Page 42 - Physical chemistry eng

2.2 WORK 19

Work has several important characteristics:
• Work is transitory in that it only appears during a change in state of the system and
surroundings. Only energy, and not work, is associated with the initial and final
states of the systems.
• The net effect of work is to change U of the system and surroundings in accordance
with the first law. If the only change in the system results from a force acting through
a distance (as for example the movement of the mass in Figure 2.1), work has flowed
between the system and the surroundings. Work can usually be represented by a mass
in the surroundings that has been raised or lowered in Earth’s gravitational field.
• The quantity of work can be calculated using the definition
#
x f
w = F dx (2.4)
x
L i
Note that because of the scalar product in the integral, the work will be zero unless Mass
the force has a component along the displacement direction.
• The sign of the work follows from evaluating the preceding integral. If w 7 0 ,
¢U 7 0 for an adiabatic process. It is common usage to say that if w is positive, work P ,V i H 2 O 2
i
is done on the system by the surroundings. If w is negative, work is done by the system
H O
on the surroundings. The quantity of work can also be calculated from the change in 2
potential energy of the mass in the surroundings, ¢E potential = mg¢h =-w , where
g is the gravitational acceleration and ¢h is the change in the height of the mass m.
Using the definition of pressure as the force per unit area (A), the work done in moving Electrical
the mass in Figure 2.1 is given by generator
#
x f x f V f
w = F dx =- P external Adx =- P external dV (2.5)
x x Mass
L i L i LV i
The minus sign appears because F and dx are vectors that point in opposite directions.
Initial state
Note that the pressure that appears in this expression is the external pressure P external
which need not equal the system pressure P.
An example of another important kind of work, electrical work, is shown in Figure 2.2,
Mass
in which the content of the cylinder is the system. Electrical current flows through a con-
ductive aqueous solution and water undergoes electrolysis to produce H 2 and O 2 gas. The
current is produced by a generator, like that used to power a light on a bicycle through the
mechanical work of pedaling. As current flows, the mass that drives the generator is low-
P ,V H 2 O 2
ered. In this case, the surroundings do the electrical work on the system. As a result, some i f
of the liquid water is transformed to H 2 and O 2 . From electrostatics, the work done in
transporting a charge Q through an electrical potential difference is H O
f
2
w electrical = Qf (2.6)
For a constant current I that flows for a time t, Q = It . Therefore,
Electrical
w electrical = Ift (2.7) generator
The system also does work on the surroundings through the increase in the volume of
the gas phase at the constant external pressure P , as shown by the raised mass on the
i
piston. The total work done is

V f
w = w P-V + w electrical = Ift - P external dV = Ift - P external (V - V ) (2.8) Mass
i
f
LV i
Other forms of work include the work of expanding a surface, such as a soap bub- Final state
ble, against the surface tension. Table 2.1 shows the expressions for work for four dif- FIGURE 2.2
ferent cases. Each of these different types of work poses a requirement on the walls Current produced by a generator is used
separating the system and surroundings. To be able to carry out the first three types of to electrolyze water and thereby do work
work, the walls must be movable, whereas for electrical work, they must be conductive. on the system as shown by the lowered
Several examples of work calculations are given in Example Problem 2.1. mass linked to the generator.