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Combustion Chemistry Hai Wang University of Southern California 2013 Tsinghua-Princeton Summer School On Combustion Course Length: 3 hrs/day July 7 – 12, 2013 Copyright © 2013 by Hai Wang 1 This material is not to be sold, reproduced or distributed without prior written permission of the owner, Hai Wang. Background 1 http://en.wikipedia.org/wiki/File:Bunsen_burner_flame_types_.jpg 2 Background 2 • Combustion usually involves the oxidation of a (hydrocarbon CmHn) fuel to form oxidation products. Heat is released in the process. • For complete combustion, the global reaction in air can be expressed as, e.g., – CmHn + (m+n/4) O2 + (79/21)x(m+n/4) N2 mCO2 + (n/2) H2O + (79/21)x(m+n/4) N2 + Q • The above equation is balanced on a molar basis (per mole of the fuel). 3 Background 3 • Actual reaction proceeds through a series of simultaneous elementary reactions resulting from collision of two species. • Some of these species are molecules while others are unstable free-radicals. 4 Background 4 • Combustion chemistry involves a study of elementary reaction processes –Individually: fundamental reaction kinetics –collectively: reaction mechanisms and models 5 Background 5 • The end goal is to be able to predict – Local heat release rate – Ignition – Flame propagation and extinction – Coupled chemistry and fluid mechanics in flames – Pollutant (e.g., unburned HC, NOx and soot) formation – …… 6 Background 4 • The lecture series – Reviews the basic principles of thermodynamics and statistical mechanics – Discusses the nature of chain reaction mechanisms – Present simple theories of elementary chemical reactions – Explore the application of combustion chemistry in combustion studies – Present several special topics in combustion chemistry research 7 Background 5 • This series of lecture is linked to those given in the prior years – 2012 Michael Pilling • But it emphasizes the very fundamental knowledge and application of the knowledge in your work 8 Thermodynamics James Watt Sati Carnot James Prescott Joule Rudolf J. E. Clausius William Thomson Kelvin J Willard Gibbs Hermann von Helmholtz 9 Thermodynamics • Describes the driving force of a chemical process. • Determines the ideal end state of a reaction process. • The very foundation of chemical kinetics/combustion chemistry. 10 The First Law 1 • Energy is conserved: Q − W = U For a working fluid in a closed system, the heat (Q) it receives from the surrounding minus the work (W) it performs on the surrounding is equal to the change in its internal energy. • Q > 0 – receive heat from the surrounding (endothermic) Q < 0 – give off heat to the surrounding (exothermic). 11 The First Law 2 • The energy in the three forms may be transformed from one to another without limits – we know something is wrong here. • Measured by J, kJ, cal or kcal. • Internal energy is the total energy of molecules in the working fluid – a sum of kinetic and potential energies. 12 The First Law 3 • If only boundary work is done (e.g., gas expansion) under a constant pressure p, the first law may be re-written as where V is the volume, and the subscripts “1” and “2” represent the starting and ending states. • We define enthalpy as 13 Extensive versus Intensive Properties • Extensive: U, H, Q and W (J); V (cm3) • Intensive: u, h, q, w (J/mol or cal/mol) v, p, T (cm3/mol) • Thermodynamic properties are state functions • A state is usually defined by two independent intensive variables – e.g., (p, T), (p, v), (h, T) etc. • Equation of state – ideal gas where Ru is the universal gas constant (8.314 J/mol-K) 14 Two More Intensive Properties • Specific heats: – Constant volume: – Constant pressure: • For an ideal gas, h = h(T), u = u(T) etc 15 Second Law and Entropy • The Kelvin-Planck statement: It is impossible to construct a device that will operate in a cycle and produce no effect other than the raising of a weight and the exchange of heat with a single reservoir. • Entropy where (Q)int rev is the heat a working fluid receives during an infinitesimal, reversible process. 16 Entropy • A measure of molecular randomness • Ssolid < Sliquid < Sgas • For closed system, a spontaneous process (from 1 to 2) must have S2 – S1 ≥ 0 • That is, randomness always increase (a desk never cleans itself, cloths never fold themselves etc). • S increases as T , but decreases with p • The third law: S = 0 at 0 K. 17 S(T,P) • Apply the first law to a reversible constant T,P (piston) process Ideal gas law S(T,P) Standard-state entropy (1 atm) Po is the standard pressure of 1 atm 19 Three forms of enthalpy • • • • Sensible – heating/cooling Latent – melting, evaporation/condensation Reaction – due to chemical composition change Enthalpy of formation – the heat released from producing 1 mole of a substance from its elements at a constant temperature T – the enthalpy of formation is zero for the reference elements: graphite C(S), hydrogen H2, oxygen (O2), nitrogen (N2), and chlorine (Cl2). – C(S) + O2 CO2 + Q (= 393.522 kJ @298 K), hf,298K = 393.522 kJ/mol of CO2 20 Enthalpy of formation 21 Enthalpy of formation varies with T Generalize to 22 Total Enthalpy 23 Enthalpy of Reaction/Combustion • Standard enthalpy of combustion – Heat released from complete combustion of 1 mole of a fuel 24 Enthalpy of Reaction/Combustion For a generalized combustion reaction The heat of combustion is For a generalized chemical reaction The heat (enthalpy) of reaction is DH r ,T ìï üï = DH r ,298 + í å n i ' éëh (T ) - h (298)ùû - å n i éëh (T ) - h (298)ùû ý i' i ïî prod. react. ï 25þ Chemical Equilibrium • Compare The first reaction gives greater heat release, but the second reaction produces more entropy. So, how does the reaction know when to stop? 26 Chemical Equilibrium Gibbs free energy defines the compromise Equilibrium is found when dG/dε = 0 Equilibrium Constant • Quantify equilibrium • Consider the generic reaction • Keep in mind that during an equilibration process, reactants/products co-exist where ni and ni’ are the number of moles of the ith reactant and i’th product, respectively 28 Equilibrium Constant • For equilibrium at constant T & P, we have • Mass conservation requires Cannot be zero 29 Standard Gibbs Free Energy é æP g i (T , P ) = h f (T ) - Tsi (T ) = h f (T ) - T ê si ( T ) - R u ln ç èP ë æPö = h f (T ) - Tsi (T ) + R uT ln ç ÷ èP ø Standard Gibbs free energy (T, po = 1 atm) and then, öù ÷ø ú û Back to Equilibrium Constant Gibbs free energy of reaction Rearrange to give or the equlibrium constant Note Kp is a function of temperature only 31 Equilibrium Constant The equilibrium constant may also be defined by concentrations where Note Kc can be a function of pressure 32 About Equilibrium Constant • Kp is a function of temperature only • Forward/backward equilibrium constant 33 About Equilibrium Constant • Alternatively, for • The larger the equilibrium constant, the greater the completion of a reaction 34 About Equilibrium Constant 35 Adiabatic Flame Temperature Reactants (P, T0) Adiabatic Reactor (P) Products (P, Tad) Adiabaticity gives Let T0 = 298 K i.e., heat of combustion is used entirely to raise the temperature of the products 36 Adiabatic Flame Temperature 37 Adiabatic Flame Temperature Effect of Pressure 38 Equilibrium Composition Effect of Pressure 39 Thermochemical Properties 40 Thermochemical Properties The NASA Polynomials 41 Thermochemical Properties • Alex Burcat’s compilation (Elke Goos) http://garfield.chem.elte.hu/Burcat/burcat.html • Active tables (Ruscic) 42