Chemistry - A Molecular Science

Chapter 9 Reaction Energetics

The number of ways in which a system can distribute its energy increases with the

amount of energy it has to distribute, so

the entropy of a system always increases with

temperature

. Similarly, adding heat to a system always increases the entropy of the

system. In our energy-book analogy, the alphabetized arrangement would represent the order expected in a constrained, low-entropy, low-temperature system, while the random arrangement would represent the unconstrained

, high-entropy, high-temperature system.

We now examine the effect of adding a small amount of heat to a system at high and low temperatures by examining the effect of

adding one book to the alphabetized and random

systems. The additional book increases the total number of books, so the number of ways they can be distributed increases (

S > 0). However, the effect of placing a book randomly Δ

in the two systems is very different. The

additional book would probably not go into its

correct location in the alphabetized system,

so the effect of the out-of-place book on the

order of the system would be dramatic. Simi

larly, adding a small amount of heat to a

system at low temperature has a dramatic e

ffect on the entropy. However, another ‘out-of-

place’ book in a random system would be hardly noticeable. Similarly, adding a small amount of heat to a system at high temperature has only a minor impact on the entropy. Adding 1 J of heat to a solid at 5 K (very orde

red, low entropy) has a much more dramatic

effect on the entropy than adding 1 J to a vapor at 500 K (highly disordered, high entropy). We conclude that the impact of adding heat to a system is greater if the initial energy of the system is low (low T). This relationship is expressed mathematically as follows:

(^) -1
q
S J K
T
Δ≥ ⋅
Eq. 9.5
Equation 9.5 indicates that the entropy change accompanying the addition of q joules at a temperature T is greater than or equal to q/T, so
S has units of JΔ
.K
-1. Whether
greater
than
or
equal to
applies depends upon how the heat is added. If the heat is added slowly
and the system remains at equilibrium,
† the equals sign applies, but if the heat is added so
quickly that equilibrium is not maintained, th
en the greater than sign applies. Also, note
that T
ΔS
≥ q, so T
ΔS and q have the same units, which are those of energy.
† Processes that are carried out while maintaining equilibrium are said
to be
reversible

. Indeed, a reversible process is one that is at

equilibrium. Processes that do not maintain equilibrium are said to be irreversible

.

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