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Diversions

Professor Hibbert's Perpetual Motion Pages

The Second Law

The entropy of an isolated system increases in the course of a spontaneous change.

or

No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.

Entropy (represented by the letter 'S') is a thermodynamic quantity (like internal energy and enthalpy), and the entropy of a system will change when the temperature of the system changes or the composition of the system changes (because of a chemical reaction) or the volume of the system changes etc. Entropy is usually linked to 'randomness' and although this can be a useful parallel, it is not a good way to define entropy (how do you put a numerical value on randomness?). Entropy is defined by the number of ways the energy of a system can be apportioned between the atoms or molecules making up the system.

In a system consisting of a single molecule speeding around in an otherwise empty box the energy of the system can only be apportioned in one way - the one molecule has all the energy. But if that molecule breaks into two molecules now there are more ways to apportion the total energy between the two molecules. This means the entropy of the system has increased.

The Second Law of Thermodynamics states that in all the processes we observe around us, the total entropy of the universe always increases. In any process the thermodynamic system will probably experience a change in entropy, and the entropy of the surroudings (everything which is external to system) will also probably change. The Second Law of Thermodynamics requires that the sum of these two entropy changes always be positive (increasing entropy of the universe).

The Clausius inequality

For an irreversible process dS > dq/T

Other state functions

Helmholtz function:

A = U - TS

Gibbs function ('free' energy):

G = H - TS

The Second Law of Thermodynamics is phrased in terms of the entropy change for the whole universe (and this change must be positive). This isn't always a useful way to approach processes like chemical reactions occuring in a beaker or flask. The Helmholtz and Gibbs functions are derived from considerations of the Second Law so that changes in the values of these functions for (for example) the chemicals reacting in a beaker or flask can be used to determine if the reaction is spontaneous (because it doesn't violate the Second Law) or is not spontaneous (because it would violate the Second Law).

 

Back to 'Perpetual Motion.'