Part IV — Work
Lecture 12 — PV work
Recall the notion of a thermodynamic process: change of state via some external intervention.
Common processes include:
•
Adding or removing heat
•
Expanding or compressing the system
Often, the process involves requires or generates work. We say, work is done on the system, or done
by the system. Sign convention: work done on the system is positive, work done by the system is
negative. (We are keeping track of the energy of the system.)
Recall that being able to calculate the required amount of work for a process, and designing a
process so that the minimum amount of work is required, or the maximum amount of work is
generated, are central goals of thermodynamics.
An external force acting through a small displacement does a small amount of work
dW
=
F
ext
dx
=

P
ext
dV
We integrate to Fnd the total work done during the process
W
=

±
V
2
V
1
P
ext
dV
Sign convention: when we compress the system,
dx >
0 (displacement in direction of force applied)
and
dV <
0. In compressing, we do work on the system, increasing its energy (like compressing a
spring).
Work is
not
a state variable — it depends on the path (i.e., the details of the process). ±or example:
it is harder to compress a hot gas than a cold one. So consider a process in which we increase
T
by some amount and decrease
V
by some amount. If we warm Frst, the work will be greater than
if we warm after compressing. (sketch) We will see more speciFc examples of this next lecture.
To compute
W
, we need to know how
P
ext
varies as we do the volume change. If we do the change
slowly enough,
P
ext
=
P
(
V,T
) (the equilibrium system pressure) to a close approximation — nearly
balanced forces, very slow motion of the piston. This we call a reversible change — at every point
along the way, we are very close to equilibrium. Then, we can compute the work, if we have an
EOS to tell us
P
(
V,T
).
In general, if the process is done at a Fnite rate, it won’t be “reversible”. In that case,
W
=
W
rev
+
W
lost
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