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efficiency. The usual practice in chemical thermodynamics is to choose 1 atmosphere (atm) pressure and 25°C (298 K), although other conditions are used as standards by different industries and in other parts of the world. Free Energy There are two definitions of free energy and both are related to work done by the system. The Helmholtz free energy is the maximum amount of work that can be obtained from a system under perfectly reversible conditions, and is used with thermodynamic calculations of heat engines. Gibbs free energy is the net work that can be done by a system. In an electrochemical cell working reversibly at constant temperature and pressure, the net work is equal to the electrical work. Because we want electrical work, the Gibbs free energy is important to fuel cell calculations. Heat is released in the combustion of hydrogen in oxygen. In the electrochemical reaction between hydrogen and oxygen in a fuel cell, electricity and heat are produced. Although the chemical equation is written the same way for both reactions, the energy values are not equal. The heat produced by combustion does not equal the electricity produced in the fuel cell. H2 + 1⁄2 O2 → H2O(liquid) The HHV for the combustion of hydrogen is 285.8 kJ/mole, but the Gibbs free energy for the reaction—and therefore the maximum electricity produced by a fuel cell—is only 237.2 kJ/mole. The difference, 48.6 kJ/mole, appears as heat produced in the fuel cell. We can show this by the following equation for the fuel cell reaction. H2 + 1⁄2 O2 → H2O(liquid) + 237.2 kJ/mole electricity + 48.6 kJ/mole heat In sum, all fuel cells operating on hydrogen and oxygen produce heat in addition to the elec- tricity. The distribution of energy produced between electricity and heat shown above, however, is for a perfect fuel cell operating in a thermodynamically reversible manner. Actual, practical fuel-cell devices incur losses due to inefficiencies of the electrochemical reactions and due to electrical and ionic resistance as the current flows through the fuel cell. These generically are classed as internal resistance losses, and manifest as additional heat produced by the fuel cell at the cost of the electrical generation. Nevertheless, the sum of the electricity and the heat produced by the fuel cell must equal the HHV (or LHV, if the water vapor produced is not condensed). Heat of Formation and Free Energy of Formation The definition of the heat of formation is the heat released or required when chemicals are formed from their elements in their standard state. The heat of formation of the elements in their standard state is, by definition, zero. The equation for the formation of methane from its elements is given below. 2 H2 + C → CH4 The heat of formation for this reaction at 25°C is listed in the Joint Army-Navy-Air Force (JANAF) Thermodynamic Tables as -74.9 kJ/mole. The minus sign indicates that the methane 2PDF Image | Hydrogen Production: Fundamentals
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