Milk and the Second Law

Picture this. You go to a store asking to buy a gallon of milk. You are presented with two options:
First, a gallon of milk produced by milking the cow that the store owner, who also happens to be a farmer, keeps in her backyard.  The cow eats grass (which grows for free on her sprawling back yard), is healthy and, other than the occasional methane emission, is fairly clean. That gallon of milk costs about a buck fifty ($1.50)
Your second option is much cooler. The farmer takes the milk produced by the same cow.  Then she bottles those methane emissions we mentioned earlier (i.e., the cow farts). Both the bottled gases and the milk are shipped to a processing plant. There, the milk is fractioned into individual proteins, lipids, carbohydrates and water. The separation process is quite energy intensive, but fear not, the processed farts allow you to recoup about 15% of the energy required to separate the milk (the rest comes from coal or natural gas). Once the milk is separated, then it is reconstituted into better, purer, better defined milk.  It then gets packaged and sent back to the store, where the store owner offers it to you for about a hundred bucks ($100).
Which would you choose?
Well, if you are the US government, clearly you pick the second option.
There is a program being funded by ARPA-E, the super advanced division of the Department of Energy dealing with alternative means to fuel our growing national fleet of cars, that does what is equivalent to the second cow.
It goes like this: they take electricity (which is produced cleanly through wind turbines, PV cells, or slightly less green from natural gas) and combine it with carbon dioxide (CO2) in a “super bug”. This super bug, a weird species of bacteria that can only be found in the most inhospitable corners of the planet, is capable of combining electricity with CO2 to produce larger chain hydrocarbons, typically up to C5 and C6, at about 9% efficiency. Those can then be fermented through a less scary bug, beer yeast, to produce up to about 20% ethanol, or a heavily engineered yeast to produce about 4% butanol or propane diol. In other words, you can take electricity and convert it to an ok substitute for gasoline at about anywhere from 3% to 18% efficiency.  That “gasoline” will then be burned in an internal combustion engine for a car at about 20% efficiency, resulting in an overall system efficiency of conversion of energy-to-miles of anywhere between half a percent to 4%. It would only cost about $100 to do your daily commute (of roughly 20 miles).  Sweet, right?
Or… Maybe you could just take that electricity you had at the very beginning, stick it in a battery and run an electric car.  That would have an energy-to-miles efficiency of about 90%, give or take. Your daily commute would cost $1.50.
In the real world, no one would buy the $100 gallon of milk. If you were the store owner, you would see the 125 people that live in your town and like milk go to your store, and every single one of them would buy the milk that came directly from the cow. Problem is you only have the one cow, and that’s about enough to supply milk for only one person per day (knowing absolutely nothing about cows, I have no idea if this is true or not, but assume a lazy cow that only produces milk for the one guy per day).
However, the US government wants to help you.  So, they offer you a loan of $1,250 There are two things you can do with that money:
First, you could buy 125 cows, as it turns out each cow costs about 10 bucks. You also have a big enough back yard so that the cows can eat for free in perpetuity (BTW, these cows live for more than 50 years, do not need a bull to stay productive, and never decrease their milk output… Cool cows, huh?). That way you would have enough milk for everyone, for the next 50 years, as soon as you could buy those cows.
Or, with the same amount of money, you could build a prototype of the milk producing plant and get enough milk to supply one person for one day.  Oh, by the way, that would take about 5 years.
This is now absurd, right? Who on their right mind would do the second option? Feed the entire population of the town -essentially forever- against building a prototype (which may very well fail, by the way) that may supply enough milk for one guy for one day.  Oh, and by the way, that one guy just may not feel like paying $100 for that one gallon of milk if there is natural milk available for $1.50.  Who would even consider the second option?? Care to make a guess?? You are right!!! The US government.
If you take every number above and multiply it by one million you get a very close estimate of driving cars in the US. There are about 125 million drivers in the US, and it would cost roughly $1.25 B to create the infrastructure that would allow them to drive their cars 100% on electricity.
I have no idea of how much it would actually cost to build the pilot plant that converts electricity to liquid gasoline, or milk to reconstituted milk, but I can tell you that between DOE, ARPA-E and their cousins, they are spending at least that amount of money on biofuel research and other schemes as outlandish as the one described above.
Another great example is – from the same research section that brought us reconstituted milk – taking hydrogen, engineering an algae to process hydrogen and CO2 and convert them to methane and higher order carbon species. Guess where the hydrogen came from in the first place… Give up? OK, I’ll tell you.  It came from methane reforming, where you take methane and combine it with water and a bunch of energy to produce hydrogen and carbon monoxide. So, wait a minute… You take methane, which is clean and abundant in the US. You make hydrogen out of the methane.  Then you take the hydrogen and run it through a very complex genetically engineered algae in hopes that it will combine that hydrogen with CO2 and give you some higher order hydrocarbons, although you know most of it – if it even works – will become methane… AGAIN!!
How about just taking the methane and sticking it in the same car.  Oh… You don’t like that… You need to add a cumbersome tank to your car. And it smells bad. Ok. So let’s take the methane and stick it on a high efficiency combined cycle power plant and produce electricity at 60% efficiency, and then stick those electrons on the same electric car from before. Total efficiency: 54%. Efficiency of the methane-hydrogen-methane-and a-bit-of-gasoline scheme? I don’t really know… Maybe 0.005%.