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

7–5 ■ PROPERTY DIAGRAMS INVOLVING ENTROPY

Property diagrams serve as great visual aids in the thermodynamic analysis

of processes. We have used P-vand T-vdiagrams extensively in previous

chapters in conjunction with the first law of thermodynamics. In the second-

law analysis, it is very helpful to plot the processes on diagrams for which

one of the coordinates is entropy. The two diagrams commonly used in the

second-law analysis are the temperature-entropyand the enthalpy-entropy

diagrams.

Consider the defining equation of entropy (Eq. 7–4). It can be

rearranged as

(7–14)

As shown in Fig. 7–16,dQrev intcorresponds to a differential area on a T-S

diagram. The total heat transfer during an internally reversible process is

determined by integration to be

(7–15)

which corresponds to the area under the process curve on a T-Sdiagram.

Therefore, we conclude that the area under the process curve on a T-S dia-

gram represents heat transfer during an internally reversible process. This

is somewhat analogous to reversible boundary work being represented by

Qint rev

2

1

T¬dS¬¬ 1 kJ 2

dQint revT¬dS ¬¬ 1 kJ 2

344 | Thermodynamics

The power output of the turbine is determined from the rate form of the

energy balance,

Rate of net energy transfer Rate of change in internal, kinetic,

by heat, work, and mass potential, etc., energies

The inlet state is completely specified since two properties are given. But

only one property (pressure) is given at the final state, and we need one

more property to fix it. The second property comes from the observation that

the process is reversible and adiabatic, and thus isentropic. Therefore, s 2 

s 1 , and

State 1:

State 2:

Then the work output of the turbine per unit mass of the steam becomes

wouth 1 h 2 3317.22967.4349.8 kJ/kg

P 2 1.4 MPa

s 2 s 1

f¬h 2 2967.4 kJ>kg

P 1 5 MPa

T 1 450°C

f¬

h 1 3317.2 kJ>kg

s 1 6.8210 kJ>kg#K

W

#

outm

#

1 h 1 h 22

m

#

h 1 W

#

out
m

#

h 2 ¬¬ 1 since Q

#

0, ke pe 02

E

#

inE

#

out

E

#

inE

#

out^ ^ dEsystem/dt^ ¬¬^0

∫

Internally

reversible

process

T

S

dA = T dS

= δQ

Area = T dS = Q

1

2

FIGURE 7–16

On a T-Sdiagram, the area under the
process curve represents the heat
transfer for internally reversible
processes.

0 (steady)

⎭⎪⎪⎬⎪⎪⎫ ¡

1444444442444444443

SEE TUTORIAL CH. 7, SEC. 5 ON THE DVD.

INTERACTIVE

TUTORIAL