as more than 602 billion trillion. Needless to say, it would take a long time to count Avogadro’s Number.

What does this esoteric but fundamental metric of modern chemistry have to do with an average Toronto citizen’s daily water consumption? Avogadro’s Number is based on the gram—remember, it represents the number of particles of a substance that make up a gram-mole. And the gram used to be based on the weight of a cubic centimetre of water at exactly 3.98 degrees Celsius.

The gram is the basis of another unit of measure, which unlike Avogadro’s Number millions of people have heard of and use every day as they peruse labels on goods at the supermarket. That unit of measure is the calorie. Most people understand the calorie as something to minimize in their diet, or at least to hold in some sort of balance. In fact the calorie is a neutral unit of measure, devoid of moral judgement. It simply represents the amount of energy it takes to increase the temperature of one gram of water by one degree Celsius. For convenience, when related to human metabolism, we use the kilocalorie, or Calorie (with a capital “C”), also known as the Food Calorie. So Food Calories represent the amount of energy required to raise one kilogram of water by one degree Celsius.

As I said in the article about the 80-year-old-retiree and Olympic athlete, most people have no idea of how much energy that is. It is actually quite a lot. A stark example might help to illustrate.

Let’s say you are sitting in a tank that contains, in addition to yourself, five oil barrels worth of water. One oil barrel holds roughly 159 liters, so you’re sitting in 5 x 159 = 795 liters. A liter of water weighs just over one kilogram (1,000 grams). You would therefore need 795,000 calories or 795 food Calories to raise the temperature of that water by a single degree Celsius.

An average man generates around 2,400 Food Calories of energy every day; an average woman, around 2,000. That works out to an average of 100 Calories per hour for a man, and just over 83 for a woman.

Now, I haven’t given the starting temperature of that water. And that is a critical factor. A man who weighs 80 kilograms will be outweighed nearly ten to one by the water he is sitting in. Water is an excellent conductor of heat, so it matters hugely how warm the water is. The mass of water is so much greater than that of a man or woman. Therefore, according to the Second Law of Thermodynamics, the temperature of the water will eventually dictate the temperature of all the contents of the tank, including the man or woman (assuming that the tank itself is well insulated).

If the temperature of the water in the tank is lower than but close to that of a human’s natural body temperature of 37 degrees Celsius, then it is not an immediate problem for a man or woman sitting in the tank. But if the temperature is, say, 20 degrees, 17 degrees lower than natural body temperature, then it is a problem. The average man would have to continue belting out his 100 calories per hour for 7.95 hours just to raise the temperature of the water in the tank to 21 degrees; that is still 16 degrees shy of the human body temperature. He would have to do that at the same rate for more than 135 hours, or nearly six days, without impairment of his ability to continue to do so, in order just to raise the temperature of the surrounding water up to his own body heat. He would be dead of hypothermia long before that. The woman, with her lower caloric output and body mass, would be in trouble faster than the man. This guide from Princeton University gives a sobering idea of the effects of temperatures even a few degrees below body temperature; to convert to Celsius, use this online calculator from the U.S. National Weather Service Forecast Office.

This ought to give an idea of why we humans use other sources of energy to handle our water. Not only is water heavy, but as you can see in the example above it takes a lot of energy to heat it up. Your daily shower is so enjoyable because the water is at about 43 degrees Celsius, well above our body temperature. We could not raise the temperature of the 80 liters of water that Environment Canada says we would use over a four-minute shower under our own steam; we need to heat the water using some other kind of energy.

Many Ontarians, myself included, use electricity from the grid to do that work. Lately there has been a big debate in this province over the best way to replace major electric generation infrastructure and especially the 6,000 megawatts of coal-fired capacity. Love coal or hate it, it provides reliable large-scale power; the kind of power that reliably moves and heats huge amounts of water. Most of us Ontarians have not experienced the dearth of energy that necessitates curtailment of our daily water use. (As I mentioned a week ago, the average Toronto citizen uses 253 liters of water a day.) If we had, we might understand the inherent problems associated with intermittent electricity generation like wind and solar. We need lots of energy to move and heat water.

Wind and solar simply—physically—cannot do that job. The province would go hypothermic in a hurry if we were to really rely on wind and solar. So the only sources that can carry our water, so to speak, are coal, natural gas, nuclear, and hydro. We have mostly tapped out our hydro; that means we really only have coal, gas, and nuclear. And we have legislated coal out of our generation mix, so we are left with gas and nuclear.

Gas dumps half a kilogram of pollution for every kilowatt-hour it puts into the grid; nuclear produces thousands of times less than that for an equal amount of power.

The choice is clear.

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