**3. Fuel cell thermodynamic efficiency**

In the process of energy conversion in a fuel cell, the initial chemical energy between the enthalpy of the products and reactants is converted into electrical energy and thermal energy, as stated in the first law of thermodynamics. The efficiency of any energy conversion device is defined as the ratio between useful energy output and energy input [19–22]:

$$
\eta = \frac{\text{actual electrical work}}{\text{maximum available work}}
$$

$$
\eta = \frac{\Delta \mathbf{G}}{\Delta \mathbf{H}} = \frac{\Delta \mathbf{H} - \mathbf{T} \Delta \mathbf{S}}{\Delta \mathbf{H}} \tag{43}
$$

Themaximum possible thermodynamic efficiency of a fuel cell can be written as [9]:

$$\eta == 1 - \frac{\text{TAS}}{\Delta \text{H}} \tag{44}$$

In the case of a fuel cell, the useful energy output is the electrical energy produced, and the energy input is the enthalpy of hydrogen, that is, hydrogen's HHV. Assuming that all of the Gibbs free energy can be converted into electrical energy (the reaction is reversible), the maximum theoretical efficiency of a fuel cell is [23, 24] (**Figure 3**):

$$\eta = \frac{\Delta \mathbf{G}}{\Delta \mathbf{H}} = \frac{237.34}{286.02} \ge 100\% = \\$3\%$$

For hydrogen's LHV, the fuel cell efficiency would be [26]:

$$\eta = \frac{\Delta \mathcal{G}}{\Delta \mathcal{H}} = \frac{228.74}{241.98} \times 100\% = 94.5\%$$

The LHV has higher efficiency compared to HHV, because the reversible efficiency of the fuel cell decreases as the operating temperature increases [27].

The expected fuel cell efficiency is not always achieved due to thermodynamic and electrochemical irreversible losses [28].

### **4. Irreversible losses**

Other than calculating energy quantities during the conversion of chemical energy to electrical energy, there is also the matter of electron flow through

materials in the fuel cell process. The single fuel cell provides a voltage dependent on operating conditions such as temperature, applied load and fuel/oxidant flow rates [29, 30]. If a fuel cell is supplied with reactant gases, but the electric current is not closed, it will not generate any current, and one would expect the cell potential to be at the theoretical cell potential for the given conditions (temperature, pressure and concentration of reactants). In reversible conditions, the energy loss is the heat lost towards the environment, TΔs, due to negative entropy [12].

E ¼ Etherm � ηact � ηohm � ηconc (45)

q ¼ TΔs � nFE ¼ ΔH � ΔG � nFE (47)

nFT (46)

where E is the cell potential, Etherm is the thermodynamic potential, ηact is the voltage loss due to activation polarisation, ηohm is the voltage loss due to ohmic polarisation and ηconc is the voltage loss due to mass transport polarisation and the

<sup>S</sup> <sup>¼</sup> <sup>E</sup>

In addition, the related heat lost for irreversibility can be calculated as (**Figure 4**):

Thermodynamics is used to understand the process of energy conversion in fuel cells. The determination of a fuel cell's performance depends on thermodynamic evaluation. The heat potential of a fuel is given by the enthalpy of the reaction. Not all heat potential of a fuel can be used to perform useful work; the reversible work of a fuel is defined by Gibbs free energy, which is the electrical work. The study of the electrical effects shows that the molar flow of the fuel used is proportional to the electric current and the reversible work is proportional to the reversible voltage. The cell voltage varies with temperature, pressure and reactant/product activities. Irreversible losses cause a difference in the efficiency of reversible and real processes, with efficiency of real processes always less than reversible processes. The losses are due to two major reasons, namely, irreversible kinetic losses and fuel utilisation losses.

We greatly appreciate the National Research Foundation and the Tertiary Education Support Programme for financial support as well as the Chemistry

Department at the University of the Western Cape.

*H2/O2 polarisation curve at equilibrium and voltage losses in fuel cell [30].*

entropy generation results [38–41]:

*DOI: http://dx.doi.org/10.5772/intechopen.90141*

*Fuel Cell Thermodynamics*

**5. Conclusion**

**Figure 4.**

**Acknowledgements**

**15**

However, in practice, the thermodynamic cell potential is decreased from its ideal potential, usually less than 1 V, due to irreversible losses known as overpotential or polarisation [17]. The fuel cell performance overpotential is due to [14, 31]:


The standard measure of performance is the polarisation curve, which represents the cell voltage behaviour against operating current density (**Figure 4**). From the figure, the voltage loss caused by mixed potential and crossover, activation polarisation, ohmic polarisation and mass transport losses is the most significant in the tail of the I-V curve. The maximum fuel cell is then examined through the reversible voltage of the system, which is calculated using thermodynamics and the actual voltage of the system [36]. The final voltage is lower than the thermodynamic voltage and is usually between 0.5 and 1.0 V. Although polarisations cannot be eliminated, material choice and electrode designs can contribute to their minimisation [37]:

*Fuel Cell Thermodynamics DOI: http://dx.doi.org/10.5772/intechopen.90141*

materials in the fuel cell process. The single fuel cell provides a voltage dependent on operating conditions such as temperature, applied load and fuel/oxidant flow rates [29, 30]. If a fuel cell is supplied with reactant gases, but the electric current is not closed, it will not generate any current, and one would expect the cell potential to be at the theoretical cell potential for the given conditions (temperature, pressure and concentration of reactants). In reversible conditions, the energy loss is the heat

However, in practice, the thermodynamic cell potential is decreased from its

overpotential or polarisation [17]. The fuel cell performance overpotential is due to

i. Activation overpotential: The activation polarisation is related to the charge transfer processes occurring during the electrochemical reactions on electrode surfaces. The losses are caused by the slowness of the reactions taking place on the surface of the electrodes [32]. Activation polarisation depends on the nature of type of electrode, ionic interactions, ion-solvent interactions and the

ii. Ohmic overpotential: In most fuel cells, the most important contribution to this resistance is the electrolyte, due to the ionic nature of its conductivity, resistance to the flow of electrons through the electrodes and the contact

iii. Mass transport (concentration) overpotential: Concentration polarisation occurs due to a decrease in the concentration of the reactants at the electrode-

electrolyte interface. Due to diffusion or convection problems in the

iv. Fuel crossover overpotential: 'Crossover' is one of the common effects occurring in alcohol fuel cells [22]. Although the electrolyte, a polymer membrane, is not electrically conductive and practically impermeable to reactant gases, some amount of fuel will diffuse from anode to cathode to react with oxygen, resulting in fewer electrons in the generated current of electrons that travel through an external circuit [34]. With this transit the cathode potential decreases, thus reducing the overall efficiency of a fuel cell. It occurs when the intermediates generated by fuel oxidation have higher concentration than oxygen at the cathode. The increase of temperature

The standard measure of performance is the polarisation curve, which represents the cell voltage behaviour against operating current density (**Figure 4**). From the figure, the voltage loss caused by mixed potential and crossover, activation polarisation, ohmic polarisation and mass transport losses is the most significant in the tail of the I-V curve. The maximum fuel cell is then examined through the reversible voltage of the system, which is calculated using thermodynamics and the actual voltage of the system [36]. The final voltage is lower than the thermodynamic voltage and is usually between 0.5 and 1.0 V. Although polarisations cannot be eliminated, material choice and electrode designs can contribute to their

electrolyte, the concentration of the reactants is not maintained at the initial level. Reaction product accumulation can also cause a dilution of reactants. The concentration gradient thereby formed causes a drop in electrode

lost towards the environment, TΔs, due to negative entropy [12].

electrode-electrolyte interface [33].

*Thermodynamics and Energy Engineering*

resistance at the cell terminals.

activity, and the terminal voltage is reduced.

escalates the crossover effect [35].

minimisation [37]:

**14**

[14, 31]:

ideal potential, usually less than 1 V, due to irreversible losses known as

$$\mathbf{E} = \mathbf{E}\_{\text{therm}} - \eta\_{\text{act}} - \eta\_{\text{ohm}} - \eta\_{\text{conc}} \tag{45}$$

where E is the cell potential, Etherm is the thermodynamic potential, ηact is the voltage loss due to activation polarisation, ηohm is the voltage loss due to ohmic polarisation and ηconc is the voltage loss due to mass transport polarisation and the entropy generation results [38–41]:

$$\mathbf{S} = \frac{\mathbf{E}}{\mathbf{n} \mathbf{F} \mathbf{T}} \tag{46}$$

In addition, the related heat lost for irreversibility can be calculated as (**Figure 4**):

$$\mathbf{q} = \mathbf{T}\Delta\mathbf{s} - \mathbf{n}\mathbf{F}\mathbf{E} = \Delta\mathbf{H} - \Delta\mathbf{G} - \mathbf{n}\mathbf{F}\mathbf{E} \tag{47}$$

**Figure 4.** *H2/O2 polarisation curve at equilibrium and voltage losses in fuel cell [30].*

## **5. Conclusion**

Thermodynamics is used to understand the process of energy conversion in fuel cells. The determination of a fuel cell's performance depends on thermodynamic evaluation. The heat potential of a fuel is given by the enthalpy of the reaction. Not all heat potential of a fuel can be used to perform useful work; the reversible work of a fuel is defined by Gibbs free energy, which is the electrical work. The study of the electrical effects shows that the molar flow of the fuel used is proportional to the electric current and the reversible work is proportional to the reversible voltage. The cell voltage varies with temperature, pressure and reactant/product activities. Irreversible losses cause a difference in the efficiency of reversible and real processes, with efficiency of real processes always less than reversible processes. The losses are due to two major reasons, namely, irreversible kinetic losses and fuel utilisation losses.

### **Acknowledgements**

We greatly appreciate the National Research Foundation and the Tertiary Education Support Programme for financial support as well as the Chemistry Department at the University of the Western Cape.

*Thermodynamics and Energy Engineering*

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*Fuel Cell Thermodynamics*

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*DOI: http://dx.doi.org/10.5772/intechopen.90141*

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