Appendix G Forces, Energy, and Work
Appendix G Forces, Energy, and Work
The aim of this appendix is to describe a simple model that will help to clarify the meaning
of energy and mechanical work in macroscopic systems. The appendix applies fundamental
principles of classical mechanics to a collection of material particles representing a closed
system and its surroundings. Although classical mechanics cannot duplicate all features of
a chemical system—for instance, quantum properties of atoms are ignored—the behavior
of the particles and their interactions will show us how to evaluate the thermodynamic work
in a real system.
In broad outline the derivation is as follows. An inertial reference frame in which New-
ton’s laws of motion are valid is used to describe the positions and velocities of the particles.
The particles are assumed to exert central forces on one another, such that between any two
particles the force is a function only of the interparticle distance and is directed along the
line between the particles.
We define the kinetic energy of the collection of particles as the sum for all particles
of^12 mv^2 (wheremis mass andvis velocity). We define the potential energy as the sum
over pairwise particle–particle interactions of potential functions that depend only on the
interparticle distances. The total energy is the sum of the kinetic and potential energies.
With these definitions and Newton’s laws, a series of mathematical operations leads to the
principle of the conservation of energy: the total energy remains constant over time.
Continuing the derivation, we consider one group of particles to represent a closed ther-
modynamic system and the remaining particles to constitute the surroundings. The system
particles may interact with an external force field, such as a gravitational field, created by
some of the particles in the surroundings. The energy of the system is considered to be the
sum of the kinetic energy of the system particles, the potential energy of pairwise particle–
particle interactions within the system, and the potential energy of the system particles in
any external field or fields. The change in the system energy during a time interval is then
found to be given by a certain sum of integrals which, in the transition to a macroscopic
model, becomes the sum of heat and thermodynamic work in accord with the first law of
thermodynamics.
A similar derivation, using a slightly different notation, is given in Ref. [ 44 ].