The first law, as we have seen, deals with the conservation of energy as the system changes from one state to another, but it does not specify which particular changes will occur spontaneously. The reason why some changes have a natural tendency to occur is not that the system is moving to a lower-energy state but that there are changes in the randomness of the system. This can be seen by considering a specific example: the diffusion of one gas into another occurs without any external intervention - i.e. it is spontaneous - and yet there are no differences in either the potential or kinetic energies of the system in its equilibrium state and in its initial state where the two gases are segregated. The driving force for such spontaneous processes is the tendency for an increase in the chaos of the system - the mixed system is more disordered than the original.

A convenient measure of the randomness or disorder of a system is the entropy (S). When a system becomes more chaotic, its entropy increases in line with the degree of increase in disorder caused. This concept is encapsulated in the second law of thermodynamics which states that the entropy of an isolated system increases in a spontaneous change.

The second law, then, involves entropy change, A S, and this is defined as the heat absorbed in a reversible process, qrev, divided by the temperature (in kelvins) at which the change occurred.

For a finite change

and for an infinitesimal change dqrev dS = -

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