Forces and dynamics - Physical Processes in Earth and Environmental Sciences - page 47

much work?” Since Joule's classic experiments (Fig. 3.16)
we can say that mechanical work, W , done on a thermal
system produces a rise in temperature that corresponds to
a particular flow of heat,

proportion indicated - the calorific value of foods and
drinks stated on their packaging is given in both heat flow
units and in energy units. The bottle of fruit juice Mike has
just drunk, for example, has provided him with either
168 kJ of mechanical energy or 40 kcal of heat energy. In
another example, a unit mass of Mississippi river water
traveling at constant mean velocity loses potential energy
to do work in descending from its source in the Rockies to
the Gulf of Mexico (about 2000 km): the total tempera-
ture change expected (it could not be practically measured
because of intervening energy changes) is 2

Q . If this occurs in a thermally
isolated system, such as a calorimeter, where no heat can
be lost or gained, then we can state that

W . Very
accurate experiments have established that one heat flow
unit, called a calorie , is equivalent to exactly 4.185 J of
work. The equivalence of thermal and mechanical energy
stamps itself more obviously on everyday life when we real-
ize that food consumption releases energy in exactly the

Q

C.

3.4.5 Work done by thermal systems

Atmospheric dynamics depends upon work done on the
ambient atmosphere during ascent and descent of air
masses. The work is a consequence of the changing vol-
ume and density of the compressible gases that make up
the atmosphere. Clearly, the net work done depends on
the actual path taken, descent or ascent. Imagine that the
volume changes during ascent or descent are recorded by
a frictionless plunger (Fig. 3.17); the relationship we need
is given by

Latent heat of evaporation, L E , 540 cal g -1

L E

100

Vapor

Liquid and vapor

W p V , where p is a function of volume

and temperature. If V is positive, that is, the volume of

air is increased during ascent, then work has been done
by the air on its surroundings to expand it (Fig. 3.18).
If

L F

Latent heat of fusion, L F ,
80 cal g -1

0

V is negative, that is, the volume of air is decreased
during descent, then work has been done on the air by its
surroundings to compress it. This concept of path depend-
ence applies to all forms of work done by both mechanical

0 600

200 400 800

Heat flow, Q (cal)

Solid and liquid

Fig. 3.15 Temperature-heat flow diagram for the phases of water.

Joule

Position 1

F = m 1 g

∆ y ∆ y

Heat flow, ∆ Q = m 2 c Position 2

Work done, W = ∆ y m 1 g

Rotating paddles turned by a falling mass, m 1 , create a rise in
temperature within the mass, m 2 , of water of specific heat, c, in
the thermally isolated calorimeter. Energy conservation means
that the loss in potential energy of the mass ( = the work done on
the paddles) must be equivalent to the gain in thermal energy
by heat flow into the water. 1 kg of water would require a descent
of almost a kilometer to raise the temperature by 1 º C

Fig. 3.16 Sketch to illustrate principles of Joule's apparatus.