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

when the direction of work is taken to be from the system (otherwise it

would be P dV). The pressure Pin the P dVexpression is the absolute pres-

sure, which is measured from absolute zero. Any useful work delivered by a

piston–cylinder device is due to the pressure above the atmospheric level.

Therefore,

(8–12)

A reversible process cannot involve any heat transfer through a finite tem-

perature difference, and thus any heat transfer between the system at tem-

perature Tand its surroundings at T 0 must occur through a reversible heat

engine. Noting that dS
dQ/Tfor a reversible process, and the thermal effi-

ciency of a reversible heat engine operating between the temperatures of T

and T 0 is hth
 1 T 0 /T,the differential work produced by the engine as a

result of this heat transfer is

(8–13)

Substituting the dWand dQexpressions in Eqs. 8–12 and 8–13 into the

energy balance relation (Eq. 8–11) gives, after rearranging,

Integrating from the given state (no subscript) to the dead state (0 subscript)

we obtain

(8–14)

where Wtotal usefulis the total useful work delivered as the system undergoes a

reversible process from the given state to the dead state, which is exergyby

definition.

A closed system, in general, may possess kinetic and potential energies,

and the total energy of a closed system is equal to the sum of its internal,

kinetic, and potential energies. Noting that kinetic and potential energies

themselves are forms of exergy, the exergy of a closed system of mass mis

(8–15)

On a unit mass basis, the closed system(or nonflow) exergyfis expressed as

(8–16)

where u 0 ,v 0 , and s 0 are the properties of the systemevaluated at the dead

state. Note that the exergy of a system is zero at the dead state since e
e 0 ,

v
v 0 , and s
s 0 at that state.

The exergy change of a closed system during a process is simply the dif-

ference between the final and initial exergies of the system,

(8–17)

 1 U 2 U 12 P 01 V 2 V 12 T 01 S 2 S 12 m

V 22 V 12

2

mg 1 z 2 z 12

¢X
X 2 X 1 
m 1 f 2 f 12 
 1 E 2 E 12 P 01 V 2 V 12 T 01 S 2 S 12

 1 ee 02 P 01 vv 02 T 01 ss 02

f
 1 uu 02 P 01 vv 02 T 01 ss 02 

V^2

2

gz

X
 1 UU 02 P 01 VV 02 T 01 SS 02 m

V^2

2

mgz

Wtotal useful
 1 UU 02 P 01 VV 02 T 01 SS 02

dWtotal useful
dWHEdWb,useful
dUP 0 dVT 0 dS

dQ
dWHET 0 dS

dWHE
a 1 

T 0

T

b dQ
dQ

T 0

T

dQ
dQ 1 T 0 dS 2 S

dW
P dV
 1 PP 02 dVP 0 dV
dWb,usefulP 0 dV

436 | Thermodynamics