A fuel cell vehicle draws 50 kW of power at 70 mph and is 40% efficient at rated power. You are asked to size the fuel cell system so that a driver can go at least 400 miles at 70 mph before refueling. Specify the minimum volume and weight requirements for the fuel cell system (fuel cell fuel tank): Fuel cell power density is 1.5 kW/L and 1 kW/kg (note: the values taken into account efficiency already). Fuel tank energy density (compressed hydrogen with the tank mass taken into account): 4 MJ/L and 8 MJ/kg.

  a) fuel cell weight and volume: 50 kg, 33.3 L

  b) fuel tank weight and volume: 321 kg, 643 L

Explanation:

Fuel Cell

Delivery of 50 kW from a source with a power density of 1.5 kW/L requires a source that has a volume of ...

  (50 kW)/(1.5 kW/L) = 33.3 L

The weight of the power source is 1 kW/kg, so will be ...

  (50 kW)/(1 kW/kg) = 50 kg

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Fuel Tank

400 miles at 70 mph will take (400/70) h ≈ 5.71429 h. In that time, the energy used by the vehicle power plant is ...

  (50 kW)(5.71429 h)(3600 s/h) = 1028.57 MJ

Since the power plant is 40% efficient, it must be supplied with 2.5 times that amount of energy, or 2571.43 MJ.

The tank volume and mass will then be ...

  volume = 2571.43 MJ/(4 MJ/L) = 642.9 L

  mass = 2571.43 MJ/(8 MJ/L) = 321.4 kg

Comment on fuel tank volume

It appears the fuel tank would need to be equivalent in size to a sphere about 1.1 m in diameter.

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