Heat Balance in Fuel and Electrolytic Cells

The negative entropy of the H2/O2 PEMFC reaction (AS° = -163.3 J mok K at 25°C, [Chapter 10, Table 10.4]) shows that about 17% of the total available energy, AH° = -285.83 kJ mol [Chapter 10, Table 10.4], should be released in the form of heat, TAS°, even when the fuel cell is in the hypothetical equilibrium state and current is zero. 

When current is larger than zero, additional heat will be produced due to internal resistance of the cell and overpotentials at the electrodes. As a result, when a fuel cell operates at current density, j, the magnitude of the released heat rate, 2pc W/cm is defined as follows  

Therefore, if the fuel cell is supposed to work at a constant temperature, a heat removal procedure should be considered. Otherwise, the fuel cell can be overheated and destroyed. In a PEMFC at common operations, current densities (0.5-0.7 A cm ) up to about 50% of the energy of chemicals, Aj/7, are converted to heat, and the remaining 50% to electric energy. In this fuel cell, one-third of the heat comes from the entropy term and two-thirds are from the overpotentials at the electrodes and from the Joule heating, rpcj. In the preceding example, at 0.7 A cm-, the generated electric power density is 0.513 W cm-, the reversible heat rate due to the entropy of the reaction is 0.176 W cm, and the heat rate generated due to the overpotentials and crossover is 0.524 W cm.  

Note that for some fuel cells the entropy of the fuel cell reaction could be positive. An example is C(s) + (l/2)02(g) = CO(g) or C(s) + OjCg) = C02(g). These reactions provide a standard thermodynamic efficiency, S pc= greater than 100% 

However, in some cases. Equation 8.13 could not be an accurate approximation, particularly in a case when concentrated aqueous solutions are the participating chemicals. An example of a dramatic difference between thermodynamic efficiency and its standard value is given in Ref. [7] for an electrolytic systan where highly concentrated aqueous solutions are used. 

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