Thermodynamics and Chemistry

APPENDIX G FORCES, ENERGY, AND WORK

G.4 MACROSCOPICWORK 493

Combining Eqs.G.3.2–G.3.5and rearranging, we obtain

X

i

Z

FisurdriDÅ

0

@

X

i

1

2 miv

2

i C

X

i

X

j>i

ijC

X

i

ifield

1

A (G.3.6)

Comparison of the expression on the right side of this equation with Eq.G.2.6shows that
the expression is the same as the change ofEsys:

ÅEsysD

X

i

Z

Fisurdri (G.3.7)

Recall that the vectorFisuris the force exerted on particlei, in the system, by the particles in
the surroundings other than those responsible for an external field. ThusÅEsysis equal to
the total work done on the system by the surroundings, other than work done by an external
field such as a gravitational field.

It might seem strange that work done by an external field is not included inÅEsys. The

reason it is not included is thatifieldwas defined to be a potential energy belonging

only to the system, and is thus irrelevant to energy transfer from or to the surroundings.

As a simple example of how this works, consider a system consisting of a solid

body in a gravitational field. If the only force exerted on the body is the downward

gravitational force, then the body is in free fall butÅEsysin the lab frame is zero; the

loss of gravitational potential energy as the body falls is equal to the gain of kinetic

energy. On the other hand, work done on the system by an external force thatopposes

the gravitational force is included inÅEsys. For example, if the body is pulled upwards

at a constant speed with a string, its potential energy increases while its kinetic energy

remains constant, andEsysincreases.

G.4 Macroscopic Work

In thermodynamics we are interested in the quantity of work done onmacroscopicparts of
the system during a process, rather than the work done on individual particles. Macroscopic
work is the energy transferred across the system boundary due to concerted motion of many
particles on which the surroundings exert a force. Macroscopicmechanicalwork occurs
when there is displacement of a macroscopic portion of the system on which a short-range
contact forceacts across the system boundary. This force could be, for instance, the pressure
of an external fluid at a surface element of the boundary multiplied by the area of the surface
element, or it could be the tension in a cord at the point where the cord passes through the
boundary.
The symbolwlabwill refer to macroscopic work measured with displacements in the
lab frame.
At any given instant, only the system particles that are close to the boundary will have
nonnegligible contact forces exerted on them. We can define aninteraction layer, a thin
shell-like layer within the system and next to the system boundary that contains all the
system particles with appreciable contact forces. We imagine the interaction layer to be
divided into volume elements, or segments, each of which either moves as a whole during
the process or else is stationary. LetRbe a position vector from the origin of the lab frame