Essay 2

Physical Background of Heat Conduction

2.1 Physical Nature

The first topic in our course is heat conduction. An illustration

of heat conduction is displayed in Fig. 2.1. It can easily be
understood that the copper rod is an effective pathway for heat
flow from the flame of the candle to the hand of the person
who is holding the rod. However, by observation of the heat-
conducting rod, nothing can be seen of the heat that is flowing.
Conduction is the mode of heat flow that cannot be directly
observed. Its occurrence can only be inferred from the effects
that heat flow has on the objects that are involved in the
conduction process.

The conduction process occurs at the molecular or sub-

molecular scale. In metallic objects, where there are free Fig. 2. 1 Illustration of heat conduction.
electrons, the unrestricted movement of the free electrons The person who is holding the copper
rod is experiencing the heat that is
causes them to be effective heat carriers. On the other hand, conducted from the flame to his/her
dielectric materials only contain bound electrons, but not free hand.
electrons. For such materials, heat conduction occurs by means
of molecules and atoms.

To best explain the heat conduction process, it is useful to recall some facts from basic physics.
First, the motion of molecules and sub-molecular particles ceases at absolute zero. At
temperatures above absolute zero, the mean kinetic energy of a cloud of small particles increases
with increasing temperature. As a consequence, the higher the temperature, the greater is the
kinetic energy. Another fact from basic physics teaches the outcome of collisions between
particles which possess different magnitudes of kinetic energy. That outcome is that the collision
increases the kinetic energy of the particle which initially possesses the lower kinetic energy, and
decreases the kinetic energy of the particle whose kinetic energy is initially higher. Since kinetic
energy can be regarded as equivalent to temperature, the collision process increases the
temperature of one of the colliding particles and decreases the temperature of the other.

This phenomenon is illustrated in Fig. 2.2. That figure consists of three parts, (a), (b), and (c).
Each of the parts shows a cluster of particles. In part (a), one of the particles is shown by color to

2.1
possess a higher temperature and a higher kinetic energy than the others. The higher temperature
particle is receiving heat continuously from an external source. Part (b), which corresponds to a
time that is slightly later than that of part (a), shows the effect of collisions between the higher
temperature particle and its immediate neighbors. Those collisions raise the temperatures of the
immediate neighbors. With the further passage of time, the immediate neighbors collide with
their immediate neighbors, thereby increasing the temperatures of the latter.

Fig. 2. 2 Schematic illustration of the process of heat conduction. Collisions cause a transfer of kinetic energy which, in
effect, is equivalent to the transfer of heat.

2.2 Thermal Conductivity vs. Electrical Conductivity

The effectiveness by which heat is transferred between hotter and cooler zones depends on a
material property called the thermal conductivity. Materials which contain free electrons are the
best conductors of heat and possess a high value of the thermal conductivity. In fact, aside from
one exception, the very best heat-conducting materials are also the very best conductors of
electricity. In the absence of free electrons, the magnitude of the thermal conductivity is much
lower than that of free-electron-possessing materials. However, the thermal conductivity is never
zero for any material. This non-zero thermal conductivity law does not hold for electric
conductivity.

To illustrate this fact, suppose that a person is doing some handyman electrical wiring at home
and does not have the proper tape or wire nuts to cover the joining of two wires. The person
twists the two wires together and throws a switch to initiate current flow. If the person is a risk
taker, he/she might grasp the joint and feel a shock, the magnitude of which depends on the
surface on which the person is standing. If, on the other hand, the person grasps the joint with a
piece of paper, it is unlikely that any shock would be felt. Next, suppose an experiment is to be
performed to determine the thermal insulating properties of paper. For this purpose, a penpoint-
type soldering iron will be used. Before the soldering iron is plugged into a wall outlet, a piece of
paper is stretched over the pointed end. When the current flow is initiated, an unpleasant burn
will result if the person would grasp the paper cover. This example indicates that electric
insulators and thermal insulators are not correlated.

2.2
The process of heat conduction in thermal insulators has no counterpart for electric insulators.
That heat conduction process for thermal insulators can be illustrated by making reference to Fig.
2.2. In this regard, now envision that the dashed lines which interconnect the individual spheres
(atoms) are elastic springs which permit the atoms to vibrate but which limit the extent of their
motion. As the atoms vibrate, they collide and exchange kinetic energy. This is the process of
heat conduction in the absence of free electrons.

2.3 Tables of Thermal Conductivity Values

Values of the thermal conductivity of metals and dielectric materials are conveyed in Tables 2.1
and 2.2, respectively. It is interesting to point out that the values of the thermal conductivities for
diamond and pyrolitic graphite, both excellent electric insulators, far exceed those for the best
thermal conducting metals.


Table 2. 1 Thermal conductivity of common metals as a function of temperature. [ ]
·

2.3
Table 2. 2 Thermal conductivity of dielectric materials as a function of temperature.

2.4