Environmental Engineering Reference
In-Depth Information
quantity that accounts for the character of the exchange of energy between a thermodynamic system
and its environment.
3.3.1
Work Interaction
Newtonian mechanics employs the concept of work as the exertion of a force acting through a
displacement or a couple acting through an angular displacement.
2
We say that the amount of
work required to lift a mass
m
through a vertical distance
r
in the earth's gravitational field is the
product of the magnitude of the gravity force,
mg
, times the distance
r
, where
g
is the magnitude
of the local acceleration of gravity. In thermodynamics, by convention, positive work is defined
to be the product of the force exerted by a system on the environment times any displacement of
the environment that occurs while the force is acting. (By Newton's principle, the force that the
system exerts on the environment is equal in magnitude but opposite in direction to the force that
the environment exerts on the system.) If the force
F
en
exerted on the environment by the system
is accompanied by an incremental displacement
dr
en
of the environment in the direction of
F
en
,
the increment of work may be expressed as
d
W
≡
F
en
dr
en
(3.2)
When the system does work on the environment,
d
W
is positive; when the environment does work
on the system, then
d
is negative.
There are many simple examples of a work interaction. If a gas is contained in a circular
cylinder capped at one end and fitted with a movable piston at the other, then the force exerted by
the gas on that portion of the environment that is the movable piston is
pA
, where
p
is the gas
pressure and
A
is the piston face area. If the piston is displaced an incremental distance
dr
en
in the
direction of the pressure force
pA
, the positive work increment
d
W
W
in this displacement is
d
W
=
pAdr
en
=
p
(
Adr
en
)
=
pdV
(3.3)
where
dV
Adr
en
is the increment in the volume
V
of the gas in the cylinder. Or the work
interaction with the environment may involve the movement of an increment of electric charge
dQ
en
through an increase in electric potential
=
φ
en
, such as when a current flows from the system
to and from an electric motor in the environment, for which the work increment is
d
W
=
φ
en
dQ
en
(3.4)
Another common example is the rotation of the shaft of a turbine (a material system) that applies
a torque
T
en
(or couple) to an electric generator (the environment) attached to the turbine, rotating
it through an increment of angle
d
θ
en
in the same direction as the torque, giving rise to a positive
work increment,
d
W
=
T
en
d
θ
en
(3.5)
2
A couple is the product of the distance separating two equal but opposite forces times the magnitude of the
force.
