What are the properties and impediments of a liquid air fueled engine? I recently came across a very interesting article that suggested the possibility of using liquified gases like air, nitrogen, or oxygen as a power source for cars.  It appears that this company is moving forward with the idea, but surely the concept is not entirely novel.  See, for example, claims from over a century ago to have invented a car using liquid air.  Why has this concept not been explored more thoroughly?  It seems to me that some basic questions are as follows:
What is the recoverable energy content per volume of liquid air?
How does this compare with gasoline or aviation fuel?
What are the practical problems with the of handling liquid air?
Could liquid air be used more effectively in something other than the four-stroke-cycle?
 A: I found the most informative resource to be the article on Wikipedia about Liquid nitrogen cars.  I hope you don't mind if I limit my discussion to mostly liquid Nitrogen instead of a full air mix.
http://en.wikipedia.org/wiki/Liquid_nitrogen_vehicle
Reading the claims, I was fairly convinced... initially.  We can tick off all the different areas one by one and it does quite well.  I could write a lot about each of these:


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*Fuel infrastructure

*Round-trip efficiency for electricity to useful work

*Fuel tank size and complexity

*Fuel hazard

*Engine size and complexity


Liquid Nitrogen fairs quite well on all of these if you read the above Wikipedia page.  The problem, however, is what they don't write.  Let's zoom in on the fuel tank size and complexity issue.  Wikipedia cites:

For an isothermal expansion engine to have a range comparable to an internal combustion engine, a 350-litre (92 US gal) insulated onboard storage vessel is required.

The source they provide for this is a rather good read actually.  However, the relative competitiveness of the idea crumbles once you begin to better understand the specifics of the energy density.  Quote from the source:

Even though these specific energy values are superior to those of most electrochemical batteries, the energy density of LN2 is at best 70 W-hr/l when used in an isothermal expansion process, which results in a 350 liter (90 gal) onboard storage vessel being needed to provide a vehicle with a range comparable to internal combustion engines.

Let's start with this fact, isothermal expansion is not a reasonable assumption to make.  A car's engine does not have infinite time in which to expand the gas in its piston.  The quote about the 90 gallon tank was thus, taken somewhat out of context.  Now, that, alone, doesn't kill the idea there, but there remains another damming detail.  Let's multiply:
$$ 70 \frac{\text{W-hr}}{L} \times 350 L = 24.5 \text{kW-hr} $$
They used an unrealistically efficient cycle with a tank energy content of this, which is less than the usable energy of cars out there today.  Here are my common benchmarks for this:


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*Toyota Corolla, 13 gallon tank, 20% efficiency, 103 kWh usable energy

*Tesla Roadster, 56 kWh battery capacity

*Chevy Volt, 16 kWh battery capacity


If we compare a liquid Nitrogen car to the Chevy Volt it might not be so bad.  But why would we do that?  That car can still augment its range with gasoline.  A part of the argument for electric cars is that you don't have the same energy loss from idling.  Would that be true for a liquid Nitrogen car?  There is no reason to believe that.
Let's say we assume a reasonable efficiency of half the isothermal process, which is illustrated in Figure 2 of the reference.  Let's also say we'll hold 50 kWh of usable energy in the tank (even though this could still cause range problems).  We've increased the tank size by a factor of 4 and the weight of the full tank is now around $1000 kg$.  This is close to what many cars weigh.
The energy content relative to gasoline, as well as the alternatives, kills the idea.  It would seem to require extremely optimistic assumptions to make it a reasonable proposal before we even get into the discussion about infrastructure needed to make it happen.  The most fair comparison would be to other cars that also use alternative fuels, but it fails there too.  EVs seem to have better viability on the basis of simple energetics.  Maybe you're concerned that we'll run out of Lithium.  A vehicle powered by compressed natural gas (not even the super-high pressure tanks that many have hope in) would blow it away, and the tank would be more manageable.  Plus the fuel would be (dramatically) cheaper.  Plus the infrastructure would be there.  Plus, the engine is a proven design.  We could do better with coal-to-liquids, we could probably do better with biofuels.
