The overall reaction occurring in the fuel cell is:
H2 + 0.5 O2 ? H2O
The maximum amount of electrical energy that can be generated by a fuel cell can be determined from the ion (proton) flow. Every mole of molecular hydrogen (H2) fed to a fuel cell has the potential to generate two moles of electrons at the anode. Every mole of electrons carries 9.65 * 104 Coulombs of charge (Faraday’s constant). A coulomb/sec is an ampere (1 amp of current). The power generated by 1 amp of current depends on the voltage (V) at which the current is generated (P=I*V).
a.) Assume that the fuel cell generates electricity at a voltage of 1.2 V. Calculate the ideal electrical power (in MW) that would be generated by the fuel cell if fed hydrogen at a rate of 10,000 kilogram/hr.
b.) If the fuel cell operates at 50% efficiency, how much power could be generated if 10,000 kilograms/hr of hydrogen were fed to the fuel cell?
c.) If the same amount of electricity in part b) had been generated by a power plant burning natural gas (with an efficiency of 35% in converting the heat of combustion of the natural gas into electricity), how much natural gas would have been used (in kg/hr and in BTU/hr)? Assume that the heating value of natural gas is 1000 BTU/scf.
d.) If the 10,000 kg/hr of hydrogen had been used as a combustion fuel, what heat would have been provided (in BTU/hr)? Assume the heat of combustion is 61,000 BTU/lb.
e.) Calculate the net energy used producing electrical power with the fuel cell as opposed to combusted natural gas at a power plant (energy content of the natural gas that would be used at the power plant – heat of combustion that would have been liberated if hydrogen had been combusted at a power plant).
f.) Repeat parts a.) – e.) above, however now assume that the natural gas power plant is 40% efficient. With these assumptions, does using the fuel cell increase overall energy efficiency?