 # Thermodynamic Analysis Theory

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Chapter-V
THEORITICAL ANALYSIS
The performance of the PEM fuel cell is evaluated by a thermodynamic analysis, which is of two types, viz., energy analysis and exergy analysis. The energy analysis is made by applying the first law of thermodynamics to the fuel cell. The efficiency is defined by considering the heat input to the fuel cell and the work output from the fuel cell. In the exergy analysis the fuel cell and the surrounding environment are considered together. The efficiency is defined based on the maximum or available energy which is calculated by considering the entropy lost to the environment. Thus the exergy analysis takes into account the second law of thermodynamics in addition to the first law. In this chapter a theoretical analysis
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5.1.2 Activation Overpotential
The Tafel equations can be used to determine the activations overpotential at the anode and the cathode because the values of the exchange current densities are quite low.
At the anode,
V_(act,Anode)=(RT_FC)/(α_A nF) ln⁡(i/i_0 )
At the cathode,
V_(act,Cathode)=(RT_FC)/(α_C nF) ln⁡(i/i_0 ) (12) where, i is current density (A/cm2), i0 is exchange current density (A/cm2), R is universal gas constant (8.314 J/mole-K), n is number of electrons involved and, F is Faraday's constant (96485 C/mole).
Exchange current density:
It may be determined in two different forms based on the cell operating temperature and pressure. In electrochemical reactions i0 is similar to the rate constant in the chemical reactions and it is a function of temperature
Based on temperature; i_0 (T)=1.08×〖10〗^(-21)×exp(0.086T_FC )
In this study i0 at 353 K and 5 atm, is assumed to be 4.4 × 10-7 A/cm2 as a reference
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In this study, H2 reacted , n O2 reacted are assumed as 80 and 50%, respectively.
5.1.9 Energy Efficiency
The energy efficiency of PEM fuel cell can be defined as the following form,
Energy efficiency=(Power output from the fuel cell)/(Rate of heat input to the fuel