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

7–9 ■ THE ENTROPY CHANGE OF IDEAL GASES

An expression for the entropy change of an ideal gas can be obtained from

Eq. 7–25 or 7–26 by employing the property relations for ideal gases (Fig.

7–31). By substituting ducvdTand PRT/vinto Eq. 7–25, the differ-

ential entropy change of an ideal gas becomes

dscv¬ (7–30)

dT

T

R¬

dv

v

354 | Thermodynamics

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

energy balance to be

Rate of net energy transfer Rate of change in internal,

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

For continuous operation (365  24 8760 h), the amount of power pro-

duced per year is

At $0.075/kWh, the amount of money this turbine can save the facility is

That is, this turbine can save the facility $737,800 a year by simply taking

advantage of the potential that is currently being wasted by a throttling

valve, and the engineer who made this observation should be rewarded.

Discussion This example shows the importance of the property entropy since

it enabled us to quantify the work potential that is being wasted. In practice,

the turbine will not be isentropic, and thus the power produced will be less.

The analysis above gave us the upper limit. An actual turbine-generator

assembly can utilize about 80 percent of the potential and produce more

than 900 kW of power while saving the facility more than $600,000 a year.

It can also be shown that the temperature of methane drops to 113.9 K (a

drop of 1.1 K) during the isentropic expansion process in the turbine instead

of remaining constant at 115 K as would be the case if methane were

assumed to be an incompressible substance. The temperature of methane

would rise to 116.6 K (a rise of 1.6 K) during the throttling process.

$737,800/yr

 1 0.9837 107 kWh>yr 21 $0.075>kWh 2

Annual power savings 1 Annual power production 21 Unit cost of power 2

0.9837 107 kWh>yr

Annual power productionW

#

out¢t^1 1123 kW^21 8760 h>yr^2

1123 kW

 1 118.2 kg>s 21 232.3222.8 2 kJ>kg

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

0 (steady)

⎭⎪⎪⎬⎪⎪⎫ ¡

1444444442444444443

SEE TUTORIAL CH. 7, SEC. 9 ON THE DVD.

INTERACTIVE

TUTORIAL