Thermodynamics and Chemistry

CHAPTER 3 THE FIRST LAW

3.7 SHAFTWORK 83

!

w

bc

bc

(a)

!

w

bc

(b)

Figure 3.11 Shaft workwfor a fixed magnitude of shaft rotationÅ#as a function

of the angular velocity!Dd#=dt. The open circles indicate work in the limit of

infinite slowness. (a) System A of Fig.3.10. (b) System B of Fig.3.10.

In contrast to system A, the shaft work in system B has no reversible limit, as discussed
in the next section.

3.7.1 Stirring work

The shaft work done when a shaft turns a stirrer or paddle to agitate a liquid, as in system
B of Fig.3.10on the preceding page, is calledstirring work.
In system B, when the angular velocity!is zero and the water in which the stirrer is
immersed is at rest, the torquessysandbare both zero. When!is finite and constant, the
water is stirred in a turbulent manner and there is a frictional drag force at the stirrer blades,
as well as frictional forces at the shaft bearings. These forces make the value ofsyshave
the opposite sign from!, increasing in magnitude the greater is the magnitude of!. As a
result, the stirring work for a fixed value ofj# 2 # 1 jdepends on!in the way shown in
Fig.3.11(b). The work is positive for finite values of!of either sign, and approaches zero
in the limit of infinite slowness.
Stirring work is an example ofdissipative work. Dissipative work is work that is
positive for both positive and negative changes of the work coordinate, and that therefore
cannot be carried out reversibly. Energy transferred into the system by dissipative work is
not recovered as work done on the surroundings when the work coordinate is reversed. In
the case of stirring work, if the shaft rotates in one direction work is done on the system;
if the rotation direction is reversed, still more work is done on the system. The energy
transferred to the system by stirring work is converted by friction within the system into the
random motion of thermal energy: the energy is completelydissipated.
Because energy transferred to the system by dissipative work is converted to thermal
energy, we could replace this work with an equal quantity of positive heat and produce
the same overall change. The replacement of stirring work with heat was illustrated by
experiment 3 on page 61.
The shaft rotation angle#, which is the work coordinate for stirring work, is a property
of the system but is not a state function, as we can see by the fact that the state of the system
can be exactly the same for#D 0 and#D2. The work coordinate and work coefficient