Thermodynamics and Chemistry

APPENDIX G FORCES, ENERGY, AND WORK

G.2 THESYSTEM ANDSURROUNDINGS 490

(a)

̊ij

̊i k

bc ̊kl

bc bc

bc

bc

bc

bc

bc

b b

bb

b b

b b

b b

b

b b

b

b

bb

bb

b

bbbbbb

b

b

(b)

̊ij

̊i k 00 ̊i k^0

bc bc

bc

bc

bc

bc

bc

bc

b b

bb

b b

b b

b b

b

u u

u

u

uu

uu

u

uuuuu u

u

u

Figure G.1 Assignment of particles to groups, and some representative particle–

particle potential functions (schematic). The closed dashed curve represents the sys-

tem boundary.

(a) The open circles represent particles in the system, and the filled circles are particles

in the surroundings.

(b) The filled triangles are particles in the surroundings that are the source of a con-

servative force field for particles in the system.

thepotential energyof the particles. Note that the kinetic energy depends only on particle
speeds and the potential energy depends only on particle positions.
The significance of Eq.G.1.11is that the total energyEtotdefined by Eq.G.1.12is
conserved. This will be true provided the reference frame used for kinetic energy is inertial
and the only forces acting on the particles are those responsible for the particle–particle
potential functions.

G.2 The System and Surroundings

Now we are ready to assign the particles to two groups: particles in the system and those in
the surroundings. This section will use the following convention: indicesiandjrefer to
particles in thesystem; indiceskandlrefer to particles in thesurroundings. This division
of particles is illustrated schematically in Fig.G.1(a). With this change in notation, Eq.
G.1.12becomes

EtotD

X

i

1

2 miv

2

iC

X

i

X

j>i

ijC

X

i

X

k

ikC

X

k

1

2 mkv

2

kC

X

k

X

l>k

kl (G.2.1)

A portion of the surroundings may create a time-independent conservative force field
(an “external” field) for a particle in the system. In order for such a field to be present,
its contribution to the force exerted on the particle and to the particle’s potential energy
must depend only on the particle’s position in the lab frame. The usual gravitational and
electrostatic fields are of this type.
In order to clarify the properties of a conservative external field, the indexk^0 will be
used for those particles in the surroundings that are not the source of an external field, and
k^00 for those that are, as indicated in Fig.G.1(b). Then the force exerted on system particle
idue to the field isFifieldD

P

k^00 Fik^00. If this were the only force acting on particlei,
the change in its kinetic energy during a time interval would be

R

Fifielddri(Eq.G.1.4).