Concise Physical Chemistry

c05 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

78 ENTROPY AND THE SECOND LAW

by the cold one. The process involves no change in energy or enthalpy; hence the first

law tells us nothing about it. To look at the situation more quantitatively, suppose that

the bricks are of equal size and have the same heat capacityC. Suppose further that

one brick is at 400 K and the other is at 200 K. After sufficient time, both will be at

300 K, assuming no heat is lost to the surroundings.

S=Cln

T 2

T 1

=Cln

300

400

=− 0. 288 C

for the hot brick, but

S=Cln

T 2

T 1

=Cln

300

200

= 0. 405 C

for the cold brick. The result that the positive entropy change is greater than the

negative change is independent of the initial temperatures, heat capacities, sizes of

the bricks, and so on. Entropy for the spontaneous processalways increasesfor

spontaneous heat transfer. The only way to get away from the inequalities of
Sfor

hot and cold bricks would be to makeT 1 =T 2 but then no heat would flow.

5.3.3 Chemical Reactions

The order or disorder within a system undergoing chemical reaction changes, some-

times dramatically. For example, combination of equal volumes of H 2 (g) and O 2 (g)

produces a negligible volume of H 2 O(l) plus^1 / 2 volume of O 2 (g) left over after the

hydrogen is all used up. The volume of the system goes from 2 to^1 / 2 , so we expect

an entropy change on that basis alone. The initial volume is now larger than the

final volume at constant pressure, so, in contrast to the expansion case, the entropy

change of this reaction is negative; the final state is moreorderedthan the initial

state. The negative
rSis in opposition to the direction of the chemical reaction. The

first and second laws operating simultaneously on the system through
rH−T
rS

give a term−T
rS^3 which is positive but which is smaller than
rH. Hence
rS

is negative for this spontaneous (sometimes explosive) reaction. This is an example

of the very common tendency of reactions to go in the direction of aspontaneous

creation of orderfrom a disordered system, provided that there is enough enthalpy

decrease to drive the entropy change “backwards.” Some creationists believe that a

spontaneous ordering process is impossible, but they are wrong.

5.4 THE THIRD LAW

The third law of thermodynamics states that the entropy, unlike the energy and

enthalpy, has a natural zero point. The entropy of a perfect crystal is zero at 0 K.

(^3) The product of two negative numbers.