Question

A fuel cell is an electrochemical device that reacts hydrogen with oxygen from the air to produce water and DC electricity. A proposed application is replacement of the gasoline-fueled internal combustion engine in an automobile with a 100 kW fuel cell. You are on a summer internship with a gas supplier planning to transport hydrogen to service stations for the use in cars powered by fuel cells. The hydrogen is to be transported in tube trailers, each of which has 10 tubes of length 10.5 m and a diameter of 0.56 m. Hydrogen in the tubes at 2600 psig and an average temperature of 298 K is discharged at service stations to a final pressure of 55 psig, Refueling each fuel-cell-powered automobile is estimated to require 40.0 kg of hydrogen. a) You and your office-mate - an intern from a different university- have been asked to estimate the number of automobiles that can be refueled by one tube-trailer load of hydrogen. He does a very quick calculation and comes up with a value of 95 cars. Specualte how he did it and provide support for your speculation. What was his mistake? b) Do the calculation using the SRK equation of state. Use the following correlation developed specifically for hydrogen:23 α=1.202exp(-0.3228Tr). c) Do the calculation using the law of corresponding states. d) In which of the three estimates would you have the greatest confidence, and why?

Answer 1

(a). Length of tube = 10.5 m

Radius of tube = 0.56 / 2 = 0.28 m

Volume of tube = $\pi$ r²h

= $\pi$ * (0.28)² * 10.5

= 2.5861 m3

Volume of tube trailer = 10 * 2.5861 m3

= 25.861 m3 = 25861 L

Pressure = 2600 psig = 177.91 atm

Temperature = 298 K

Using PV = nRT

177.91 * 25861 = n * 0.0821 * 298

n = 188055.59

Mass of 188055.59 moles of H2 gas = 188055.59 * 2

= 376111.18 g = 376.11 kg

Mass of hydrogen required per automobile = 40 kg

Number of automobiles that can be refueled by one tube-trailer = 376.11 / 40

= 9.40 cars