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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 97
system can be distributed over the energy states for a speci�ed total energy. As
explained in Section 3A.2(a) on page 80 the molecular interpretation of helps
to explain why, in the thermodynamic de�nition given by [3A.1a–80],dS =
qrev/T , the entropy change depends inversely on the temperature. In a system
at high temperature themolecules are spread out over a large number of energy
states. Increasing the energy of the system by the transfer of heat makes more
states accessible, but given that very many states are already occupied the pro-
portionate change inW is small. In contrast, for a system at a low temperature
fewer states are occupied, and so the transfer of the same energy results in a
proportionately larger increase in the number of accessible states, and hence
a larger increase inW. �is argument suggests that the change in entropy for
a given transfer of energy as heat should be greater at low temperatures than
at high, as in the thermodynamic de�nition. As discussed in Section 3C.2(a)
on page 93, the statistical de�nition of entropy also justi�es the �ird Law
of thermodynamics. �e law states that the entropy of all perfect crystalline
substances is zero at T = 0. At a molecular level the absence of thermal motion
in a perfectly localized crystalline solid is interpreted as there is only one way
to arrange the molecules like that.�us,W = 1 and from S = k lnW it follows
that S = 0 as stated by the law.