Physical Chemistry
Lecture 14
Entropy
State functions
State functions have the following
quality:
∆U
=
∫ dU
= 0
where the integral sign indicates the
integral is taken over any closed path
Equivalent to saying that the integral is
exact
Reversible heat transfer in a
Carnot cycle
In the four-step
cycle
qh
Th
+
qc
Tc
= 0
A general cycle may
be subdivided into
many Carnot cycles
dqrev
∫ T
= 0
Entropy
The function represented by the heat
transferred reversibly divided by the
temperature has the qualities of a state
function
Clausius called this function the
entropy


Greek τροπε - transformation
Symbol S
dS
∫
= 0
Entropy change in irreversible
processes
Irreversible change of state
dU
= dq + dw = dq − Pext dV
Reversible change between same two
states
dU
= dqrev
+ dwmax
= TdS
− PdV
Equality gives a special requirement
TdS
= dq +
(P − Pext ) dV
Irreversibility and entropy
change
Possible conditions for actual processes



Condition 1: P > Pext; dV > 0
Condition 2: P < Pext; dV < 0
Condition 3: P = Pext; dV = 0
Under all conditions, - (Pext- P)dV ≥ 0
In any actual process in an isolated
system:


dq = 0
TdS ≥ 0
Entropy changes in real
systems
The change in the entropy determines
whether the process is spontaneous
The principle of Clausius:
“The entropy of an isolated system will
always increase in a spontaneous
process.”
Known as the second law of
thermodynamics
Calculation of entropy changes
Can calculate changes of entropy in a manner
analogous to other state variables
dS
 ∂S 
= 
 dT
 ∂T V
 ∂S 
+ 
 dV
 ∂V T
Must know derivatives to carry out integration
May also express entropy as a function of
other variables
dS
 ∂S 
= 
 dT
 ∂T  P
 ∂S 
+   dP
 ∂P T
Summary
Entropy is a state function
Entropy changes can be used to
determine spontaneity of processes in
isolated systems


Principle of Clausius
Second law of thermodynamics
Must evaluate derivatives to predict
changes