"the manufacture of 1 kWh of lithium-ion battery storage requires 400 kWh of energy, the factory would require 20,000 GWh of electricity per year to manufacture all these batteries."
The 20,000 GWh figure is clearly bollocks, one factory a hectare in size is not going to be using the same amount of electrical power as the whole of Nigeria.
edit - also, one thing I do not understand with their argument, is if Tesla's illustration is really supposed to show that the factory can run entirely on rooftop solar, why would it feature around 100 large wind turbines dotted all across the hillside?
Here's an offtopic thing which annoys me and many people do wrong. It is important to do significant figures right.
2.28 GW is the most you should ever write with that calculation. What you wrote went down to hundredths of a watt (if I can count).
Nobody should care about the third significant figure in such a comparison, much less the twelfth. The second digit is even of questionable accuracy. Strict significant figure rule following isn't important in casual contexts, but deciding which digits are actually relevant is imporant. Is accounting for leap days really important here?
Also, the output is roughly the installed maximum capacity of the Hoover dam, but about 5 times larger than it's actual yearly production.
So currently for batteries used by Tesla, that is getting the lithium from Chile and Argentina, then transporting it to battery factories in China, then shipping them to their car factory in California, as opposed to getting lithium from Nevada, to a factory in Nevada, to the other side of the same Nevada factory, as you also make the cars there.
The total embodied energy is going to get absolutely slashed.
edit - btw, I accidentally fat fingered the down button on your comment that had the link to - http://www.withouthotair.com/ - sorry. I hope that isn't what prompted you to remove the comment.
No that wasn't the reason, though its nice of you to mention it.
I'd re-read the withouthotair site the other evening after seeing Elon's presentation, as he made a similar case regarding the area of the USA needed to be powered by solar. I was a bit bummed out by the conclusion for the UK and wondered what the global equivalent was, as the UK is low on solar. I then noticed I'd skipped a chapter that does the rough calculations for other regions (http://www.withouthotair.com/c30/page_231.shtml) the basic answer being that Solar may just save us, but it'll be an incredible amount of work, both political and engineering.
(Which is basically the same answer as for the UK, though in the UK solar is mostly replaced with wind/wave/hydro as we're relatively blessed with those).
I think he may be underestimating the future efficiency gains.
There is already 30% efficient directly illuminated multi-junction PV on the market ( http://www.emcore.com/wp-content/uploads/ZTJ-Cell.pdf ), they are just so damn expensive at the moment that only the space industry are using them.
Also, while it is a huge amount of work, it is no worse than many other industries, the economics are starting to make it a good investment for big finance, and we are not likely to run short of either silicon or lithium along the way.
The Without Hot Air site seems to have got its sums wrong. It continually makes the point that we'd need to cover the whole UK in renewable energy generation, and that still wouldn't be enough.
However, we already generate 7.5% of our energy from renewables and clearly 7.5% of the country isn't covered in windfarms/solar/biofuels. Therefore he must have made a mistake somewhere: if reality disagrees with theory, the theory must be wrong.
7.5% of our energy or 7.5% of our electricity? It's the latter. We're still consuming the output of the North Sea plus a little bit more in petrol and diesel.
The 20,000 GWh figure is clearly bollocks, one factory a hectare in size is not going to be using the same amount of electrical power as the whole of Nigeria.
edit - also, one thing I do not understand with their argument, is if Tesla's illustration is really supposed to show that the factory can run entirely on rooftop solar, why would it feature around 100 large wind turbines dotted all across the hillside?