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

Proof that Steady-Flow Devices Deliver the

Most and Consume the Least Work when

the Process Is Reversible

We have shown in Chap. 6 that cyclic devices (heat engines, refrigerators, and
heat pumps) deliver the most work and consume the least when reversible
processes are used. Now we demonstrate that this is also the case for individ-
ual devices such as turbines and compressors in steady operation.
Consider two steady-flow devices, one reversible and the other irre-
versible, operating between the same inlet and exit states. Again taking heat
transfer to the system and work done by the system to be positive quantities,
the energy balance for each of these devices can be expressed in the differ-
ential form as

Actual:

Reversible:

The right-hand sides of these two equations are identical since both devices
are operating between the same end states. Thus,

or

However,

dqrevT¬ds

dwrevdwactdqrevdqact

dqactdwactdqrevdwrev

dqrevdwrevdh
dke
dpe

dqactdwactdh
dke
dpe

Chapter 7 | 365

second T dsrelation by setting ds0:

Thus,

This result could also be obtained from the energy balance relation for an

isentropic steady-flow process. Next we determine the enthalpies:

State 1:

State 2:

Thus,

Discussion Note that compressing steam in the vapor form would require

over 500 times more work than compressing it in the liquid form between the

same pressure limits.

wrev,in 1 3194.52675.0 2 kJ>kg519.5 kJ/kg

P 2 1 MPa

s 2 s 1

f¬h 2 3194.5 kJ>kg¬¬ 1 Table A–6 2

P 1 100 kPa

1 sat. vapor 2

f¬

h 1 2675.0 kJ>kg

s 1 7.3589 kJ>kg#K

¬¬ 1 Table A–5 2

wrev,in

2

1

v¬dP

2

1

dhh 2 h 1

T¬dsdhv¬dP¬ 1 Eq. 7-24 2

ds 0 ¬ 1 isentropic process 2

f¬v¬dPdh