the reduction of entropy in the hotter object is more than matched by the increase in

entropy of the cooler object. This must always be the case since the change in entropy

equals the heat divided by the temperature, so a hotter object “expels” less entropy than

the colder object “absorbs.” In our example, we treated the two objects as being at

constant temperatures, but even if their temperatures changed, the spontaneous flow of

heat would still cause the entropy of the system to increase.

What is the change in entropy of

the system during this

spontaneous heat transfer?

ǻS = ǻS 1 + ǻS 2

ǻS = í4.4 + 8.5 = 4.1 J/K

21.6 - Entropy and disroder (oops: disorder)

Entropy: Sometimes defined as a measure of

the disorder of a system.

The concept of entropy as disorder has entered popular culture thoroughly enough that

this section both uses, and critiques, this popular definition. Entropy often is described

as measuring the order, or really the disorder of a system. A system that has more

disorder has more entropy. For instance, when a new deck of playing cards is shuffled,

it goes from being well ordered (the cards are arranged by suit and number) to

disordered (the cards can be in many possible arrangements). The deck’s entropy has

increased.

In thermodynamics, entropy is more often discussed in terms of heat and temperature.

The entropy of an object increases as its temperature increases. For instance, when ice

is heated so that it melts, and then the liquid is further heated until it turns into steam,

the water’s entropy increases. On the other hand, in ice the water molecules are

“ordered” because of their crystalline structure. In a gas, the molecules have no defined

positions, they move randomly, and a particular water molecule may wander far from its

initial position. Transferring thermal energy into the system increases its temperature,

and its “disorder” increases as its temperature increases.

In some respects these examples work well, providing a visual sense or metaphor to the abstraction of entropy. On the other hand, they are not

particularly rigorous, and they do not necessarily link the underlying reality of entropy í its relation to heat í to what we actually see.

For instance, what we perceive as more “ordered” might in fact have greater entropy. Consider the example of ice cubes and liquid water. What

looks more “orderly”: a glass containing jagged irregular chunks of ice, or the same glass filled with an equivalent amount of liquid water? The

glass of water “looks” more orderly, but considering water at the molecular level, the ice is more orderly.

Something is also missing if entropy is only considered to be the “disorder” of a system. Consider an unusual trick deck of cards in which every

card is the two of spades. You can shuffle all you like without creating a more “disordered” deck. Entropy as disorder depends on the number

of different ways the elements of a system can be arranged. For instance, you can create more disorder by shuffling a standard 52-card deck

than one that consists of, say, only 13 cards since the 52-card deck can be arranged in many more ways (8.07×10^67 ) than can the 13-card one

(only 6.23×10^9 ).

In summary, considering entropy as disorder, and increasing entropy as increasing disorder, can be a useful metaphor at times, but it also has

its limits and potential traps.

Entropy and disorder

“Popular” definition of entropy: measure

of disorder

As temperature increases, so does

disorder

(^388) Copyright 2007 Kinetic Books Co. Chapter 21