Thermodynamics and Chemistry

APPENDIX G FORCES, ENERGY, AND WORK

G.4 MACROSCOPICWORK 494

R

ri 

ri

bc

rs

b



Figure G.2 Position vectors within the system. Segmentof the interaction layer

lies within the heavy curve (representing the system boundary) and the dashed lines.

Open circle: origin of lab frame; open square: point fixed in system boundary at

segment; filled circle: particlei.

to a point fixed in the boundary at segment, and letribe a vector from this point to
particlei(Fig.G.2). Then the position vector for particleican be writtenriDRCri.
LetFsurbe the total contact force exerted by the surroundings on the system particles in
segment:FsurD

P

iïiF
sur
i , whereïiis equal to^1 when particleiis in segmentand
is zero otherwise.
The change in the system energy during a process is, from Eq.G.3.7,

ÅEsysD

X

i

Z

FisurdriD

X

X

i

Z

ïiFisurd.RCri/

D

X

Z

FsurdRC

X

X

i

Z

ïiFisurdri (G.4.1)

We recognize the integral

R

FsurdRas the macroscopic work at surface element,
because it is the integrated scalar product of the force exerted by the surroundings and the
displacement. The total macroscopic work during the process is then given by

wlabD

X

Z

FsurdR (G.4.2)

Heat,qlab, can be defined as energy transfer to or from the system that is not accounted
for by macroscopic work. This transfer occurs by means of chaotic motions and collisions
of individual particles at the boundary. With this understanding, Eq.G.4.1becomes

ÅEsysDqlabCwlab (G.4.3)

withwlabgiven by the expression in Eq.G.4.2andqlabgiven by

qlabD

X

X

i

Z

ïiFisurdri (G.4.4)