Post on 18-Jul-2020
AAE 439
Ch5 –23
5.4 THERMOCHEMISTRY BASICS
AAE 439
Ch5 –24
Energies in Chemical Reactions
Enthalpy of Combustion (Reactions):
Heat of Combustion:
– QCV
REACTANTS Stoichiometric fuel-oxidizer (air)
mixture at standard state conditions: Tref and pref.
PRODUCTS Complete combustion
at standard state conditions: : Tref and pref.
Hin= H
reactant Hout= H
product
Δhrxn
≡ qCV
= hprod
− hreac
ΔHrxn
= Hprod
−Hreac
ΔhC= −Δh
rxn
Graphical Interpretation
AAE 439
Ch5 –25
ENTHALPY DEFINITION
Absolute Enthalpy Enthalpy for calorically perfect gas.
Relative Enthalpy cp is not known at low temperatures. Enthalpy based on reference temperature (25°C).
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 = 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 .
Heat of Reaction:
Hess’s Law uses standard heats of formation to calculate Heat of Reaction for any reaction.
ΔH
abs= c
pdT
0
T
∫
ΔHrelative
= cp
dTTref
T
∫
ΔHf°
ΔHf° = 0
ΔHrxn°
ΔH
rxn° = n
pΔH
f,products°∑ − n
rΔH
f,reactants°∑
AAE 439
Ch5 –26
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.
Heat of Vaporization
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.
H2O s( )→H
2O l( ) ΔH = 6.00 kJ at 273°K
H2O l( )→H
2O g( ) ΔH = 40.7 kJ at 373°K
AAE 439
Ch5 –27
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: ∆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.
c
p= ∂h
∂T
⎛⎝⎜
⎞⎠⎟
p
h = c
pdT∫
AAE 439
Ch5 –28
Example
AAE 439
Ch5 –29
5.5 Concept of Adiabatic Flame Temperature
AAE 439
Ch5 –30
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)
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.
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).
Constant–Volume (Isochoric) Process:
Constant–Pressure (Isobaric) Process:
E = U + Epotential
+ Ekinetic
= Q −Wshaft
−Wflow
dU = Q
dU = Q − p dV
H =U + pV
⎫⎬⎭
dH = Q
E =U ⇔ dE = dU = (δQ −δWshaft
−δWflow
)
W = − p
(ext )dV
V1
V2∫ ⇔ δWflow
= p dV
AAE 439
Ch5 –31
Definitions
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
Hreactant(T
i,p) = H
product(T
ad,p)
hreactant(T
i,p) = h
product(T
ad,p)
AAE 439
Ch5 –32
Definitions
Constant-Volume Adiabatic Flame Temperature
Perfect Gas Law:
Per-Mass-of-Mixture:
Ureactant
(Tinitial
, pinitial
) = Uproduct
(Tad
, pfinal
)
Hreactant
−Hproduct
− V (pinitial
− pfinal
) = 0
hreactant
− hproduct
−ℜ(T
initial
Mreactant
−T
ad
Mproduct
) = 0
nih
ireactant∑ − n
ih
iproduct∑ −ℜ(n
reactantT
initial− n
productT
ad) = 0
pinitial
V = niℜT
initialreactants∑ = n
reactantsℜT
initial
pfinal
V = niℜT
adproducts∑ = n
productsℜT
ad
M
reactants≡
mmix
nreactants
Mproducts
≡m
mix
nproducts
AAE 439
Ch5 –33
Examples
Example #1: Estimate the constant-pressure adiabatic flame temperature for the combustion of
a stoichiometric CH4–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 CO2,
H2O, N2.
Product mixture enthalpy is estimated using constant specific heats evaluated at 1200 °K.
AAE 439
Ch5 –34
Examples
Example #2: Estimate the constant-volume adiabatic flame temperature for a stoichiometric
CH4–air mixture using the same assumptions as in Example #1. Initial conditions are Ti=298 °K, pi=1 atm.
AAE 439
Ch5 –35
5.6 Chemical Equilibrium
AAE 439
Ch5 –36
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?
AAE 439
Ch5 –37
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:
Composition at high temperature:
Case Study: α = 1: No heat released, mixture temperature, pressure and composition
remain unchanged.
α = 0: Maximum heat released, mixture temperature & pressure would be
highest possible allowable by 1st LTD.
CO + 12 O
2→ CO
2
CO + 12 O
2⎡⎣ ⎤⎦cold
reactants→ (1−α ) CO
2+α CO + α
2O
2
⎡
⎣⎢
⎤
⎦⎥
hotproducts