AAE THERMOCHEMISTRY BASICS

Transcription

1 5.4 THERMOCHEMISTRY BASICS Ch5 23

2 Energies in Chemical Reactions Enthalpy of Combustion (Reactions): Q CV H in = H reactant H out = H product REACTANTS Stoichiometric fuel-oxidizer (air) mixture at standard state conditions: T ref and p ref. PRODUCTS Complete combustion at standard state conditions: : T ref and p ref. Δh rxn q CV = h prod h reac ΔH rxn = H prod H reac Graphical Interpretation Heat of Combustion: Δh C = Δh rxn Ch5 24

3 ENTHALPY DEFINITION Absolute Enthalpy Enthalpy for calorically perfect gas. ΔH abs = T 0 c p dt Relative Enthalpy c p is not known at low temperatures. ΔH relative = Enthalpy based on reference temperature (25 C). T T ref c p dt Standard Heat (or Enthalpy) of Formation: ΔH f 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 (p STD = 1 atm, T STD = 25 C denoted by superscript ). The most stable form of an element at these conditions is referred to as the reference state and is defined as ΔH f = 0. Heat of Reaction: ΔH rxn Hess s Law uses standard heats of formation to calculate Heat of Reaction for any reaction. ΔH rxn = n p ΔH f,products n r ΔH f,reactants Ch5 25

4 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 2 O s Heat of Vaporization ( ) H 2 O( l) ΔH = 6.00 kj at 273 K 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 2 O l ( ) H 2 O( g) ΔH = 40.7 kj at 373 K Ch5 26

5 Comments on Enthalpy Constant pressure processes common and for a perfect gas enthalpy is a function of temperature only: 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 state: H rxn ( H Reaction ), H vap, H fusion Enthalpy of Formation Heat absorbed or evolved when 1mole is formed from its constituent atoms or reference conditions. Enthalpy of Reaction c p = h = h T Products formed from reference conditions. We distinguish between exothermic or endothermic reaction. c p dt p Ch5 27

6 Example Ch5 28

7 5.5 Concept of Adiabatic Flame Temperature Ch5 29

8 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 W shaft W flow Inside a rocket combustion chamber, fluid velocity (E kin ) is small and height changes of the fluid mass (E pot ) is negligible. Energy contained in the fluid is governed by the internal energy of the hot combustion gas. E = U de = du = (δq δw shaft δw flow ) Work contribution in a rocket combustion chamber results from changes in specific volume of pressure. The fluid doesn t perform any mechanical work (W shaft =0). V 2 W = p (ext ) dv δw flow = p dv V 1 Constant Volume (Isochoric) Process: du = Q Constant Pressure (Isobaric) Process: du = Q p dv H = U + pv dh = Q Ch5 30

9 Definitions Constant-Pressure Adiabatic Flame Temperature H reactant (T i,p) = H product (T ad,p) h reactant (T i,p) = h product (T ad,p) Absolute enthalpy of the reactants at initial state (for example: T i =298 K, p=1atm) equals absolute enthalpy of products at final state (T=T ad, 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

10 Definitions Constant-Volume Adiabatic Flame Temperature U reactant (T initial, p initial ) = U product (T ad, p final ) H reactant H product V(p initial p final ) = 0 h reactant h product R( T initial M reactant T ad M product ) = 0 n i h i n i h i R(n reactant T initial n product T ad ) = 0 reactant product Perfect Gas Law: p initial V = p final V = reactants products n i RT initial = n reactants RT initial n i RT ad = n products RT ad Per-Mass-of-Mixture: M reactants m mix n reactants M products m mix n products Ch5 32

11 Examples Example #1: Estimate the constant-pressure adiabatic flame temperature for the combustion of a stoichiometric CH 4 air 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 CO 2, H 2 O, N 2. Product mixture enthalpy is estimated using constant specific heats evaluated at 1200 K. Ch5 33

12 Examples Example #2: Estimate the constant-volume adiabatic flame temperature for a stoichiometric CH 4 air mixture using the same assumptions as in Example #1. Initial conditions are T i =298 K, p i =1 atm. Ch5 34

13 5.6 Chemical Equilibrium Ch5 35

14 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

15 Thought Experiment Consider the combustion of CO and O 2 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 O 2 CO 2 Composition at high temperature: CO + 1 O 2 2 cold (1 α ) CO 2 + α CO + α reactants 2 O 2 Case Study: = 1: No heat released, mixture temperature, pressure and composition remain unchanged. = 0: Maximum heat released, mixture temperature & pressure would be highest possible allowable by 1 st LTD. hot products Ch5 37