chap5_23_37 - AAE 439 5.4 THERMOCHEMISTRY BASICS Ch5 23 AAE...

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Unformatted text preview: AAE 439 5.4 THERMOCHEMISTRY BASICS Ch5 23 AAE 439 Energies in Chemical Reactions QCV Enthalpy of Combustion (Reactions): H in = H reactant REACTANTS Stoichiometric fuel-oxidizer (air) mixture at standard state conditions: Tref and pref. H out = H product PRODUCTS Complete combustion at standard state conditions: : Tref and pref. h rxn qCV = h prod - h reac H rxn = H prod - H reac Graphical Interpretation Heat of Combustion: h C = -h rxn Ch5 24 AAE 439 ENTHALPY DEFINITION H abs = c p dT 0 T Absolute Enthalpy Enthalpy for calorically perfect gas. Relative Enthalpy H relative = c p dT cp is not known at low temperatures. Tref Enthalpy based on reference temperature (25C). H f T Standard Heat (or Enthalpy) of Formation: Enthalpy of Formation of a substance is the enthalpy change for the formation of one mole of the substance from its elements at standard conditions (pSTD = 1 atm, TSTD = 25C denoted by superscript ). The most stable form of an element at these conditions is referred to as the reference state and is defined as H f = 0. Heat of Reaction: H rxn H = n p H - n r H rxn f,products f,reactants Hess's Law uses standard heats of formation to calculate Heat of Reaction for any reaction. Ch5 25 AAE 439 ENTHALPY DEFINITION Heat of Fusion Energy required for the phase change from solid to liquid. Example: Melting of ice requires 6 kJ/mol at 0 C. H 2O s H 2O l Heat of Vaporization () () H = 6.00 kJ at 273K Energy required for the phase change from liquid to gas. Example: At the boiling point (100 C), the phase change from liquid to gas requires 40.7 kJ/mol. H 2O l H 2O g () () H = 40.7 kJ at 373K Ch5 26 AAE 439 Comments on Enthalpy Constant pressure processes common and for a perfect gas enthalpy is a function of temperature only: h cp = T p Sensible Enthalpy: Heat of a gas/gas mixture due to a temperature change. Changes in Enthalpy are also associated with chemical reactions or changes of h = c p dT state: Hrxn (HReaction), Hvap, Hfusion Enthalpy of Formation Heat absorbed or evolved when 1mole is formed from its constituent atoms or molecules @ reference conditions. Enthalpy of Reaction Products formed from reactants @ reference conditions. We distinguish between exothermic or endothermic reaction. Ch5 27 AAE 439 Example Ch5 28 AAE 439 5.5 Concept of Adiabatic Flame Temperature Ch5 29 AAE 439 TD PROCESSES in CHEM. SYSTEMS Chemical systems (chemical reactions) are treated as either constant-volume or constant-pressure processes. Energy Equation (1st Law of TD) E = U + E potential + E kinetic = Q - Wshaft - Wflow Inside a rocket combustion chamber, fluid velocity (Ekin) is small and height changes of the fluid mass (Epot) is negligible. Energy contained in the fluid is governed by the internal energy of the hot combustion gas. E =U dE = dU = ( Q - Wshaft - Wflow ) Work contribution in a rocket combustion chamber results from changes in specific volume of pressure. The fluid doesn't perform any mechanical work (Wshaft=0). W = - p(ext ) dV V1 V2 Wflow = p dV ConstantVolume (Isochoric) Process: ConstantPressure (Isobaric) Process: dU = Q dU = Q - p dV dH = Q H = U + pV Ch5 30 AAE 439 Definitions H reactant (Ti , p) = H product (Tad , p) h reactant (Ti , p) = h product (Tad , p) Constant-Pressure Adiabatic Flame Temperature Absolute enthalpy of the reactants at initial state (for example: Ti=298 K, p=1atm) equals absolute enthalpy of products at final state (T=Tad, p=1atm). Composition of combustion products must be known. At typical flame temperatures, products dissociate and mixture is comprised of many species. Graphic Illustration Ch5 31 AAE 439 Definitions U reactant (Tinitial , p initial ) = U product (Tad , p final ) H reactant - H product - V(p initial - p final ) = 0 Tinitial Tad h reactant - h product - ( - )=0 Mreactant Mproduct i i product i i Constant-Volume Adiabatic Flame Temperature reactant nh - nh - (n reactant Tinitial - n product Tad ) = 0 Perfect Gas Law: p initial V = p final V = reactants n i Tinitial = n reactants Tinitial i ad products n T m mix n reactants = n products Tad Mproducts m mix n products Per-Mass-of-Mixture: Mreactants Ch5 32 AAE 439 Examples Example #1: Estimate the constant-pressure adiabatic flame temperature for the combustion of a stoichiometric CH4air mixture. The pressure is 1 atm and the initial reactant temperature is 298 K. Assumptions: "Complete Combustion" (no dissociation), i.e. product mixture consists only of CO2, H2O, N2. Product mixture enthalpy is estimated using constant specific heats evaluated at 1200 K. Ch5 33 AAE 439 Examples Example #2: Estimate the constant-volume adiabatic flame temperature for a stoichiometric CH4air mixture using the same assumptions as in Example #1. Initial conditions are Ti=298 K, pi=1 atm. Ch5 34 AAE 439 5.6 Chemical Equilibrium Ch5 35 AAE 439 What happens in chemical reactions? How are mixtures of products composed? What does the composition of a product mixture depend on? How can we determine an equilibrium point/composition? Ch5 36 AAE 439 Thought Experiment Consider the combustion of CO and O2 in a fixed-volume, adiabatic reaction chamber. As the reactions proceed, both temperature and pressure rise until a final equilibrium condition is reached. Combustion Reaction: CO + 1 O2 CO2 2 Composition at high temperature: CO + 1 O2 cold (1 - ) CO2 + CO + O2 2 reactants 2 hot products Case Study: = 1: = 0: No heat released, mixture temperature, pressure and composition remain unchanged. Maximum heat released, mixture temperature & pressure would be highest possible allowable by 1st LTD. Ch5 37 ...
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This document was uploaded on 01/15/2012.

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