So... not to stir up a hornets nest... but everyones aware that electric cars produce more pollution than gas right?
Let's look at some facts here. First off, the efficiency of a thermal power plant is somewhere around 33% to 48%, at least according to wikipedia. Let's split the difference and say 41% for a thermal plant. The typical thermal efficiency of a a gasoline engine is about 18% to 20%. Let's split the difference and say 19%. Thus, a thermal power plant is more than twice as efficient as a gasoline engine in terms of changing chemical potential energy to useful output.
But there are some caveats. Firstly, the electricity needs to be transmitted. High voltage power lines are extremely efficient, about 94% according to this article. That means that the chemical energy (lets assume from coal) reaching the charging station is 41% x 94% = 38.5%. And then there is the charging process. According to this article, the charge efficiency of a Li-Ion battery is about 97%, which makes sense to me, as batteries usually don't run too hot. The charging devices however probably are responsible for some loss. Let's assume they are 80% efficient. That gives us 38.5% x 80.0% x 97% = 30%. Thus, according to this, 30% of the coal chemical potential energy makes it to the engine.
But what about engine efficiency? Well electric motors run very cool, and have very high efficiencies, typically around 90%. I wouldn't be surprised if Tesla's motor is better. This means that if a coal power plant powered a Tesla, 30% x 90% = 27% of the energy would reach the wheels of the car, compared with a gasoline powered car, where 19% of the gasoline's potential energy comes out of the engine, never mind the losses in the transmission lines. Thus, a coal powered Tesla is 40% more energy efficient than a gasoline powered car.
However, there is one problem. Generating energy by coal produces more CO2 than generating it by gasoline. According to this article, coal generates about 215 pounds CO2 per btu of energy, while gasoline generates 157 pounds CO2 per btu. However, even with this, by my calculations, an equivalent gas powered car still emits 3.8% more CO2 than our coal powered Tesla.
Elon Musk made this claim in an interview, that even if a coal power plant generates the electricity, a Tesla still emits less CO2. My referenced back of a napkin calculations above support this assertion.