Science to Live By: Energy Part Four: Electrical Efficiencies


© J. Dirk Nies, Ph.D.

Electricity and natural gas provide about ninety percent of the energy we use in our homes. This month, I will focus on electricity, the most high value and versatile form of energy used in our economy. Specifically, I will address the generation and distribution of electricity to our homes. This information will be helpful in making informed choices regarding this vital part of our lives.

I begin by introducing to you a Frenchman who lived at the turn of the nineteenth century, prior to the age of electricity. His name is Nicolas Léonard Sadi Carnot (named after a Persian poet, philosopher and moralist of the thirteenth century, Sa’di of Shiraz). As we shall see, his fundamental insights profoundly influence how we design and operate power plants today.

True to his namesake, Sadi sought to live his life according to high moral standards. As a young man, he compiled a list of rules of conduct which, translated from French, included: “Say little about what you know and nothing at all about what you don’t know. When a discussion degenerates into a dispute, keep silent. Do not do anything that the whole world cannot know about.” In 1812, 16-year-old Sadi Carnot entered the prestigious École Polytechnique in Paris to begin his college education. As a student, he loved solving industrial engineering problems and he developed a special interest in the theory of gases. After graduation, Carnot began his career as a military engineer in the French Army.

In 1821, he traveled to Magdeburg, Germany to visit and consult with his father, Lazare, who was then living in exile. Lazare Carnot was a distinguished mathematician, accomplished engineer and had been a leading statesman and military strategist during the French Revolution and under Napoleon Bonaparte. Both father and son wished to improve the economic and political status of France and they both were fascinated by the design of machines. Regarding the importance of the steam engine, Sadi wrote: “To take away today from England her steam engines would be … to dry up all her sources of wealth, to ruin all on which her prosperity depends, in short, to annihilate that colossal power. The destruction of her navy, which she considers her strongest defense, would perhaps be less fatal.”

Upon returning to Paris, Sadi applied what he learned from his father to his investigations of the scientific principles underlying the operation of steam engines. He knew that a perpetual motion machine was impossible to construct. To him this meant that the efficiency of any machine, including any steam engine, could never be greater than 100 percent. But he wondered whether there was an inherent limit to the efficiency of a steam engine that was lower than this. Could he show by a simple, yet well-constructed argument, that there was “a limit which the nature of things will not allow to be passed by any means whatever?”

Carnot was probably the first person in the world to conceptualize a steam engine as a machine that did work when heat flowed from a higher to a lower temperature. He comprehended that motive power could be produced when heat “dropped” from the higher temperature of the boiler to the lower temperature of the condenser, somewhat like falling water provides power to a waterwheel. He also realized that a hot steam engine works only so long as there is some way to cool down and let off steam.

Through the genius of his imaginative “ideal” heat engine, his impeccable logic and simple arithmetic, he was able to show that there was a fundamental limit to their efficiency. In his Réflexions sur la Puissance Motrice du Feu (Reflections on the Motive Power of Fire) published in 1824, Carnot tackled the concepts of energy, heat, power and efficiency. His paper outlined the basic energetic relations between the flow of heat and the generation of motive power by his idealized Carnot engine. He proposed that the maximum possible efficiency of any heat engine depended upon the temperatures of its hot and cold heat reservoirs.

The theoretical and practical significance of his work was almost completely unappreciated during his short lifetime; he died in 1832 at age 36 during a cholera epidemic in Paris. But within a few decades, his insights were to become the foundation of modern thermodynamics, the science of heat, work and the flow of energy. In 1848, with the development of the absolute thermodynamic temperature scale by Lord Kelvin (absolute zero = 0 kelvin), the maximum efficiency of a thermal engine could be calculated. Stated simply, engine efficiency can be no greater than the difference between the hot and cold operating temperatures divided by the hot temperature, when temperatures are expressed in kelvins (K).

Now how does all this relate to the generation and distribution of electricity? All power plants that consume fuel (uranium, coal, oil, natural gas or biofuel of any kind) can be thought of as massive thermal engines that are coupled to huge electrical generators. They all create a hot temperature, they all convert this heat into mechanical motion, and they all use this mechanical motion to generate electricity. And because they are thermal engines, they are all subject to the same inherent limitations.

To quantify these limitations, let’s apply Carnot’s efficiency rule to a typical coal-fired power station in which the steam turbines are running at their standard operating temperature of 1,000 degrees Fahrenheit (811 K) and the temperature of the cooling water is about 95 degrees Fahrenheit (308 K). The difference between these hot and cold temperatures is 503 K. Dividing this difference by the hot temperature, we find the maximum possible efficiency of turning heat from fuel into mechanical motion is 62 percent (503 K/811 K = 0.62). This limit, which comes purely from “the nature of things,” means that, at best, no more than a 62 percent portion of the energy in the fuel can be harnessed by the power plant to do the work of spinning magnets within the wire coils of its generators to produce electrical current.

In practice, according to the US Energy Information Administration, the maximum generating efficiency of coal-fired power plants in operation today is a much lower 46 percent and most plants are less efficient than this. When losses associated with transmission and distribution of electricity across the grid to our homes and businesses are also taken into account, the effective efficiency drops even lower to 32 percent. Thus, for every three lumps of coal burned by our electrical utility company, we receive only one lump worth of energy at our breaker panel. Typically the rest of the energy is lost to the environment as waste heat.

This 3-to-1 ratio of fuel energy consumed to electrical energy delivered holds true for any fuel used by a commercial power plant (unless there are other practical constraints which drop efficiencies a little further, such as occur with nuclear power).

We’ve made great strides since Sadi Carnot wrote of the enormous commercial value of steam engines that turn fuel into power (in his day they operated at a meager 3 percent efficiency). However, using thermal engines to generate electricity means that much energy necessarily “goes up in smoke.” Electricity is so integral to our lives and our economy that, now more than ever, we need efficient, diversified, resilient and cost-effective ways to generate and deliver electrical power to our homes and businesses. I highlight the life of Sadi Carnot to inspire those, especially the young, who are called to design and implement the power systems of the future. In the meantime, when I remember to flip off the light switch as I leave the room, not only do I feel thankful that I could turn the lights on, but I am also consoled to know that I am conserving three times that much energy at the power plant when they’re off.