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

Potential energy is also a form of mechanical energy, and thus it can be

converted to work entirely. Therefore, the exergyof the potential energy of a

system is equal to the potential energy itself regardless of the temperature

and pressure of the environment (Fig. 8–5). That is,

Exergy of potential energy: (8–2)

where gis the gravitational acceleration and zis the elevation of the system

relative to a reference level in the environment.

Therefore, the exergies of kinetic and potential energies are equal to them-

selves, and they are entirely available for work. However, the internal energy u

and enthalpy hof a system are not entirely available for work, as shown later.

xpe
pe
gz¬¬ 1 kJ>kg 2

426 | Thermodynamics

m

Wmax = mgz

z

⋅

⋅ ⋅

FIGURE 8–5

The work potentialor exergyof
potential energy is equal to the
potential energy itself.

EXAMPLE 8–1 Maximum Power Generation by a Wind Turbine

A wind turbine with a 12-m-diameter rotor, as shown in Fig. 8–6, is to be

installed at a location where the wind is blowing steadily at an average veloc-

ity of 10 m/s. Determine the maximum power that can be generated by the

wind turbine.

Solution A wind turbine is being considered for a specified location. The max-

imum power that can be generated by the wind turbine is to be determined.

Assumptions Air is at standard conditions of 1 atm and 25°C, and thus its

density is 1.18 kg/m^3.

Analysis The air flowing with the wind has the same properties as the stag-

nant atmospheric air except that it possesses a velocity and thus some

kinetic energy. This air will reach the dead state when it is brought to a com-

plete stop. Therefore, the exergy of the blowing air is simply the kinetic

energy it possesses:

That is, every unit mass of air flowing at a velocity of 10 m/s has a work

potential of 0.05 kJ/kg. In other words, a perfect wind turbine will bring the

air to a complete stop and capture that 0.05 kJ/kg of work potential. To

determine the maximum power, we need to know the amount of air passing

through the rotor of the wind turbine per unit time, that is, the mass flow

rate, which is determined to be

Thus,

This is the maximum power available to the wind turbine. Assuming a con-

version efficiency of 30 percent, an actual wind turbine will convert 20.0 kW

to electricity. Notice that the work potential for this case is equal to the

entire kinetic energy of the air.

Discussion It should be noted that although the entire kinetic energy of the

wind is available for power production, Betz’s law states that the power output

of a wind machine is at maximum when the wind is slowed to one-third of its

initial velocity. Therefore, for maximum power (and thus minimum cost per

Maximum power
m# 1 ke 2 
 1 1335 kg>s 21 0.05 kJ>kg 2 
66.8 kW

m

#


rAV
r

pD^2

4

V
 1 1.18 kg>m^32

p 1 12 m 22

4

1 10 m>s 2 
1335 kg>s

ke

V^2

2

1 10 m>s 22

2

a

1 kJ>kg

1000 m^2 >s^2

b
0.05 kJ>kg

10 m/s

FIGURE 8–6

Schematic for Example 8–1.