Efficiency Myths

Laymen and scientists have fairly similar perceptions of the meaning of “efficiency”, but very different views of what is achievable.

Processes and machines transform energy from one form to another. Efficiency is the fraction of the input power that is usefully available at the output.

For example, the purpose of a light bulb is to produce light visible to the human eye, so we would say that its input is electric power, and its (much smaller) useful output is visible light power (aka luminous flux). The rest of the input power ends up as waste heat.

A very important category of machines is the heat engine. What heat engines have generically in common is that they involve heat flows. There are many embodiments of this idea. External combustion engines such as steam engines and steam turbines, internal combustion engines such as gasoline and diesel engines, furnaces, refrigerators, air conditioners, and heat pumps can all be thought of in heat engine terms. These applications taken together represent a large fraction of the energy “sinks” on the planet.

Although the following doesn’t quite capture the full variety of lay views of efficiency, a typical layperson’s way of thinking is to have faith in future technological progress: “As time goes on, scientists and engineers will find new ways of improving efficiency. There will always be improvements. Eventually efficiency will approach 100% for most machines and processes. As improvements are being made, we can maintain our lifestyle while reducing our energy consumption.” In a previous posting, it was noted that the efficiency with which coal is burned to make electricity is about 40%. Seemingly there is a lot of room for improvement.

This view of efficiency and progress is badly mistaken. Ironically, it is the scientists of whom the public expects the future improvements who realize best that most of the available improvements in process and machine efficiency have already been made.

Theoretical work on heat engine efficiency has been under way at least since 1824, when a French engineer named Sadi Carnot made a very significant observation about this category of machines. With the intent to apply his research to improving steam engines, he studied an abstract representation of a heat engine that involved working with a gas that undergoes processes at a constant temperature (isothermal processes), alternating with processes in which heat is not transfered into or out of the system (adiabatic processes). According to the laws of thermodynamics, heat always flows from hotter to cooler places. Such processes depend on the relationship between the volume, pressure, and temperature of the gas, called an “equation of state”. The simplest equation of state for gases is the “ideal gas law” PV=nRT that many people learn about in high school. Carnot found that if one assumes the ideal gas law applies, then the efficiency of the system depends only on the hotter temperature T2 and the cooler temperature T1: Efficiency=(T2-T1)/T2 .

It turns out that his work has much wider applications than just to ideal gases. His abstract engine, now called the “Carnot cycle”, is actually the upper limit on the efficiency of many practical processes. We can see from the formula that, in order to have an efficiency approaching unity (aka 100%), it it necessary to either have the hotter temperature T2 approach infinity, or the lower temperature T1 approach absolute zero. Yet intuition should warn us that achieving either of those itself costs an enormous amount of energy! This means that in practice, heat engines must make do with whatever temperature differential they can get, and they can never approach 100% efficiency.

Let’s return to the observation that coal fired power plants actually achieve about 40% efficiency. The reality is that there ISN’T a lot of room for improvement, given coal combustion can only be driven so hot, and the spent heat has to be released to the ambient temperature. Power plants fueled with natural gas are somewhat more efficient than their coal counterparts mostly because gas burns hotter than coal. Small incremental efficiency improvements can still be made, yes, but most of the easy efficiency improvements have already been wrung. At 40% efficiency we are already approaching the asymptotic limits of what is possible. Future improvements will suffer from the law of diminishing returns, and increasingly expensive efforts will yield ever smaller results.

With regard to devices that are not heat engines, there are often other good theoretical models that impose limits of efficiency well below 100%. Important devices of interest include light bulbs. Incandescent bulbs have an efficiency around 2%, fluorescents around 10%, and light emitting diodes (LEDs) up to about 20%.[1] With light bulbs, part of the trick to achieving high efficiency is limiting the emission spectrum of the light to the visible range. Light sources differ so much in how they produce light that their theoretical maximum efficiency must be addressed using different models. For instance, incandescents can be modelled approximately as what physicists call “blackbody radiators”. We won’t go into the details of what that means, but from this model it is clear that incandescents are inherently inefficient because they have a very wide emission spectrum that reaches well beyond the visible, particularly on the infrared side (which has longer wavelength and lower frequency than visible light).

In general, the lesson is that all energy transformations involve loss. Therefore it is important to minimize the number of transformations that our energy supplies must undergo before they are put to their final use. Thus efficiency is always something of an obstacle, but often not the only one. For instance electricity storage techniques (such as rechargable batteries, capacitors, and pumped water reservoirs), are held back by their cost, the limited availability of certain resources, ecology, and energy density as well as efficiency.

[1] http://en.wikipedia.org/wiki/Luminous_efficacy

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