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

the work associated with the expansion or contraction of an elastic solid bar

by replacing pressure Pby its counterpart in solids,normal stresssn
F/A,

in the work expression:

(2–30)

where Ais the cross-sectional area of the bar. Note that the normal stress

has pressure units.

Work Associated with the Stretching of a Liquid Film

Consider a liquid film such as soap film suspended on a wire frame

(Fig. 2–33). We know from experience that it will take some force to stretch

this film by the movable portion of the wire frame. This force is used to

overcome the microscopic forces between molecules at the liquid–air inter-

faces. These microscopic forces are perpendicular to any line in the surface,

and the force generated by these forces per unit length is called the surface

tensionss, whose unit is N/m. Therefore, the work associated with the

stretching of a film is also called surface tension work.It is determined from

(2–31)

where dA
 2 b dxis the change in the surface area of the film. The factor 2

is due to the fact that the film has two surfaces in contact with air. The force

acting on the movable wire as a result of surface tension effects is F
 2 bss

where ssis the surface tension force per unit length.

Work Done to Raise or to Accelerate a Body

When a body is raised in a gravitational field, its potential energy increases.

Likewise, when a body is accelerated, its kinetic energy increases. The con-

servation of energy principle requires that an equivalent amount of energy

must be transferred to the body being raised or accelerated. Remember that

energy can be transferred to a given mass by heat and work, and the energy

transferred in this case obviously is not heat since it is not driven by a tem-

perature difference. Therefore, it must be work. Then we conclude that

(1) the work transfer needed to raise a body is equal to the change in the

potential energy of the body, and (2) the work transfer needed to accelerate

a body is equal to the change in the kinetic energy of the body (Fig. 2–34).

Similarly, the potential or kinetic energy of a body represents the work that

can be obtained from the body as it is lowered to the reference level or

decelerated to zero velocity.

This discussion together with the consideration for friction and other

losses form the basis for determining the required power rating of motors

used to drive devices such as elevators, escalators, conveyor belts, and ski

lifts. It also plays a primary role in the design of automotive and aircraft

engines, and in the determination of the amount of hydroelectric power that

can be produced from a given water reservoir, which is simply the potential

energy of the water relative to the location of the hydraulic turbine.

Wsurface

2

1

ss dA¬¬ 1 kJ 2

Welastic

2

1

F dx

2

1

sn A dx¬¬ 1 kJ 2

68 | Thermodynamics

x

F

FIGURE 2–32

Solid bars behave as springs under the
influence of a force.

dx

F

Movable

wire

Rigid wire frame

Surface of film

b

x

FIGURE 2–33

Stretching a liquid film with a
movable wire.

x 1 = 1 mm

Rest

position

F 1 = 300 N

x 2 = 2 mm

F 2 = 600 N

FIGURE 2–31

The displacement of a linear spring
doubles when the force is doubled.