Thermodynamic Efficiency of a Fuel Cell

The question to answer now is What are the actual electrical work and maximum available work for a given process  

Maximum Electrical Work for a Reversible Process Consider a generic reversible system with mechanical and electrical work and heat transfer at constant temperature. From the first law of thermodynamics for a simple compressible system 

The work can be divided into mechanical expansion work and electrical work  

The differential change in the Gibbs free energy for a constant-temperature reaction is 

Since this derivation was done for a reversible system, it is an expression of the maximum electrical woric possible from a system. Therefore the change in Gibbs free energy is related to the maximum conversion of chemical to electrical energy for a given reaction. From Eq. (3.78) the direction of spontaneous reaction is that of decreasing free energy. 

The thermal efficiency, E, of an energy conversion machine is described as the quantity of useful energy,, generated relative to the change in stored chemical energy, AH, which is liberated when a fuel is reacted with an oxidant  

As previously defined in the ideal case of an electrochemical converter, such as a fuel cell, 

TAS is the reversible heat exchanged with the external environment 

In the specific case of a fuel cell, if the fuel is hydrogen and the oxidant oxygen, the entire reaction in the cell is given by the following chemical equation [8]  

The Physical Chemistry of Materials Energy and Environmental Applications 

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The thermodynamic efficiency of a fuel cell is defined as the ratio between AG° and the enthalpy of reaction, AH°, p = AG°IAH°, and is not, unlike thermal external or internal combustion engines, limited by the ideal Carnot cycle. 

FIGURE 1.3 Thermodynamic efficiencies of a fuel cell and a hypothetical Camot heat engine, plotted as a function of temperature. A fuel cell that forms water in a gaseous phase has a higher efficiency compared to a fuel cell that produces liquid water. The efficiency difference corresponds to the enthalpy of vaporization. 

This also corresponds to the condition of open circuit reversible voltage, with no current flowing through the external circuit. Such a condition leads to the maximum electrical energy conversion and Equation 4.57 for reversible thermodynamic efficiency of a fuel cell can also be expressed as... 

The maximum (thermodynamic) efficiency of a fuel cell, 4,i, pc defined by the ratio of the useful Gibbs energy of the total cell reaction, G, to the whole energy of chemicals (fuel and oxidizer), A, which is enthalpy ... 

Maximum (thermodynamic) efficiency of a fuel cell [dimensionless]... 

Thermodynamic Efficiency of a Fuel Cell 97 The differential change in enthalpy for a given reaction is... 

Therefore, an expression of the maximum possible thermodynamic efficiency of a fuel cell can be written as... 

Relating Temperature Change to Maximum Efficiency Recall the expression for maximum thermodynamic efficiency of a fuel cell, and noting that the enthalpy of reaction for... 

Euel cells convert chemical energy directly into electricity, an inherently efficient process. Hence the thermodynamically attainable efficiencies are around 100%. The efficiency of a fuel cell is given by... 

In practice the situation is less favorable due to losses associated with overpotentials in the cell and the resistance of the membrane. Overpotential is an electrochemical term that, basically, can be seen as the usual potential energy barriers for the various steps of the reactions. Therefore, the practical efficiency of a fuel cell is around 40-60 %. For comparison, the Carnot efficiency of a modern turbine used to generate electricity is of order of 50 %. It is important to realize, though, that the efficiency of Carnot engines is in practice limited by thermodynamics, while that of fuel cells is largely set by material properties, which may be improved. 

Of course, since AG and AH are used in the definition (3.16), the theoretical efficiency of a fuel cell depends on the redox reaction on which it is built. In any case the theoretical efficiency, calculated from thermodynamic quantities, corresponds to an operative condition of infinitesimal electronic flow (by definition of reversible process), which practically means no current drawn from the converter. As it is shown in the following sections, also at open-circuit (no current through the external circuit) the voltage of real fuel cells is slightly lower than °, and the main problem of the electrochemical energy conversion is to obtain potentials in practical conditions (when current is drawn) as near as possible the open-circuit voltage, in order to maximize the real efficiency of the device. 

The efficiency of conventional internal combustion engines is limited to a theoretical maximum coming from the Camot-process. In contrast, the efficiency of a fuel cell is not limited due to thermodynamics, but due to the enthalpy of the electro-chemical processes [29]. 

The efficiency of a fuel cell is primarily determined by the thermodynamics of electrochemical hydrogen combustion. Only Gibbs free enthalpy can be converted into electricity. As shown in Fig. 4.26, additional losses in the fuel cell stack are encountered maiifly by limitations in the electrochemical kinetics of oxygen reduction, ohmic resistances in the electrolyte membrane and the current collectors as well as mass transport losses in the electrodes. All these losses cause the operating voltage of the fuel cell to deviate from the theoretical cell voltage. In the... 

Since the maximum electrical work in a fuel cell is limited by the available Gibbs free energy, the maximum thermodynamic or reversible efficiency of a fuel cell is defined as the ratio of Gibbs free energy change for conversion into electrical energy to the net fuel energy available in the form of enthalpy of formation as... 

Note that Gibbs function decreases with increase in temperature. Thus, the reversible work and thermod5mamic efficiency of a fuel cell decrease wifh increase in temperafure. This is in contrast to the reversible thermodynamic efficiency of a Carnot heat engine where the efficiency or reversible work increases with increase in temperature. 

Efficiency of a fuel cell under load [dimensionless] Maximum (thermodynamic) efficiency of an electrochemical energy conversion system [dimensionless]... 

The reversible efficiency jjFCrev of the fuel cell is defined as the ratio of the Gibbs free enthalpy ArG and the reaction enthalpy A H at the thermodynamic state of the fuel cell. 

This deviation from the thermodynamic reversible behavior leads to a decrease of the cell voltage by ca. 0.4-0.6 V, which reduces the energy efficiency of the fuel cell by a factor eE = E(j)/ Eeq, called voltage efficiency (eE = 0.80/1.23 = 0.65 for a cell voltage of 0.80 V), so that the overall energy efficiency at 25°C for the H2/02 fuel cell becomes 0.83 x 0.65 = 0.54. 

The thermodynamic efficiency, e, of a fuel cell is defined from ... 

The above recalls of basic thermodynamics are also useful to define the concept of theoretical fuel cell efficiency. If AG represents the useftd electrical work obtainable at the outlet of a fuel cell, and AH the inlet chemical energy, the theoretical efficiency //th can be calculated by the following equation ... 

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