The Calculus Diaries - Jennifer Ouellette [69]
Carnot knew from endless experimentation that in practice, his design would always lose a small amount of energy to friction, noise, and vibration, among other factors. He knew that in order to approach the maximum efficiency in a heat engine, it would be necessary to minimize the accompanying heat losses that occurred from the conduction of heat between bodies of different temperatures. He also knew no real-world engine could achieve perfect efficiency. These considerations brought him tantalizingly close to discovering the second law of thermodynamics.
Reflections on the Motive Power of Fire did not attract much attention when it first appeared. The principle of energy conservation was fairly new and quite controversial among scientists at the time. The work began to gain notice a few years after Carnot’s untimely death from cholera at the age of thirty-six, just one among the myriad casualties of the epidemic that swept through Paris in 1832. Most of his belongings and writings were buried with him, as a precautionary measure to prevent the further spread of the disease. Carnot was twenty years ahead of his time. His work did not immediately lead to more efficient steam engines, but he did set out the physical boundaries so precisely that Rudolf Clausius and William Thomson, Lord Kelvin, would draw on his work to build the foundations of modern thermodynamics in the 1840s and 1850s.
In the latter half of the nineteenth century, a British scientist named James Prescott Joule toyed with various energy sources to see which ones were most efficient. The choice of fuel can be critical, for different fuels have different conversion rates and produce different amounts of usable energy—and once again, where there is a rate of change, we’re bound to find a derivative. Joule came from a long line of brewers, so chemistry was in his blood, as was scientific experimentation. He and his brother experimented with electricity by giving each other electric shocks, as well as experimenting on the servants.
Fascinated by the emerging field of thermodynamics, Joule jerry-rigged his own equipment at home (using salvaged materials) to conduct scientific experiments—specifically to test the feasibility of replacing the brewery’s steam engines with the new-fangled electric motor that had just been invented by measuring their conversion rates and how much useful energy they produced. It was his very own simple optimization problem.
He found that burning a pound of coal in a steam engine produced five times as much work (then known as duty) as a pound of zinc consumed in an early electric battery. His brewery was better off with the steam engines.
Food is another energy-dense substance, typically measured in calories. A calorie is the amount of heat energy produced when food is burned to ashes under carefully controlled laboratory conditions. It is not something that is “in” food per se. Another way to define a calorie is the amount of energy (heat) required to raise the temperature of one gram of water 1 degree Celsius (1.8 degrees Fahrenheit). The exact amount of energy required to do so is 4.18 joules. Unlike nutritionists, physicists almost never refer to energy in terms of calories. They prefer joules or watts—the derivative of joules, since watts measure the rate of energy (watts=joules per second). The “calories” in food are actually kilocalories: 1,000 calories equal 1 kilocalorie. So if I run four miles, I might burn 400 food calories (kilocalories); it sounds much more impressive when transposed into 400,000 regular calories. And that Power Bar I consume post-workout contains 270 food calories, or 27,000 regular calories—over one million joules, the unit of energy named after James Joule.
Let’s see how this all applies to our intrepid Wheelman, Steve Gilmore. His body is burning food (and stored fat, assuming he has any left) for energy. But all that energy is not being harnessed for any useful purpose, other than keeping him slim and incredibly fit. He also loses a fair amount