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

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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°∑

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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

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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∫

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Ch5 –28

Example

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Ch5 –29

5.5 Concept of Adiabatic Flame Temperature

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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

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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)

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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

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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.

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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.

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5.6 Chemical Equilibrium

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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?

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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