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Entropy of Phase Changes

We would expect that a phase change would be accompanied by a change in entropy. For example, when a liquid boils, a compact condensed phase is converted into a widely dispersed vapour phase. Clearly, the molecular disorder in a gas will be greater than that in a liquid, so there must be an entropy increase upon vapourisation.

The Relationship between Entropy and Temperature

Our starting point for this discussion is the definition of a measurable entropy change: This definition may be used to calculate the entropy of a system at a temperature T2 from a knowledge of its entropy at a temperature T1 and the heat supplied to change the temperature from T1 to T2.

The Third Law of Thermodynamics

At T = 0, there is no energy corresponding to thermal motion. Further, for a perfect crystal all the atoms or ions which make up the crystal are arranged in a regular, uniform fashion. The absence of spatial disorder and thermal motion may be used to argue that such a material, under these conditions, has zeroentropy.

The Clausius Relation

We now turn to verifying that the entropy is a signpost of spontaneous change, in the sense that the total entropy must increase for any spontaneous change.

Entropy and Volume

It is appropriate to illustrate the relationship between ΔS and q with a consideration of the relationship between entropy and volume. Our consideration will be the simple case of isothermal expansion of a perfect gas, but it is possible to apply the equations to more complicated situations.

The Second Law of Thermodynamics

There are several equivalent alternative ways of representing the Second Law of Thermodynamics. One is in terms of entropy, S, a state function which is a measure of the molecular disorder of a system.


Entropy, given the symbol S, is a state function which is a measure of the disorder of a system.

The Direction of Spontaneous Reactions

Certain processes occur spontaneously – for example cooling of a hot object to the temperature of the surroundings, and expansion of a gas to fill the volume available to it. Though these processes can be made to go the other way (heating an object up, confining a gas to a smaller volume), they do not occur spontaneously, and can only be brought about by doing work upon the system of interest.