
Structure of Thermodynamic Theories 129
∑
n
i
. Then the entropy of the i-th component is simply given by eqn.(6.9) with the
possibility that the constants T
0
,V
0
can be different for the different components. An
equivalent way of handling this is to add a piece n
i
s
i
0
to each S
(i)
, and dropping the
nR piece from the earlier expression. Also, the specific heats will be different for
each component. Consequently
S =
∑
i
n
i
C
i
Rln
T
T
0
+
∑
i
n
i
Rln
V
n
i
V
0
+
∑
i
n
i
s
i
0
(6.32)
This can be rewritten as
S =
∑
i
n
i
C
i
Rln
T
T
0
+
∑
i
n
i
Rln
V
NV
0
+
∑
i
n
i
s
i
0
−R
∑
i
n
i
ln
n
i
N
(6.33)
Note that this total entropy is extensive, as each individual entropy in the sum is
extensive. The last term is the famous entropy ...