A system of physical chemistry - Index of

ENTROPY AND THERMODYNAMIC PROBABILITY 17

it is legitimate to consider that the entropy may assume in general any

value whatsoever, positive or negative, and that therefore all that we can

measure is the change in entropy resulting from a **physical** or chemical

process.

It will be pointed out later in deahng with Nernst's Heat

Theorem, that according to Planck, the Heat Theorem itself is equivalent

to regarding the entropy **of** all substances as zero at the absolute zero

**of** temperature, and possessing therefore a positive value at all other

temperatures.^ This gives us a starting point from which to calculate

not only change in entropy but its absolute value under given conditions.

This likewise agrees with the simplified expression : S

= /& log W in

which W has been defined as a quantity greater than unity, and con-

sequently S is essentially positive. Of course if we retain the constant

in the expression : S

= ^ log W + constant, the value **of** S may be

positive or negative depending upon the magnitude and sign **of** the

integration constant whether VV itself is greater than unity or not.

Classical statistical mechanics, which did not attempt to assign any

particular limit to the value **of** the entropy, is represented by the above

expression. If we assume with Planck that the integration constant is

zero, and remembering that W as defined above is greater than unity, it

follows that S is a positive term becoming zero at absolute zero. This

is equivalent to assuming the quantum hypothesis.

The general position which we have now reached as a result **of** the

considerations dealt with in this section may be summarised as follows :—

The second law **of** thermod);namics, regarded as a law **of** experience,

states that, whilst work may always be completely converted into heat,

heat on the other hand cannot be completely converted into work. In

other words, all natural spontaneous processes are thermodynamically

irreversible. In mechanics we deal only with reversible processes, and

from the standpoint **of** mechanics alone we would expect heat to be as

readily convertible into work as work into heat. Since this is not the

case there must be something characteristic **of** molecular **system**s to

which the irreversibility is due. This " something " is discovered in the

fact that heat consists **of** a chaotic motion **of** the molecules, and that as

a result **of** collisions this motion tends to become as chaotic or disordered

as possible. In other words, the irreversibility which finds expression in

the second law **of** thermodynamics is due essentially to the fact that

ordered motion always tends, **of** its own accord, to become disordered,

and chaotic motion never tends, **of** its own accord, to become ordered.

This statement is a statement **of** the second law **of** thermodynamics

not expressed simply as a result **of** experience but in terms **of** statistical

mechanics. We have therefore found a mechanical basis for the second

law.

It is obvious at the same time why Gibbs gave the significance

^According to Planck this assumption is "the very quintessence **of** the hypothesis

**of** quanta ". It must be pointed out that whilst this assumption makes the

theory **of** quanta and Nernst's Heat Theorem agree, it is not essential to the deduction

**of** the heat theorem itself, which only requires that the entropy **of** all substances

at absolute zero shall be the same, but not necessarily zero.

VOL. III. 2