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# Theoretical Maximum Efficiency: Electric vs Internal Combustion

The stark disparity in efficiency figures of electric and conventional vehicles is an oft cited reason for pursuing the electrification of our personal transportation infrastructure. However, there is a bit more nuance to the engineering reality than first meets the eye.

The thermal efficiency of a heat engine, of which the internal combustion engines found in automobiles are a common type, is defined as the ratio of useful work done by the engine to the quantity of heat energy provided to that device. Technological advancements have allowed production gasoline engines to attain thermal efficiencies approaching 40% in recent years. While this value is unimpressive in an absolute sense, it also reflects an admirable feat of engineering. To understand why, we need to consider the laws of thermodynamics.

From the first law of thermodynamics, the conservation of energy, we know that the efficiency of such an engine, or really any appliance, is limited to 100%. That is, one cannot derive more energy from the output of an engine than the energy yielded from combusting its chemical fuel. This fact makes intuitive sense and meshes well with our everyday understanding of energy. However, what is less obvious is that there is a further, more severe, limit to a combustion engine’s efficiency.

The second law of thermodynamics states that entropy, a quantitative measure of disorder, will always increase over time in an isolated system. For the purposes of this discussion, the practical upshot of the second law is that no matter what sorts of engineering tricks are implemented, there is an absolute, well-defined limit to the efficiency of a heat engine. This limit is known as the Carnot efficiency; it is derived by considering an idealized, reversible heat engine, operating between two thermal reservoirs. The Carnot efficiency is dependent only on the temperatures of the two thermal reservoirs supplying and sinking energy for the engine. The greater the difference between these temperatures, the higher the efficiency.

For typical gasoline engine combustion temperatures, while operating in reasonable ambient conditions, the Carnot efficiency can be calculated to be approximately 60%. With this theoretical maximum in mind, the 40% efficiency figure given above no longer seems as unimpressive. The Carnot efficiency of a theoretical diesel burning engine is a bit higher, as the combustion temperatures observed in a real diesel engine are greater than those found in a gasoline engine.

While electric motors, like everything else, are governed by the laws of thermodynamics, their efficiency is not delimited to a specific value as they are not heat engines. From a thermodynamic standpoint, the theoretical maximum efficiency of an electric motor is 100%; in actuality, this value is not attainable, as a motor constructed with real materials will have numerous small mechanical and electrical losses. For example, the induction motor(s) found in a Tesla Model S have a peak efficiency of approximately 94%. Other makes and models have attained even more impressive figures. Of course, it is important to realize that the efficiency of an electric motor or internal combustion engine is just one slice, albeit a critical one, of the overall efficiency of the vehicle. The end-to-end efficiency of an electric vehicle is highly dependent on the source of electricity from which it is charged. Gasoline powered vehicles also have numerous, though different, upstream considerations that have a significant impact on their overall net efficiency. Further, both gasoline and electric drivetrains have other sources of loss downstream of the power plant, primarily due to friction in the gearbox and other components.

It is also vital to stress that while attaining high efficiency is a laudable and universal engineering goal, there is far more to the comprehensive environmental impact of a vehicle. Modern electric vehicles offer a drastically higher efficiency and a lesser net environmental impact when compared to conventional internal combustion engine powered cars. The difference in environmental footprint can be further enhanced by the adoption of grid-connected renewable energy sources.

For a limited time, the Solar Initiative is offering \$300 per month for up to 36 months toward an EV loan or lease. Any EV acquired with assistance from this program must be a four wheeled vehicle that is registerable for road use in the State of Rhode Island and is powered exclusively with electricity supplied by an internal battery pack. This program is limited to 20 recipients. The application process is open through May 21st, 2022.