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Comment by mchannon | Hacker News Reader

Here's a fun little exercise with the Toyota Mirai.

Read the spec sheet, and read the wikipedia article. They claim the thing can hold 5 kg of H2, at 10,000 psi.

Look into how big the tanks are.

The math will show that at that pressure, taking up that much space, you can fit no more than about 3.7 kg of H2 in there.

The difference between the diesel emissions and mileage scandal and the Mirai is that they actually made the math work with the former, as well as large enough scale for people to care.

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The spec sheet at [0] claims:

Hydrogen storage is "Approx. 5.0 kg"

122.4L of volume (60L front, 62.4L rear)

pressure is between 70 MPa and 87.5MPa

Doing the math shows:

density of hydrogen at 70MPa equals 36.69 g/L [1]

122.4L at 36.69 g/L equals 4.49kg [2]

density of hydrogen at 87.5MPa equals 45.96 g/L [3]

122.4L at 45.96 g/L equals equals 5.63kg [4]

So the amount is somewhere between 4.5kg and 5.63kg, depending upon the final pressure after filling. Which seems to line up squarely with "Approx. 5.0kg".

[0] - https://pressroom.toyota.com/releases/2016+toyota+mirai+fuel...

[1] - http://www.wolframalpha.com/input/?i=density+of+hydrogen+at+...

[2] - http://www.wolframalpha.com/input/?i=122.4L+at+36.69+grams%2...

[3] - http://www.wolframalpha.com/input/?i=density+of+hydrogen+at+...

[4] - http://www.wolframalpha.com/input/?i=122.4L+at+45.96+g%2FL

I am highly skeptical of using Wolfram Alpha like this. It steadfastly refuses to explain how it got its answer or what sources it used. These are high pressures and large densities. Are these results of an ideal gas law calculation? Are they results from the van der Waals equation? Are they extrapolated from actual experimental data? If so, what experiment? What are the error bars? Are they talking about pure Hydrogen-1 or are they talking about the isotopic mix found in sea water? (The latter is a small correction, but it’s still something that they should explain on the site.)

If you hover over the "Variation with temperature at constant pressure" chart you get a "sources" link, which references

National Institute of Standards and Technology, NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP)

https://www.nist.gov/srd/refprop

I.e. these are standard reference curves at a fixed temperature.

If you click the link on "Hydrogen" you get a page for molecular hydrogen, H2, so not an isotopic mix. Whether that's the right input for this calculation is beyond my technical knowledge, but Wolfram is displaying its parameters quite straightforwardly.

To my reading it looks like a quite well-explained calculation, though I can see why you might think otherwise if you hadn't spotted the somewhat-hidden "sources" link.

At least Wolfram Alpha agrees with Toyota data.

Surely van der Waals should provide a better model here, as we're having pretty dense gas which is far from ideal. So I'd assume it should be van der Waals model; not sure what Wolfram Alpha actually does.

The data I found for the internal volume of the tanks says they're about 122 litres.

When I do the math with that volume, 10.000 psi, and 25 degrees, I get about 3400 moles, which is actually over 5 kg. But certainly 25 is an ideal temperature, so claiming 5 kg seems reasonable.

Can you show your working?

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