A system of physical chemistry - Index of

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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 systems 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

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