The Calculus Diaries - Jennifer Ouellette [68]
The Los Angeles Wheelmen might expend a great deal of energy biking up Fargo Street and back down again, and feel as though they’ve definitely gotten a good workout. But from a physicist’s perspective, nothing has been done. Energy is useless unless it can be harnessed to perform some task. For example, the battery packs in the Green Microgym must be connected to some kind of load before the energy they produce can be useful—say, to operate the fans or the stereo system. Energy, when harnessed, produces work, which has a very specific meaning in physics, namely, a force applied over a given distance (W = fd ). How much work a moving object is capable of performing is precisely equal to its kinetic energy.
There are many different kinds of energy that can change into each other. For example, you could also get work by burning fuel. Burning coal in power plants produces electricity by converting thermal energy (heat) into mechanical energy in a turbine. Electrical energy can change into mechanical energy. A battery relies upon a series of chemical reactions to produce an electrical current; once all the chemicals have been used up and converted into energy, the battery goes dead. And an electrical generator converts mechanical energy into electrical energy, which can then be used to power most of modern technology. All these conversions are examples of turning stored potential energy into kinetic energy.
Heat is wasted energy, for the most part, and it’s the reason no machine, no matter how well designed, can ever attain 100 percent efficiency. We know this because of the work of Sadi Carnot. Born in 1796, Carnot was the son of a French aristocrat named Lazare Carnot, who was one of the most powerful men in France prior to Napoléon’s ignominious defeat; the family fortunes rose and fell dramatically throughout young Sadi’s life in conjunction with that of the monarchy. Named for the Persian poet Sadi of Shiraz, Carnot learned mathematics, science, language, and music under his father’s strict tutelage. At sixteen, he entered the École Polytechnique, studying under the likes of Claude-Louis Navier, Siméon Denis Poisson, and André-Marie Ampère.
It was not a peaceful period in France’s history. Always opposed to the monarchy, Carnot joined in the fighting when Napoléon briefly returned from exile in 1815. When Napoléon was defeated in October of that year, Carnot’s father was exiled to Germany. He never returned to France. Carnot the younger, dissatisfied with the poor prospects offered by his military career, eventually joined the General Staff Corps in Paris and pursued his academic interests on the side.
In 1821, he visited his exiled father and brother in Germany. Apparently there was very little to do in exile, so the men took to debating the pros and cons of steam engines. Steam power was already used for draining mines, forging iron, grinding grain, and weaving cloth, but the French-designed engines were not as efficient as those designed by the British. (The efficiency of those early French engines was as low as 3 percent.) Convinced that England’s superior technology in this area had contributed to Napoléon’s downfall and the loss of his family’s prestige and fortune, Carnot threw himself into developing a robust theory for steam engines.
Carnot’s father died in 1823. That same year, Carnot wrote a paper attempting to find a mathematical expression for the work produced by one kilogram of steam; it was never published. In fact, the manuscript was not discovered until 1966. In 1824, he published Reflections on the Motive Power of Fire, which described a theoretical “heat engine” that produced the maximum amount of work for a given amount of heat energy put into the system. The so-called Carnot cycle draws energy from temperature differences between a hot reservoir and a cold reservoir (and