Page 40 - Basic physical chemistry for the atmospheric sciences

26 Basic physical chemistry

I Since T 1 = T2, the ideal gas equation reduces to Boyle s la , which can
w
'
t be written as p a 1 = p 2a2 , w h ere the a ' s are specific volumes. There­
1
fore, the last expression becomes
P2 a1 a2
ds = - R In - = - R ln- = R ln- (2.22)
gas
P 1 a2 a 1
From Eqs. (2. 2 1 ) and (2. 2 2),
a2
dsuniverse = R ln­ (2. 2 3)
a1
Hence, if the second law of thermodynamics is valid, it follows from
s
Eq . (2.20c) and (2.23) that
a2
R ln - > 0
a 1
or,

s
That i s , the gas spontaneously expand . If, on the other hand, the
gas spontaneously contracted, a 2 < a 1 and dsuniverse < 0, which would
violate the second law.

2.4 The third law of thermodynamics; absolute entropies
Although thermodynamics makes no assumptions about the structure
of matter, it is sometimes instructive to interpret thermodynamic re­
sults in terms of microscopic properties. For example, entropy may be
considered as a measure of the degree of disorder of the elements of a
s y stem: the more disorder the greater the entropy. From a molecular
viewpoint, the disorder is associated with the molecules of a system.
As in the case of energy or enthalpy, we are usually interested in
differences in entropy rather than absolute values. However, in the
case of entrop , it is possible to assign absolute valu s . This i s a
e
y
consequence of the third law of thermodynamics, which states that the
entropy o f per e ct crystals o f all pure elements and compounds is zero
f
at the absolute zero o f temperature (0 K). Consequently, the absolute
entropy of a substance at any temperature T is given by the change in
the entropy of the substance in moving from 0 K to T. The absolute
entropies of many substances (generally at 25°C and l atm - indicated
by s0 for the molar absolute entropy under standard conditions) are