Page 37 - Basic physical chemistry for the atmospheric sciences

Chemical thermodynamics 23

Lls = f dqrev (2. 1 7)
2
T
I
where, dqrev i s the quantity of heat added reversibly to a system at
temperature T. A reversible (or equilibrium) transformation is one in
which a system moves by infinitesimal amounts and infinitesimally
slowly between equilibrium states, so that the direction of the process
can be reversed at any time just by making an infinitesimal change in
the surroundings. Entropy is a function of state.
The second law of thermodynamics for a reversible transformation
states (in part) that f o r a reversible tramformation there is no change
in the entropy o f the universe (where "universe" refers to a system
and its surroundings). In other wor s , if a system receives heat revers­
d
ibly, the increase in its entropy is exactly equal in magnitude to the
decrease in the entropy of its surroundings.
The concept of reversibility is an abstraction. All natural transfor­
mations are, in fact, irreversible. In an irreversible (or spontaneous)
s
transformation a system undergoes finite changes at finite rate , and
these changes cannot be reversed simply by changing the surroundings
t
of the system by infinitesimal amoun s .
Exercise 2 .3 . Prove that for the same change f state of a system,
o
one carried out reversibly and the other irreversibly
wirrev < w rev and qirrev < qrev
where wirre v and wrev are the works of expansion done by a unit mass
s
of a system during irreversible and reversible transformation , respec­
tively , and qirrev and ev are the corresponding quantities of net heat
qr
taken in by the system.
Solution. In a reversible transformation, state functions of a system
(such as pressure) never differ from those of the surroundings by more
than an infinitesimal amount. Therefore,
Psystem = Psurroundings + d p

Hence, if a system expands reversibl , and in so doing passes from
y
state I to state 2, the work of expansion done by a u n it mass of the
system is