Carbon Footprint

Copyright ©2011 by Paul Niquette.  All rights reserved..

he puzzle included this break-down of electric power sources in the U.S. along with the bar chart below, which shows carbon footprint relative to the heat of combustion from various sources.  Let us prorate emissions of CO2 based on the respective contributions to the power grid of the main energy sources...

  • 44.9% Coal @ 92.9 g/MJ ....................... 39.5g/MJ
  • 23.4% Natural Gas @ 50.3 g/MJ ............ 11.7g/MJ
  • 31.7% Non-Fossil @ 0 g/MJ ................... 0.0g/MJ
...for a total of 53.5 g/MJ, which compares favorably to gasoline-derived heat @ 65.0 g/MJ.
hat comparison would seem to give us the solution to the puzzle... 
What is your estimate for the carbon footprint of the electric car compared to the gasoline powered car?

{a} Smaller

...however, that comparison also implies that one MJ of heat derived from burning coal at a power-plant is equivalent to one MJ of heat derived from burning gasoline inside a car's engine.  Sophisticated solvers recognize that many technical factors have been left out of the analysis, as depicted in the schematic model below...

A complete solution calls for making key assumptions beyond the scope of the puzzle.  For the plug-in electric car, those MJs of heat at the site of combustion in the power plant must be grossed up to overcome a myriad of losses in electrical energy on the pathway to becoming MJs of work at the wheels of the electric car.  Producing all that extra heat from burning fossil fuels must then be attributed to the electric car, thereby increasing the effective size of its carbon footprint.

Reasonable assumptions in the model can result in a wide range of outcomes. 

f, for example, the break-down of electric power sources included a higher percentage of coal in the mix (some regions in the U.S. come to mind, along with certain countries in the world, especially in the Far East), the carbon footprint of the electric car would be larger than previously shown.  Again, let us prorate emissions of CO2 based on respective energy contributions...
  • 44.9%  58.2% Coal @ 92.9 g/MJ ....................... 39.5  54.0g/MJ
  • 23.4%  22.0% Natural Gas @ 50.3 g/MJ ............ 11.7  11.1g/MJ
  • 31.7%  19.9% Non-Fossil @ 0.0 g/MJ ....................... 0.0g/MJ
...for a total of 53.5 65.1g/MJ which compares unfavorably to gasoline-derived heat @ 65.0 g/MJ.
The carbon footprint of the electric car is sensitive to the local mix of power-plant sources and can be larger than the carbon footprint of the gasoline-powered car!

Technical Observations:

Internal Combustion Engine Inside the Gasoline Powered Car

The carbon footprint of any vehicle must cover the requirements of tractive effort.  The 'pathway' from heat-to-work may be exceptionally short for the conventional car but not without losses. The prime mover in your car is an internal combustion engine (Otto Cycle).  Like all heat engines, its efficiency is framed by the laws of thermodynamics and thus requires more MJs of heat to be produced inside its combustion chambers than the resulting MJs of work ultimately delivered at the wheels. 
Prime Movers Outside the Electric Car
The gas-turbine is the prime mover in some electric power plants.  It is also an internal combustion engine (Brayton Cycle), which captures MJs of heat from burning fuel within its combustion chamber.  The working fluid is air, and the design maximizes its efficiency in continuously converting heat-to-work -- though not delivered directly to the wheels of a car. 
Natural gas has the smallest carbon footprint for the fossil fuels under consideration here.  Methane is 25.0% hydrogen by weight compared to octane which is only 15.8% hydrogen.  Hydrogen is mighty energetic stuff, producing 4.3 times carbon's energy per pound, while emitting only H2O into the atmosphere.
The coal-fired steam turbine is the predominant prime mover in electric power worldwide (80% by some estimates).  In its solid state, coal is not suitable for burning inside an engine. Thus, an external combustion engine (Rankine Cycle) requires MJs of heat produced outside a 'boiler' to be conducted by a temperature difference to superheat the working fluid (water vapor) inside. That impacts thermal efficiency and enlarges the carbon footprint for coal. 
Coal may be the most abundant hydrocarbon in the U.S., but according to the chart, the carbon footprint for coal is 40% larger than that for gasoline -- or diesel (fuel oil) for that matter.  To match the heat energy produced by the fire inside your car's engine, the coal-fired generating plant, which may be far way and out of mind, must emit typically 40% more CO2.
Electrical Generators Outside the Electric Car
Whether spun by gas-turbine or by steam turbine, conversion to electrical power is accomplished by generators.  Not limited per se by thermodynamics but, depending on a number of variables including load factor, electrical generators can be quite efficient.  Still, some MJs must be given up in the rotating machinery (friction, windage), which needs to be taken into account in the calculations. Meanwhile, carbon footprints for non-fossil power plants (hydroelectric, nuclear fission, solar-thermal, wind-turbines) are not affected by losses.
Electrical Distribution Outside the Electric Car
The schematic above shows electric power being stepped up in transformers at the power station for efficient delivery via the transmission grid.  MJs are lost in the transformer (core losses) and in the transmission line (copper losses, corona discharge), and more losses during the step-down through substations and distribution transformers into neighborhood wiring.
Charging and Discharging the Battery Onboard the Electric Car
Obviously, the electric car cannot directly use power from stationary facilities but must operate instead from stored charge in onboard batteries for supplying power to the traction motors.  Those conversion losses inside the car must also be charged (no pun intended) to the sources of heat at the power plant in calculating carbon footprint for the electric car.

Incidental Comments:

  • A tripartite discipline has been invoked here called prescinding, with attention in this case given exclusively to #1 Technical Factors, laying aside #2 Economic Issues (abundance/scarcity of resources, cost/pricing trends...) and #3 Human (Political) Considerations (health and environment, international dependencies).
  • Strictly speaking, carbon dioxide is not an atmospheric pollutant.  It is, after all, a principal feed-stock for the green plants. 
  • The gasoline-powered internal combustion engine is often cast as the environmental villain.  For sure, it does emit plenty of pollutants -- particulate matter, nitrogen oxides, sulfur dioxide, benzene, butadiene, formaldehyde, carbon monoxide, acetaldehyde.  But then so do power plants.  Even more. These environmental insults have been excluded from consideration in the carbon footprint puzzle. 
  • By the way, the bar-graph shows that the burning of wood has a carbon footprint 22% larger than the burning of either gasoline or fuel oil for any given amount of heat energy.  That puts in doubt environmental benefits of many popular green technology proposals especially for transportation. 
  • With regard to sustainability, the carbon footprint of biofuels must not be ignored.  As mentioned in 2009: "Whereas some biofuels can act in place of petroleum in internal combustion engines for cars and buses and trucks, there is this one critical question: If it takes more than one unit of energy from either fossil fuel or biofuel to produce one unit of energy from biofuel, what’s the point?"


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