APPENDIX G FORCES, ENERGY, AND WORK
G.5 THEWORKDONE ON THESYSTEM ANDSURROUNDINGS 495
G.5 The Work Done on the System and Surroundings
An additional comment can be made about the transfer of energy between the system and
the surroundings. We may use Eq.G.4.2, with appropriate redefinition of the quantities on
the right side, to evaluate the work done on thesurroundings. This work may be equal in
magnitude and opposite in sign to the workwlabdone on the system. A necessary condition
for this equality is that the interacting parts of the system and surroundings have equal
displacements; that is, that there be continuity of motion at the system boundary. We expect
there to be continuity of motion when a fluid contacts a moving piston or paddle.
Suppose, however, that the system is stationary and an interacting part of the surround-
ings moves. Then according to Eq.G.4.2,wlabis zero, whereas the work done on or by that
part of the surroundings isnotzero. How can this be, considering thatEtotremains con-
stant? One possibility, discussed by Bridgman,^6 is sliding friction at the boundary: energy
lost by the surroundings in the form of work is gained by the system and surroundings in
the form of thermal energy. Since the effect on the system is the same as a flow of heat
from the surroundings, the division of energy transfer into heat and work can be ambiguous
when there is sliding friction at the boundary.^7
Another way work can have different magnitudes for system and surroundings is a
change in potential energy shared by the system and surroundings. This shared energy
is associated with forces acting across the boundary, other than from a time-independent
external field, and is represented in Eq.G.2.7by the sum
P
iP
k^0 ik^0. In the usual types
of processes this sum is either practically constant, or else each term falls off so rapidly
with distance that the sum is negligible. SinceEtotis constant, during such processes the
quantityEsysCEsurrremains essentially constant.
G.6 The Local Frame and Internal Energy
As explained in Sec.2.6.2, a lab frame may not be an appropriate reference frame in which
to measure changes in the system’s energy. This is the case when the system as a whole
moves or rotates in the lab frame, so thatEsysdepends in part on external coordinates that
are not state functions. In this case it may be possible to define alocal framemoving with
the system in which the energy of the system is a state function, the internal energyU.
As before,riis the position vector of particleiin a lab frame. A prime notation will
be used for quantities measured in the local frame. Thus the position of particleirelative
to the local frame is given by vectorri^0 , which points from the origin of the local frame to
particlei(see Fig.G.3). The velocity of the particle in the local frame isvi^0 Ddri^0 =dt.
We continue to treat the earth-fixed lab frame as an inertial frame, although this is not
strictly true (Sec.G.10). If the origin of the local frame moves at constant velocity in the lab
frame, with Cartesian axes that do not rotate with respect to those of the lab frame, then the
(^6) Ref. [ 23 ], p. 47–56.
(^7) The ambiguity can be removed by redefining the system boundary so that a thin stationary layer next to
the sliding interface, on the side that was originally part of the system, is considered to be included in the
surroundings instead of the system. The layer removed from the system by this change can be so thin that the
values of the system’s extensive properties are essentially unaffected. With this redefined boundary, the energy
transfer across the boundary is entirely by means of heat.