# Internal Combustion Engines

Internal combustion engines are one example of thermal heat engines with widespread applications in power generation as well as in transportation systems. Basically, these devices burn a mixture of hydrocarbon fuels with the ambient air inside a combustion chamber (cylinder) to produce power. The power is transmitted through a shaft which can run a generator, drive the crankshaft of an automobile, or provide thrust to propel a jet aircraft. Among the most common internal combustion engines are gasoline and diesel engines and gas turbines. These devices are discussed in detail when we cover transportation systems in Transportation.

## Contents

#### Efficiency

Wouldn’t it be great if we could build a machine which puts out more work than we put into it? This machine would constantly create new energy and we would never have an energy shortage. If that were possible, we could build machines that, once started, did not need an additional expenditure of energy. This would be ideal, and many people have dreamt of making such machines. These machines, commonly known as “perpetual motion machines” (PMM), could operate forever. Sound too good to be true? It is. In the real world, all machines produce less work than the energy that goes into them. Useful energy is always lost as heat. That’s the reality but, as shown by those who attempt to design PMMs, not everybody chooses to accept it. Unfortunately, the first law of thermodynamics precludes constructing such machines.

Not only is the construction of such engines impossible, the second law of thermodynamics prevents the construction of engines that can convert “all” or “nearly all” of the heat input into useful work. This can be understood by noting that heat is a less ordered form of energy than work and complete conversion of heat to work would accompany a reduction of entropy (in violation of the second law), which is impossible.

Many inventors have proposed (and still propose) devices that violate the first and second laws of thermodynamics. Some, like Maxwell,( 1 ) do so from a purely philosophical standpoint, but many have actually dared to propose such machines as practical devices.( 2 ) Many have even received patents and accumulated great wealth from their “inventions”. As you may have guessed, nobody was ever able to produce a working prototype.

Question: One of the consequences of the second law is that when-ever energy is transformed from one form to another, at least some of the energy changes to a more dispersed form such as heat (recall that heat is a less ordered form of energy). Is it possible to design devices that transform energy in the opposite direction, i.e. take it from a dispersed form to a more concentrated (ordered) form?

Answer: The second law only precludes going from disorder to order for isolated systems. Many practical devices are not isolated and thus do not have to follow this restriction. For example, an air conditioner works by removing heat from a room and dumping it outside at a higher temperature. In this case we are re-concentrating energy. To do so, however, we need to spend even more energy in the form of electricity.

Question: Our solar system has been moving around the sun for a very long time and does not seem to slow down. Can the motion of the solar system be considered an exception to the second law?

Answer: If we look at the grand scale, motion of the Universe indeed conforms to the rules set out by the laws of thermodynamics. Energy is continuously poured in, externally and on a massive scale, to power the motion of all the galaxies and the motion of all that is within them. Even the solar system has to adhere to the laws put forth by nature!

#### The Ceiling on Efficiency

In an attempt to improve the efficiency of the early steam engine, the French scientist Sadi Carnot proposed an ideal engine that works between two reservoirs at different temperatures. Heat is removed from a source at temperature Thot, part of which is discarded to a sink at temperature Tcold; the remainder is supplied as work. The best this engine can do is to achieve a loss of entropy from the source that just balances the gain in entropy by the sink. The net entropy production will then be zero. Under such ideal conditions, the efficiency of the engine is the maximum attainable and is equal to

${{\eta}_{ideal}}={{\eta}_{max}}=1-\frac{{T_{cold}}}{{T_{hot}}}\qquad \qquad(1)$

Tcold and Thot are temperatures of cold and hot reservoirs and must be expressed in kelvin. Kelvin temperatures are calculated by adding 273 to temperatures expressed in degrees Celsius.

Question: An inventor claims to have designed a cyclic engine that takes 1,000 Joules of heat and converts it entirely to work. How would you rate this claim?

Answer: His claim is impossible. The engine removes some heat from a reservoir, resulting in a drop in its entropy. Since work is perfectly ordered, no additional entropy is created. The net result is a decrease in the total entropy of the universe, in opposition to the principal of increasing entropy as stated by the second law.

Example: The same inventor comes back a few months later after having worked on a second engine. His new claim is that his engine can remove 1,000 J of heat from a source at 500 K, dump 400 J to a sink at a temperature of 250 K, and use the remaining 600 J as work to run a shaft. Would you invest in his company?

Solution: The ideal efficiency of an engine working between these two temperatures is 1-250/500 = 0.50; at best only 50% of the input energy can be converted to work. The proposed engine has an efficiency of 600/1000 = 0.60, higher than the ideal efficiency of 50%, which is an impossibility. Because of frictional losses, we can expect actual efficiency to be even lower than 50%. Once again, his claims cannot be realized.

#### First-Law and Second-Law Efficiencies

Real engines can never achieve the ideal efficiencies given by Carnot. First, real engines have always frictional and conductive losses that cannot be completely eliminated, thus limiting their maximum performance. Second, depending on its intended end use, a device may not be able to utilize the full potential of energy used to operate.( a ) To quantify these limitations, two types of efficiency are defined.

The first-law efficiency is defined based on the first law principle of conversion of one form of energy to another, without any consideration to the quality of the energy resource. First-law efficiency is input/output efficiency, i.e. the ratio of energy delivered in a desired form and the energy that must be expended to achieve the desired effect. It does not differentiate between the qualities of the energy sources. The first-law efficiency can be less than (heat engines), equal to (friction), or greater than (refrigerator) one. In the latter case, it is commonly referred to as “the coefficient of performance” (see below).

Question: What is the first-law efficiency for a heat engine? For an electric heater? For an electric motor? For an electric light bulb?

Answer: A heat engine is a device that converts chemical energy (fuel) to mechanical work. Therefore, the first-law efficiency is the ratio of shaft work to heat input. Typically, first-law efficiencies of 25-30% can be achieved for automobile engines. An electric heater is a device for converting electrical energy to heat; in this case the first law efficiency is the ratio of heat given off to electric work needed to operate the heater (compare this to the first law efficiency of the heat engine!). Aside from small radiant losses through the heating coil, electric heaters are very efficient devices for their stated purpose and efficiencies close to 100% are achievable. Electric motors lose some energy through friction and coil heating and are generally around 90% efficient. Incandescent light bulbs are designed to convert electricity to light. A major fraction of the energy is, however, lost through heating the filament. The efficiency is rather low at around 5%.

Unlike the first-law efficiency that ignores the qualities of the energy, the second-law efficiency compares the efficiency of an actual device (1st law efficiency) to that of the same or a similar device operated under ideal conditions. It measures the actual energy used as compared to the minimum amount of energy needed to accomplish the same task, i.e. the second-law efficiency is the ratio of the actual efficiency to that of an ideal device. By definition, the second law efficiency of all ideal devices is equal to one, and for all real devices is smaller than 1.

Question: What is the second-law efficiency of a heat engine?

Answer: To find the second-law efficiency, we must compare the heat engine to an ideal heat engine. An ideal heat engine is an engine that does not experience any frictional losses or other irreversibilities. The second law states that this engine must be a Carnot engine with the maximum theoretical efficiency given by equation 1. For example, an engine operating between a combustion temperature of 1,600 K and an exhaust temperature of 400 K has an ideal efficiency of 1-400/1600 = 0.75. For an automobile with an actual efficiency of 30% (first-law efficiency), the second-law efficiency is 0.3/0.75 = 0.40. That is, the engine operates at only 40% of its full potential.

Question: Air pollution is considered by many to be a direct result of incomplete (inefficient) combustion. Comment!

Answer: The common assumption that air pollution results from inefficient burning of fossil fuels is not correct. When a hydrocarbon fuel such as natural gas (methane) is burned in air, the product of the reaction is a mixture of water, carbon dioxide, carbon monoxide, oxides of nitrogen, and a number of other gases in such concentrations that maximize the overall entropy. Cleaner fuels, better burners, and more exotic catalysts, although they increase combustion efficiency and reduce the pollutant emissions, cannot eliminate the air pollutants all together. In other words, complete combustion (of hydrocarbons), defined as burning with carbon dioxide, water, and molecular nitrogen as their only end products, is not possible and is directly in violation of the second law of thermodynamics.

## References

(1) James Clerk Maxwell (1831-1879) was a Scottish mathematician and physicist, most known for his theoretical formulation of laws of electromagnetism.

(2) Angrist, S. W, “Perpetual Motion Machines,” Scientific American, 218:114-122, January 1968.

(3) Toossi Reza, "Energy and the Environment:Sources, technologies, and impacts", Verve Publishers, 2005

(a) The students who take a more advanced course in thermodynamics will learn of a new term, “exergy” or “availability,” that distinguishes the part of energy in a system that can be converted to work from the part that cannot (is unavailable). Unlike energy, exergy is not conserved and destroyed in all real processes.

El-Sayed, Y., The Thermodynamics of Energy Conversions, Elsevier Direct Science, 2003.

Cengel, Y. A., Heat Transfer: A Practical Approach, McGraw-Hill, Inc., 1998.

Rifkin, J., Entropy, The Viking Press, 1980.

El-Wakil, M/ M., Power Plant Technology, McGraw-Hill, Inc., 1984.

Energy and Buildings, Science Direct Elsevier Publishing Company. An international journal publishing articles about energy use in buildings and indoor environment quality.

Energy Conversion and Management, Science Direct Elsevier Publishing Company. This journal focuses on energy efficiency and management; heat pipes; space and terrestrial power systems; hydrogen production and storage; renewable energy; nuclear power; fuel cells and advanced batteries.

Energy and Buildings, Science Direct Elsevier Publishing Company, An international journal dedicated to investigations of energy use and efficiency in buildings.