1

Adiabatic Flame Temperature

ReactionQ

W

P2=Pa

T2=Ta

Consider the case where the cylinder is perfectly insulated so the process isadiabatic (Q = 0)

)()(

0)()(

1

Rii

Paii

RRii

Ppii

ThnThn

ThnThnQ

For a constant pressure process, the final products temperature, Ta, is known as the adiabatic flame temperature (AFT).

For a given reaction where the ni’s are known for both the reactants and the products, Ta can be calculated explicitly.

2

Ta,

Constant Pressure Adiabatic Flame Temperaturew/products at equilibrium

3

Constant Pressure Adiabatic Flame Temperaturew/products at equilibrium

4

Constant Volume Adiabatic Flame Temperature

ReactionQ

W

P2=PCV

T2=Ta

Consider the case where the piston is fixed and the cylinder is perfectly insulated so the process is adiabatic (Q = 0)

)()(

0)()(

1

Rii

Paii

RRii

Ppii

TunTun

TunTunQ

Note h = u + pv = u + RT, so

T) R)(Th(nTRThnR

iiP

aii 1))((

5

i

a

R

p

i

CV

R

p

R

p

R

p

p

pp

R

RR

PR

T

T

n

n

P

P

T

T

n

n

P

P

P

TRn

P

TRn

VV

Constant Volume Combustion Pressure

Assuming ideal gas behavior:

For large HCs the mole ratio term is small, e.g., for stoichiometric octaneair

22222188 4798)76.3(5.12 NOHCONOHC

i

a

i

a

i

a

R

p

i

CV

T

T

T

T

T

T

n

n

P

P06.1

5.60

64

For stoichiometric octane-air Ta is 2266K so PCV/Pi = 8.1

6

• One can calculate the AFT for the above stoichiometric reaction where the products are at equilibrium.

• Note dissociation in the products will result in a lower AFT since dissociation reactions are endothermic.

Adiabatic Flame Temperaturew/Products at Equilibrium

kNjNOiOHhOgH

fHeCOdOcNObHaCONOHC

)76.3)(4

( 2222222

• Computer programs are used for these calculations