EML4450L17

# EML4450L17 - Sustainable Energy Science and Engineering...

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S ustainable E nergy S cience and E ngineering C enter Basic Fuel Cell Reactions Reference: PEM fuel cells: theory and Practice, Frano Barber, Elsevier Academic Press, 2005 The overall reaction of a PEM fuel cell is: This reaction is the same as the reaction of hydrogen combustion, which is an exothermic process (energy is released): The heat, typically given in terms of enthalpy, of a chemical reaction is the difference between the heats of formation of products and reactants: Heat of formation of liquid water: -286 kJ/mol at 25 o C and at atmospheric pressure. H 2 + 1 2 O 2 H 2 O H 2 + 1 2 O 2 H 2 O + heat Δ H = h f () H 2 O h f H 2 1 2 h f O 2 =− 286 kJ / g 0 0 286 kJ mol H 2 + 1 2 O 2 H 2 Ol + 286 kJ / mol

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S ustainable E nergy S cience and E ngineering C enter Hydrogen HHV and LHV Hydrogen heating value is used as a measure of energy input in a fuel cell. Hydrogen heating value: the amount of heat that may be generated by a complete combustion of 1 mol of hydrogen = the enthalpy of hydrogen combustion reaction = 286 kJ/mol The result of combustion is liquid water at 25 o C and the value of 286 kJ/mol is considered as Higher Heating Value (HHV). If the combustion is done with excess oxygen and allowed to cool down to 25 o C, the product will be in the form of vapor mixed with unburned oxygen. The resulting heat release is measured to be 241 kJ/mol, known as Lower Heating Value (LHV). The difference between HHV and LHV is the heat of evaporation of water at 25 o C: H 2 + 1 2 O 2 H 2 Og () + 241 kJ / mol H fg = 286 241 = 45 kJ / mol
S ustainable E nergy S cience and E ngineering C enter Theoretical Electrical Work Not all the hydrogen’s energy can be converted into electricity. The portion of the reaction enthalpy that can be converted to electricity corresponds to Gibbs free energy: Δ S is the difference between entropies of products and reactants: Δ G = Δ H T Δ S Δ S = S f () H 2 O S f H 2 1 2 S f O 2 h f (kJ/mol) s f (kJ/mol) Hydrogen 0 0.13066 Oxygen 0 0.20517 Water (liquid) -286.02 0.06996 Water (Vapor) -241.98 0.18884 At 25 o C and at one atmosphere Δ G =− 286.02 298 × 0.06996 0.13066 0.5 × 0.20517 ( ) = − 237.36 kJ / mol 48.68 kJ/mol is converted into heat.

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S ustainable E nergy S cience and E ngineering C enter Theoretical Fuel Cell Potential W e = n e FE = −Δ G Electrical work: n e = 2 (two electron per molecule); F =96,485 Coulombs/electron- mol. The theoretical potential of fuel cell at 25 o C and at one atmosphere: Temperature Effect: a, b and c are empirical Coefficients, different for each gas E = −Δ G n e F = 237,340 J / mol 2 × 96,485 As / mol = 1.23 Volts 2 15 . 298 15 . 298 15 . 298 15 . 298 1 cT bT a C dt C T S S dt C h h F n S T F n H E S T H G P T P T T P T e e + + = + = + = Δ Δ = Δ Δ = Δ
S ustainable E nergy S cience and E ngineering C enter Theoretical Fuel Cell Potential ab c H 2 28.91404 -0.00084 2.01E-06 O 2 25.84512 0.012987 -3.9E-06 H 2 O (g) 30.62644 0.009621 1.18E-06 Δ H (kJ/mol) Δ S (kJ/mol) Δ G (kJ/mol) -286.02 -0.1633 -237.34 -241.98 -0.0444 -228.74 H 2 + 1 2 O 2 H 2 Ol () H 2 + 1 2 O 2 H 2 Og Δ H T H 298.15 aT 298.15 b T 298.15 ( ) 2 2 c T 298.15 ( ) 3 3 Δ S T S 298.15 a ln T 298.15 ⎟ +Δ bT 298.15 c T 298.15 2 2 Δ a = a H 2 O a H 2 1 2 a O

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## This note was uploaded on 10/22/2011 for the course EML 4450 taught by Professor Greska during the Fall '06 term at FSU.

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EML4450L17 - Sustainable Energy Science and Engineering...

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