BioPHYSICAL chemistry

that the process will occur, while a negative ΔSmeans that

the process will not happen. If ΔSis zero, then the system

is in equilibrium and nothing will change. As an example

of entropy changes, consider the spontaneous process of

an ice cube melting in a cup of water (Figure 3.4). The

change in entropy is given by the transfer of heat, q, from

the cup to the ice cube, with the ice cubes and water being

at the specific temperatures of Tcubeand Twater:

(3.15)

where qis positive for the ice cube since it receives heat andqis negative

for the water since the heat leaves the water. The ice cube is at a lower

temperature than the water. Thus, the overall value of the entropy change

is positive and the ice cube can melt based upon the second law. From

a molecular view, the water in the cup is in equilibrium between the

frozen and liquid states. In order to melt the ice, the attractive forces

that hold the ice molecules together must be overcome. The energy to

remove the molecules from the ice comes from the surroundings of the

ice; this is called the enthalpy of fusion.In general, the enthalpy of fusion

provides a measure for the energy required to make a transition from a

solid to a liquid state.

Interpretation of entropy

Entropy, which literally means “a change within,” was first coined by

Rudolf Clausius in 1851, one of the pioneers in the development of

thermodynamics. Whereas entropy can be defined formally in terms of

various parameters, its nature can be shown qualitatively with some

simple examples. First, consider a cup of boiling water (Figure 3.5). When

the water is at 100°C the escaping vapor can perform work. As the cup cools,

no work is performed but heat flows from the cup to the surroundings,

raising the temperature of the surroundings. The cooling continues until

equilibrium is reached and the temperatures of the cup and surroundings

are equal. The energy that was once present in the hot cup, and potentially

capable of performing work, is no longer available. This irreversible process

corresponds to an increase in the entropy through the randomness of the

cooling process that will never recover into a cup of boiling water. As

a second example, consider the letters on this page. As part of a written

text all of the letters are organized in specific patterns. Consider taking

the 123 characters from this sentence and randomly distributing them

throughout the page in a chaotic pattern that has no meaning. The change

into the random distribution corresponds to an increase in entropy. The

ΔS

q

T

q

cube Twater

=−

52 PARTI THERMODYNAMICS AND KINETICS

Entropy

increases

Partially melted ice cubes

Figure 3.4The
entropy of a cup of
ice cubes increases as
the ice cubes melt.