Entropy and the Second Law
Entropy is a measure of the different ways a thermodynamic system can be arranged (Wikipedia). The second law of thermodynamics states that the entropy of a system spontaneously proceeds to the state of maximum entropy (Wikipedia). Therefore, the entropy of an isolated system can never be decreased.
Entropy is a state function; the change in entropy can be found from the final and initial states regardless of the path. The change in entropy of a reversible process can be found by
Where ΔS is the change of entropy, dQ is the heat transfered to the system reversibly, and T is the temperature at which heat transfer occurs.
It is important to note that the entropy of a system may decrease as long as the net entropy change of the surroundings is greater than zero. For example, if our system is water placed into a freezer, the entropy of the system decreases as the liquid becomes ice. However, the energy removed from that system is transferred to the surroundings as hot air is blown out the back of the refrigerator. This results in a net increase in entropy of the surroundings that is at lease as large as, and usually much larger than, the decrease experienced by the system.
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