Environmental Engineering Reference
In-Depth Information
Absent any other force applied to the body, its energy
E
is unchanged despite its movement within
the region of space available to it. We may call this the
principle of conservation of energy
.
A simple example of the motion of a body that possesses kinetic and potential energy is that of
a satellite moving in orbit around the earth. The potential energy is that of the satellite mass in the
earth's gravitational field, which increases inversely in proportion to the distance of the satellite
from the center of the earth. If the satellite is in an eccentric orbit about the earth, the conservation
of energy requires that the satellite speed (and kinetic energy) is a maximum where it dips closest
to the earth's surface.
It is possible to change the energy
E
of a body by acting upon it with an external force. In
the case of the satellite, a quick impulse from its rocket engine can change its velocity and kinetic
energy, thereby changing its total energy
E
. The amount by which the total energy
E
is changed is
directly related to the amount of the rocket impulse. It is thereby possible to extend the statement
of the conservation of energy by taking into account the changes in
E
brought about by external
impulses applied to the moving body. This is the most general form of the principle of conservation
of energy.
3.2.2
The Energy of Atoms and Molecules
The matter of a macroscopic body is composed of microscopic atoms and/or molecules (themselves
aggregates of atoms). Sometimes, as for gases, these molecules are so widely separated in space
that they may be considered to be moving independently of each other, each possessing a distinct
total energy. Otherwise, in the case of liquids or solids, each molecule is under the influence of
forces exerted by nearby molecules, and we can only distinguish the aggregate energy of all the
molecules of the body. We call this energy the
internal energy
and give it the symbol
U
. Even
though the motion of microscopic molecules is not describable by Newtonian mechanics, it is still
possible to consider their total energy to be the sum of the kinetic energies of their motion and the
potential energies of their intermolecular forces.
It is not possible to observe directly the energies of individual atoms of a thermodynamic
substance, but changes in its internal energy are indirectly measurable by changes in temperature,
pressure, and density. These observables, called thermodynamic state variables, are the surrogates
for specifying internal energy.
3.2.3
Chemical and Nuclear Energy
Molecules are distinct stable arrangements of atomic species. Their atoms are held together by
strong forces that resist rearrangement of the atoms. To disassemble a molecule into its component
atoms usually requires the expenditure of energy, so that the molecules of a body may be considered
to possess an energy of formation related to how much energy was involved in assembling them
from their constituent atoms. If the internal energy
U
of a material body is changed, but the
individual molecules remain intact, then their chemical energy of formation remains unchanged
and contributes nothing to the change in
U
. On the other hand, if a chemical change occurs, so
that new molecular species are formed from the atoms present in the original species, there will
be a redistribution of energy among the components of the internal energy, of which the chemical
energy of formation of the molecules must be taken into account.
A similar energy change accompanies the formation of new atomic nuclei in the fission of the
nuclei of heavy elements or the fusion of light ones. Because the binding forces that hold nuclei
