ThermoFluidCalc Report

Fuel Cell Thermodynamics — 2026-09-29 07:21:04
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🔋 Fuel Cell Thermodynamics

Analyze thermodynamic limits, Nernst potential, and efficiencies of PEM and Solid Oxide fuel cells (SOFC).

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated
Fuel Cell Thermodynamics Thermodynamics
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👁️ Views 109
⚡ Solves 89
💾 Downloads 408 📦 Fortran Code 11.4 KB
📅 Released Jun 2026
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📝 Configuration

🔋 Cell Type & Conditions
80.0 °C
⛽ Gas Pressures
Air: ~0.21 atm O₂
⚙️ Electrochemical Parameters
Typical: 0.3–0.7
PEM: ~10⁻⁴, SOFC: ~10⁻²
Key Equations:

ENernst = E°+ (ΔS/nF)(T−298) + (RT/nF)ln(PH₂·PO₂0.5)
Vact = (RT/αnF)·arcsinh(i/2i₀)
Vohm = i·Rarea
Vconc = −(RT/nF)·ln(1−i/ilim)
Vcell = ENernst − Vact − Vohm − Vconc
η = (ΔG/ΔH)·(Vcell/ENernst)

📊 Results

Configure inputs and click Analyze to view results.

📘 Methodology

Nernst Equation

The open-circuit voltage depends on temperature and reactant partial pressures via the Nernst equation: E = E°(T) + (RT/nF)·ln(PH₂·PO₂0.5/PH₂O). Higher T reduces E for H₂ cells but improves kinetics.

Polarization Losses

Three loss mechanisms reduce cell voltage under load: Activation (sluggish electrode kinetics, dominant at low i), Ohmic (membrane/electrode resistance, linear in i), and Concentration (mass transport, dominant near ilim).

Cell Types

  • PEM: 60–80°C, H₂ fuel, Pt catalyst
  • SOFC: 700–1000°C, fuel flexible, ceramic electrolyte
  • DMFC: 60–90°C, liquid methanol, portable
  • AFC: 60–90°C, pure H₂/O₂, KOH electrolyte

📘 Calculation Methodology: Fuel Cell Thermodynamic Nernst Potential & Efficiency

Mathematical Model & Theory

Fuel cells convert chemical free energy directly into electrical work. The theoretical reversible cell EMF is determined by Gibbs free energy change $\Delta G$ via the Nernst equation:

$$E_{Nernst} = -\frac{\Delta G^\circ}{n F} + \frac{R T}{n F} \ln\left(\frac{P_{H_2} P_{O_2}^{0.5}}{P_{H_2O}}\right), \quad \eta_{max} = \frac{\Delta G}{\Delta H}$$
$$P_{elec} = I \cdot V_{cell} = I \cdot (E_{Nernst} - \eta_{act} - \eta_{ohm} - \eta_{conc})$$

Assumptions

  • Reversible electrochemical hydrogen-oxygen reaction ($H_2 + rac{1}{2}O_2 o H_2O$, $n = 2$ electrons per mole $H_2$).
  • Faraday constant $F = 96,485 ext{ C/mol}$.

Academic References

  1. Larminie, J., & Dicks, A.: Fuel Cell Systems Explained, Wiley.
  2. O'Hayre, R. et al.: Fuel Cell Fundamentals, Wiley.

Worked Engineering Example

Problem Statement:
A PEM fuel cell operates at $25^\circ\text{C}$ ($\Delta G^\circ = -237.13\text{ kJ/mol}$, $\Delta H^\circ = -285.83\text{ kJ/mol}$). Calculate theoretical reversible cell voltage and thermodynamic efficiency.

Step-by-step Solution:
1. $E^\circ = -(-237,130) / (2 \times 96485) = 237,130 / 192,970 \approx 1.229\text{ V}$.
2. $\eta_{th} = 237.13 / 285.83 \times 100\% = 82.96\%$.
Final Result:
Theoretical cell EMF is $E^\circ = \mathbf{1.229\text{ V}}$ with thermodynamic limit of $\mathbf{83.0\%}$.