Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

790 | Thermodynamics

this fuel mixture. Determine (a) the theoretical air–fuel ratio
for this reaction; (b) the product–fuel ratio for this reaction;
(c) the air-flow rate for a fuel mixture flow rate of 5 kg/s; and
(d) the lower heating value of the fuel mixture with 200 per-
cent theoretical air at 25°C. Answers:(a) 14.83 kg air/kg fuel,
(b) 30.54 kg product/kg fuel, (c) 148.3 kg/s, (d) 43,672 kJ/kg fuel

15–106 The furnace of a particular power plant can be con-
sidered to consist of two chambers: an adiabatic combustion
chamber where the fuel is burned completely and adiabati-
cally, and a heat exchanger where heat is transferred to a
Carnot heat engine isothermally. The combustion gases in the
heat exchanger are well-mixed so that the heat exchanger is
at a uniform temperature at all times that is equal to the tem-
perature of the exiting product gases,Tp. The work output of
the Carnot heat engine can be expressed as

where Qis the magnitude of the heat transfer to the heat
engine and T 0 is the temperature of the environment. The
work output of the Carnot engine will be zero either when
TpTaf(which means the product gases will enter and exit
the heat exchanger at the adiabatic flame temperature Taf, and
thus Q0) or when TpT 0 (which means the temperature

WQhCQa 1 

T 0

Tp

b

of the product gases in the heat exchanger will be T 0 , and

thus hC 0), and will reach a maximum somewhere in

between. Treating the combustion products as ideal gases

with constant specific heats and assuming no change in their

composition in the heat exchanger, show that the work output

of the Carnot heat engine will be maximum when

Also, show that the maximum work output of the Carnot

engine in this case becomes

where Cis a constant whose value depends on the composi-

tion of the product gases and their specific heats.

15–107 The furnace of a particular power plant can be con-

sidered to consist of two chambers: an adiabatic combustion

chamber where the fuel is burned completely and adiabati-

cally and a counterflow heat exchanger where heat is trans-

ferred to a reversible heat engine. The mass flow rate of the

working fluid of the heat engine is such that the working

fluid is heated from T 0 (the temperature of the environment)

to Taf(the adiabatic flame temperature) while the combustion

products are cooled from Tafto T 0. Treating the combustion

products as ideal gases with constant specific heats and

assuming no change in their composition in the heat

exchanger, show that the work output of this reversible heat

engine is

WCT 0 a

Taf

T 0

 1 
ln

Taf

T 0

b

WmaxCTafa 1 


B

T 0

Taf

b

2

Tp 2 TafT 0

FIGURE P15–106

Heat

exchanger

Tp = const.

Q

Fuel

Air

Adiabatic

combustion

chamber

Surroundings

T 0

W

T 0

Tp

Adiabatic

combustion

chamber

W

T 0

T 0

Taf

Heat T 0

exchanger

Surroundings

Fuel Air

T 0

FIGURE P15–107