Chemistry Reference
In-Depth Information
is due to random thermal bombardment of the molecules on the walls. The ten-
sion of rubber against restraining clamps is due to random coiling and uncoiling
of chain molecules. The molecules of an ideal elastomer are independent agents.
There is no intermolecular attraction, by definition. (If there is appreciable inter-
molecular attraction,
the material will not exhibit high elasticity, as we saw
earlier.)
Gas molecules tend to their most likely distribution in space. The molecules
of an ideal elastomer tend to their most probable conformation, which is that of a
random coil. The most probable state in either case is that in which the entropy is
a maximum.
If the temperature of an ideal gas is increased at constant volume, its pres-
sure rises in direct proportion to the temperature. Similarly, the tension of a rub-
ber specimen at constant elongation is directly proportional to temperature. An
ideal gas undergoes no temperature change on expanding into a vacuum. An
ideal rubber retracting without load at constant volume undergoes no tempera-
ture change. Under adiabatic conditions, an ideal gas cools during expansion
against an opposing piston, and a stretched rubber cools during retraction against
a load.
Table 4.3
lists the thermodynamic relations between pressure, volume, and
temperature of an ideal gas and its internal energy
U
and entropy
S
. We see
that the definition of an ideal gas leads to the conclusion that the pressure
exerted by such a material is entirely due to an entropy contribution. If an ideal
gas confined at a certain pressure were allowed to expand against a lower pres-
sure, the increase in volume would result in the gas going to a state of greater
entropy. The internal energy of the ideal gas is not changed in expanding at
constant temperature.
4.5.2.2
Thermodynamics of Rubber Elasticity
In an ideal gas we considered the relations between the thermodynamic properties
S
and
U
, on the other hand, and the state variables
P
,
V
, and
T
of the substance.
With an ideal elastomer we shall be concerned with the relation between
U
and
S
and the state variables force, length, and temperature.
The first law of thermodynamics defines the internal energy from
dU
dq
1
dw
(4-6)
(The increased
dU
in any change taking place in a system equals the sum of the
energy added to the system by the heat process,
dq
, and the work performed on it,
dw
.)
The second law of thermodynamics defines the entropy change
dS
in any
reversible process:
TdS
5
dq
rev
(4-7)
