Page 76 - Modern physical chemistry

4.3 Heat 65

Wherever two phases meet, there is a surface, an interface, between them. If S is the
area of this surface in a given system and r is the energy associated with formation of
unit area, the work needed to expand the area by dS is
dw=ydS. [4.6]
Property r is the surface tension for the two phases. Note that if r were negative, lower
interfacial energy would result on making the surface more irregular. When both phases
are fluid, the process would not stop until the surface wove back and forth, insofar as
possible, through the whole system. In effect, only one phase would remain. Such a
process does not occur spontaneously. So we expect r in (4.6) to be positive.
The electrical work done by a voltage l driving charge d,Q through a system is

dw=td[l. [4.7]
Similarly, the work done on increasing a magnetic field in volume V by dB is

dw=VHdB. [4.8]
Here B = pH and H is the magnetic intensity, B the magnetic induction. The work done
on increasing an electric field in volume V by dD is

dw=VEdD. [4.9]
Here D = EE and E is the electric intensity, D the electric displacement.
Qualitatively, work is energy that is being transported by some concerted movement.

4.3 Heat
The temperature is not necessarily uniform in a given system or between two systems
in contact with each other. But the zeroth law tells us that energy in the form of heat then
moves against the temperature gradient, acting to smooth out temperature differences.
Consider a small region in the given system through which the temperature T varies in
the x direction. Across an interior surface dS' which is oriented perpendicular to the gra-
dient aT/ ax, the movement of heat in the positive x direction in time dt is expressed as

aT
dq=-K- dSdt. [4.10]
ax
Factor K is a function of the conducting material, the temperature, and the pressure. It
is called the conduction coefficient.
The process involves hot molecules bombarding colder neighboring molecules, passing
energy on in a random fashion. Also, hot molecules may travel into colder regions and
cold ones into hotter regions, adding to the transport of energy. Thirdly, hot molecules
may radiate some of their energy as electromagnetic waves. This could then be absorbed
in the colder regions, exciting the molecules in a random manner.
Heat flow can be controlled by altering the conducting material and its thickness,
thus altering K and the gradient aT/ ax . Or the speed of the process may be increased.
A vacuum conducts only by radiation. Such transmission can be reduced to a negligible
amount by silvering a dividing surface, as in a thermos or a Dewar flask. A process carried
out without heat flow in or out is said to be adiabatic. Then at each stage, we have

dq=O. [4.11]
Qualitatively, heat is energy that is being transported by random chaotic movements.