# Entropy

## Read in this section

### 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

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.