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FSU EML 4450 - Direct Energy Conversion: Fuel Cells

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Sustainable Energy Science and Engineering CenterDirect Energy Conversion: Fuel CellsReferences: Direct Energy Conversionby Stanley W. Angrist, Allyn and Beacon, 1982. Fuel Cell Systems, Explained by James Larminie and Andrew Dicks, Wiley, 2003.Fuel Cell Technology Hand Book, Edited by Gregor Hoogers, CRC Press, 2002Sustainable Energy Science and Engineering CenterHydrogen - Oxygen Fuel Cell12345679101112H2→ 4H++4e−At the anode the hydrogen gas ionizes releasing electrons and creating H+ions (or protons). This reaction releases energy. O2+ 4e−+ 4H+→ 2H2OAt the cathode, oxygen reacts with electrons taken from the electrode, and H+ions from the electrolyte, to form waterAn acid with free H+ions. Certain polymers can also be made to contain mobile H+ions - proton exchange membranes (PEM)Sustainable Energy Science and Engineering CenterFuel Cell Input and OutputHydrogen EnergyFuel CellOxygen EnergyElectricity Energy = VItHeatWaterPower = VI; Energy = VItGibbs free energy: Energy available to do external work, neglecting any work done by changes in pressure and/or volume. In a fuel cell, the external work involves moving electrons round an external circuit. It is the change in Gibbs free energy ΔG, difference between the Gibbs free energy of the products and the Gibbs free energy of the reactants or inputs is important.Sustainable Energy Science and Engineering CenterHydrogen-oxygen Fuel CellThe basic reaction:OHOHOHOH2222222122→+→+The product is one mole of H2O ( 18g = 1 gmole) and the reactants are one mole of H2(2g = 1 gmole) and a half a mole of O2 (32g = 1 gmole). The molar specific Gibbs free energy, in ‘per mole’ form is commonly used. 222)(21)()(tanOHHtsreacproductsgggggggO−−=Δ−=ΔmolekJgmolekJg/6.199/237−=Δ−=ΔLiquid water product at 298K Gaseous water product at 873K Negative sign indicates that the energy is releasedgSustainable Energy Science and Engineering CenterIf there are no losses, then all the Gibbs free energy is converted into electrical energy. Two electrons pass round the external circuit for each water molecule produced and each molecule of hydrogen used. For one mole of hydrogen used, 2N electrons pass round the external circuit- where N is the Avogadro’s number. If -e is the charge of one electron, then the charge that flows is -2Ne = -2F coulombsF is the faraday constant, or the charge on one mole of electrons. The electrical work done moving this charge round the circuit is (E is the voltage of the fuel cell) Electrical work done = charge × voltage = -2FE joulesWith no losses, we have 9Fuel Cell Input and OutputH2→ 2H++2e−O2+ 2e−+ 2H+→ H2OΔg =−2FEE =−Δg 2FSustainable Energy Science and Engineering CenterFour quantities called "thermodynamic potentials" are useful in the chemical thermodynamics of reactions and non-cyclic processes. They are internal energy, the enthalpy, the Helmholtz free energy and the Gibbs free energy. The four thermodynamic potentials are related by offsets of the "energy from the environment" term TS (energy you can get from the system’s environment by heating and the "expansion work" term PV (work to give the system final volume V at constant pressure. 6∆U = Q - W H = U + PVF = U - TS Helmoltz free energyG = U - TS + PV Gibbs free energyQ: heat added to the systemW: work done by the systemU: internal energyT: absolute temperatureS: final entropyV: final volumeThermodynamic PotentialsSustainable Energy Science and Engineering CenterSecond Law of ThermodynamicsA fuel cell represented as a control volume. E stands for electrical potential, measured in volts.For any isolated system, the 2ndlaw states that ΔSisolated≥ 0Sgen=ΔStotal=ΔSsys+ΔSsurr≥ 0Total change in entropy of both the system and surroundingsentropy change in the components of the systementropy change in the surroundingsSustainable Energy Science and Engineering CenterSecond Law of ThermodynamicsConsidering the chamber in which chemical reaction takes place, the system is a control volume with mass flowing across its boundaries. The entropy change for the system is the difference between the entropy of products, SPand the reactants, SR with N representing the number of moles of each component in the reaction. Any heat produced or consumed in the reaction is included in theexpression for the surroundings, where Qsurris the heat transferred from the system to the surroundings and Tois the temperature of the surroundings.ΔSsys= Sp− SR= NP∑s P− NR∑s RΔSsurr=QsurrToSgen= SP− SR()sys+QsurrToSustainable Energy Science and Engineering CenterThe Maxwell RelationsConsider a simple compressible control mass of fixed chemical composition. The following relations are found to be useful in the calculation of entropy in terms of other measurable quantities. The thermodynamic property relations arevdPTdsdhPdvTdsdu−=−=Entropy can not be measuredWe eliminate entropy from these equation by introducing two new forms of the thermodynamic property relation. Helmholtz function: A = U - TS ; a = u - Ts da = du - Tds - sdT = -sdT - PdvGibbs function: G = H - TS; g = h - Tsdg = -sdT + vdPSustainable Energy Science and Engineering CenterChemical ThermodynamicsChemical reactions proceed in the direction that minimizes the Gibbs energy G. The change in G is negative as the reaction approaches equilibrium and at chemical equilibrium the change in G is zero. The maximum work that an electrochemical cell can perform is equal to the change in G as reactants go to products. This work is done by the movement of electrical charge through a voltage, and at equilibrium SdTTdSVdPPdVWQdGSdTTdSVdPPdVdUdGSdTTdsPVUdSdTTdSdHdGGWcell−−++−=−−++=−−+=−−=Δ−=δδ)(maxFor a spontaneous reaction at constant temperature and pressure in a closed system and doing only expansion-type work, we will getdG=δQ−TdS≤0Sustainable Energy Science and Engineering CenterFor a reversible process:If the system is restricted to doing expansion work thennis the number of molesFor isothermal processstands for standard reference stateThe effect of temperature and pressure on ΔGδQ=TdSδW=PdVdG = VdP − SdTPV=nRTIdeal gas lawdG = nRTdPPG2− G1= nRTlnP2P1⎛ ⎝ ⎜ ⎞ ⎠ ⎟ G2= Go+ nRTlnP2Po⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Chemical ThermodynamicsSustainable Energy Science and Engineering CenterEquilibrium of a gas mixture:For a chemical reaction occurring at constant pressure and temperature, the reactant gases A and B form


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