If a Mirai ran on liquid hydrogen, how many miles per gallon would it get?

The shocking answer is 18.

But wait. The EPA says the Mirai has a fuel economy of 67 MPGe. How could being liquid make that much of a difference. Is it because it is so cold it doesn’t have much energy?

No, the difference is between MPG and MPGe. Whereas a gallon is a unit of volume, a Gasoline Gallon Equivalent, 1 GGE, is a unit of energy defined as 33.7 kWh. 1 GGE of liquid hydrogen has a volume of 3.7 gallons. So one gallon of it can only take you 67/3.7 = 18 miles.

This comes about because the density of liquid hydrogen is 0.07085 kg/L (kilograms per liter). Water is more than 14 times as dense. A gallon of liquid hydrogen therefore weighs 0.07085*3.785 = 0.268 kg and can only get you 67*0.268 = 18 miles.

But then what’s the point of liquid hydrogen if isn’t dense?

Well, the combined capacity of the Mirai’s two tanks is 122.4 liters. That volume of hydrogen at room temperature and 70 MPa pressure weighs 5 kg, a density of 5/122.4 = 0.04085 kg/L. Liquid hydrogen is therefore 0.07085/0.04085 = 1.73 times as dense as H70.

So, light as it is, liquid hydrogen requires only 58% of the volume of H70. It does this by reducing the distance between hydrogen molecules by a factor of the cube root of 1.73, namely 1.2.

So then why have these two big tanks taking up space under and behind the rear seats when liquid hydrogen can shave 42% off its volume?

Well, the trouble with liquid hydrogen is that at atmospheric pressure it must be cooled to 20 K (-253 C) to liquefy. A temperature so close to absolute zero might be ok for a huge truck but in an ordinary passenger car it would greatly increase both its complexity and cost.

If compressed, would less cooling suffice? No, compressing it to 13 atmospheres (1.3 MPa) only raises that temperature by 13 degrees.

That temperature and pressure, 33 K and 13 atmospheres, is called the critical point of hydrogen. Beyond that point there is no such thing as liquid hydrogen because there is no sharp demarcation between liquid and gas, just a compressible “supercritical” (not to be confused with political campaigns) fluid that can be shrunk by cooling, compressing, or both. (But with enough of that shrinking hydrogen solidifies, i.e. freezes.)

To save on the cost and complexity of liquid hydrogen the Mirai relies on pressure alone to save space.

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