The nice thing about many hydrocarbon gases, such as propane, is that they can be liquefied fairly easily (the pressure in LPG bottles is about 8 bar) and they do not then take as much space as in gaseous form (liquid density of propane about 500 kg/m3).Image: Wikipedia.org, CC BY-SA 3.0The same does not apply to hydrogen. For example, at 700 bar, the hydrogen is still gaseous (density 42 kg/m3).In atmospheric conditions, the density of hydrogen is 0.09 kg/m3. It has a high lower heating value: 120 MJ/kg. How many liters of (atmospheric) hydrogen would be needed to reach that earlier mentioned energy content of the 100 Ah battery (4.32 MJ)?Single choice
A
a. 4 litres
B
b. 40 litres
C
c. 400 litres
D
d. 4000 litres

Question

The nice thing about many hydrocarbon gases, such as propane, is that they can be liquefied fairly easily (the pressure in LPG bottles is about 8 bar) and they do not then take as much space as in gaseous form (liquid density of propane about 500 kg/m3).Image: Wikipedia.org, CC BY-SA 3.0The same does not apply to hydrogen. For example, at 700 bar, the hydrogen is still gaseous (density 42 kg/m3).In atmospheric conditions, the density of hydrogen is 0.09 kg/m3. It has a high lower heating value: 120 MJ/kg. How many liters of (atmospheric) hydrogen would be needed to reach that earlier mentioned energy content of the 100 Ah battery (4.32 MJ)?Single choice

A

a. 4 litres

B

b. 40 litres

C

c. 400 litres

D

d. 4000 litres

BlackTom AI · Accepted Answer

To approach this problem, I will break down the energy content and relate it to hydrogen’s density and energy density.
Option a: 4 litres. If we used 4 L of hydrogen at atmospheric conditions, the mass would be about 0.004 m3 × 0.09 kg/m3 = 0.00036 kg, which would store roughly 0.00036 kg × 120 MJ/kg ≈ 0.0432 MJ. This is far below the required 4.32 MJ, so this is far too small.
Option b: 40 litres. 40 L is 0.04 m3. The mass at atmospheric density is 0.04 m3 × 0.09 kg/m3 = 0.0036 kg. The energy content would be 0.0036 kg × 120 MJ/kg ≈ 0.432 MJ, still an order of magnitude too small to reach 4.32 MJ.
Option c: 400 litres. 400 L is 0.4 m3. Mass = 0.4 m3 × 0.09 kg/m3 = 0.036 kg. Energy = 0.036 kg × 120 MJ/kg = 4.32 MJ, which exactly matches the target energy content.
Option d: 4000 litres. 4000 L is 4.0 m3. Mass = 4.0 m3 × 0.09 kg/m3 = 0.36 kg. Energy = 0.36 kg × 120 MJ/kg = 43.2 MJ, which is ten times larger than the target 4.32 MJ. This would exceed the requirement by a wide margin.
In summary, calculating energy from hydrogen at atmospheric density using its lower heating value shows that 400 litres of hydrogen provide about 4.32 MJ, aligning with the given battery energy. The other volumes yield far too little (a, b) or far too much (d).

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