Chem_Thermodynamics_2008

Chem_Thermodynamics_2008 - AME 513 Spring 2008, F.N....

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AME 513 Spring 2008, F.N. Egolfopoulos 1 Chemical Thermodynamics 1. General Remarks If infinite time is allowed for a combustion process to be completed, then a final equilibrium state is reached that is a function of the initial equilibrium-state of the unburned reactants. The state of thermodynamic equilibrium for a simple compressible substance requires thermal (i.e. temperature uniform in space and time) and mechanical (i.e. pressure uniform in space and time) equilibrium. In multicomponent systems, as encountered in combustion, in order to have thermodynamic equilibrium the additional requirement of chemical equilibrium is needed. Chemical equilibrium is achieved when the chemical composition of the system does not change with time and is uniform in space. Chemical thermodynamics is the discipline that provides the necessary knowledge required for the development of quantitative laws that describe chemical equilibrium. Thus, given an initial unburned reactant state one can determine with great accuracy and at minimum computational cost the exact temperature and composition of the combustion products at thermodynamic equilibrium. As mentioned in the Introduction, this is very important information in terms of assessing, to the first order, the ability of the reacting mixture to burn efficiently and emit pollutants. At the same time it should be realized that combustion phenomena can not be entirely and some times even satisfactorily described based on equilibrium considerations, and other non-equilibrium processes must be also considered.
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AME 513 Spring 2008, F.N. Egolfopoulos 2 2. Chemical Equilibrium 2.1 Criterion for Chemical Equilibrium Consider a fixed mass (closed system) of a multicomponent mixture containing N chemical species. For this closed system the first law of thermodynamics dictates that during an infinitesimal change of state of the system, the amount of heat added, δ Q, the amount of work done, δ W, and the change of the energy of the system, dE, relate through: If p and V are the system pressure and volume respectively, considering only the pdV (expansion) work in (CT-2.1.1) we get: The second law of thermodynamics dictates that during any spontaneous process: TdS δ Q ( CT 2.1.3 ) where S is the system entropy and T the system temperature. Combining (CT-2.1.2) and (CT-2.1.3): Considering only the pdV mode of work and the state principle, which dictates that a state of a simple compressible substance is completely determined through two independent properties (such as S and V), then we conclude that the state of a multicomponent system is uniquely defined as follows: δ Q = dE + δ W ( CT 2.1.1 ) δ Q = dE + pdV ( CT 2.1.2 ) dE TdS pdv ( CT 2.1.4 )
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AME 513 Spring 2008, F.N. Egolfopoulos 3 where N i represents the number of moles of species i, with i=1,2,…,N. Equation (CT- 2.1.5) indicates that the energy of the multicomponent system can change by three different ways. The first term indicates that by keeping the volume and chemical composition fixed a
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This note was uploaded on 10/22/2008 for the course AME 513 taught by Professor Egolfopoulos during the Winter '08 term at USC.

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Chem_Thermodynamics_2008 - AME 513 Spring 2008, F.N....

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