Thermodynamics and Chemistry

CHAPTER 3 THE FIRST LAW

3.7 SHAFTWORK 84

(a)

MIRKO JUNGE / COMMONS.WIKIMEDIA.ORG

water

opening for

thermometer

(b)

Figure 3.12 Joule paddle wheel.

(a) Joule’s original paddle wheel on exhibit at the Science Museum, London.

(b) Cross-section elevation of paddle wheel and water in copper vessel. Dark shading:

rotating shaft and paddle arms; light shading: stationary vanes.

of work with a reversible limit are always state functions, whereas the work coordinate of
any kind of dissipative work isnota state function.
In system B of Fig.3.10, there is in addition to the stirring work the possibility of
expansion work given by∂wD pdV. When we take both kinds of work into account,
we must treat this system as having two work coordinates:#for stirring work andV for
expansion work. Only the expansion work can be carried out reversibly. The number of
independent variables in equilibrium states of this system is two, which we could choose as
TandV. Thus, the number of independent variables of the equilibrium states is one greater
than the number of work coordinates forreversiblework, in agreement with the general rule
given on page 74.

3.7.2 The Joule paddle wheel

A good example of the quantitative measurement of stirring work is the set of experiments
conducted by James Joule in the 1840s to determine the “mechanical equivalent of heat.”
In effect, he determined the quantity of dissipative stirring work that could replace the heat
needed for the same temperature increase.
Joule’s apparatus contained the paddle wheel shown in Fig.3.12. It consisted of eight
sets of metal paddle arms attached to a shaft in a water-filled copper vessel. When the shaft
rotated, the arms moved through openings in four sets of stationary metal vanes fixed inside
the vessel, and churned the water. The vanes prevented the water from simply moving
around in a circle. The result was turbulent motion (shearing or viscous flow) in the water
and an increase in the temperature of the entire assembly.
The complete apparatus is depicted in Fig.3.13on page 86. In use, two lead weights
sank and caused the paddle wheel to rotate. Joule evaluated the stirring work done on the
system (the vessel, its contents, and the lid) from the change of the vertical positionhof the
weights. To a first approximation, this work is the negative of the change of the weights’