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9. SAMPLE CALCULATIONS This section presents sample problems to aid the reader in understanding the calculations behind a fuel cell power system. The sample calculations are arranged topically with unit operations in Section 9.1, system issues in Section 9.2, supporting calculations in Section 9.3, and cost calculations in Section 9.4. A list of conversion factors common to fuel cell systems analysis is presented in Section 9.5, and a sample automotive design calculation is presented in Section 9.6. 9.1 Unit Operations The following examples are presented for individual unit operations found within a fuel cell system. Unit operations are the individual building blocks within a complex chemical process. By analyzing example problems for each unit operation, one can learn about the underlying scientific principles and engineering calculation methods that are applied to various processes. This approach will provide the reader with a better understanding of fuel cell power system building blocks as well as the interactions between unit operations. For example, the desired power output from the fuel cell unit will determine the fuel flow requirement from the fuel processor. This section starts by examining the fuel cell unit operation, and continues on to the fuel processor and power conditioner. 9.1.1 FuelCellCalculations Example 9-1 Fuel Flow Rate for 1 Ampere of Current (Conversion Factor Derivation) What hydrogen flow rate is required to generate 1.0 ampere of current in a fuel cell? (This exercise will generate a very useful conversion factor for subsequent calculations.) Solution: For every molecule of hydrogen (H2) that reacts within a fuel cell, two electrons are liberated at the fuel cell anode. This is most easily seen in the PAFC and PEFC because of the simplicity of the anode (fuel) reaction, although the rule of two electrons per diatomic hydrogen molecule (H2) holds true for all fuel cell types. The solution requires knowledge of the definition of an ampere (A) and an equivalence of electrons.56 H2 →2H+ +2e- The moles of hydrogen liberated to generate one amp can be calculated directly: 56 One equivalence of electrons is 1 g mol of electrons or 6.022 x1023 electrons (Avagadro’s number). This quantity of electrons has the charge of 96,487 coulombs (C) (Faraday’s constant). Thus, the charge of a single electron is 1.602 x10-19 C. One (1) ampere of current is defined as 1 C/sec. 9-1PDF Image | Fuel Cell Handbook (Seventh Edition)
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