The second law is concerned with entropy (S), which is a measure of disorder. The second law says that the entropy of the universe increases. An increase in disorder (overall) is therefore spontaneous. If the volume and energy of a system are constant, then every change to the system increases the entropy. If volume or energy change, then the entropy of the system can actually decrease. However, the entropy of the universe does not decrease. The molecules in one's body exist in great order; this only happens because the entropy of the rest of the universe is increased to a greater amount than the entropy of the body is decreased.

Much knowledge about entropy was developed by Carnot when he studied what is now called the Carnot Heat Cycle. (Interestingly, he was only 24 years old when he formulated the heat cycle.) Carnot studied a heat engine (heat is put into an engine and work is done). In a heat engine, a gas is reversibly heated and then cooled. A model of the cycle is as follows:

State 1 --(isothermal expansion)--> State 2 --(adiabatic expansion)--> State 3 --(isothermal compression)--> State 4--(adiabatic compression)--> State 1
State 1 to State 2: Isothermal Expansion Isothermal expansion occurs at a high temperature, Th. T = 0 and E1 = 0. Since E = q + w, w1 = - q1. For ideal gases, E is dependent on temperature only.
State 2 to State 3: Adiabatic Expansion The gas is colled from the high temperature, Th, to the low temperature, Tc. E2 = w2 and q2 = 0 (adiabatic).
State 3 to State 4: Isothermal Compression This is the reverse of the process between states 1 and 2. The gas is compressed at Tc. T = 0 and E3 = 0. w3 = - q3.
State 4 to State 1: Adiabatic Compression This is the reverse of the process between states 2 and 3. E4 = w4 and q4 = 0 (adiabatic).

The processes in the Carnot cycle can be graphed as the pressure vs. the volume. The area enclosed in the curve is then the work for the Carnot cycle because w = - integral (P dV). Since this is a cycle, E overall equals 0. Therefore, -w = q = q1 + q2 + q3 + q4

Consequences of the Carnot cycle:
- if you decrease Tc, then the quantity -w gets larger in magnitude.
- if -w > 0 then q > 0. the system (heat engine) does work on the surroundings.

The laws of thermodynamics were determined empirically (by experiment). They are generalizations of repeated scientific experiments. The second law is a generalization of experiments dealing with entropy--it is that the S of the system plus the S of the surroundings is equal to or greater then 0. Entropy is not conserved, like energy.

In implication of the second law is that in order for a reaction (or change in state) to occur spontaneously the entropy of the universe must increase or equal 0.

A Microscopic Interpretation of S:

If you arrange two identical blue balls, the order of the arrangement is equal (B1 B2 = B2 B1). If you have one blue ball and one red ball, then the arrangement can matter (B R is not equal to R B). This example demostrates the simplest example of microstate--the way of arranging and distributing molecules.
- Example 1: water S (ice) < S (water) < S (gas) Ice is a solid crystal. There are fewer ways it can be arranged than water. Gas can be arranged more ways than liquid.
- Example 2: carbon S (graphite) > S (diamond) Graphite exists as sheets of carbon atoms, and diamond is in the form of a crystal lattice. Since graphite is in sheets, it has a greater freedom of movement. (All forms of movement--vibration, translation, rotation, etc.--contribute to entropy.)
- Example 3: increase of temperature As temperature increases, the entropy of a system also increases. When temperature is increased, the molecules have more thermal energy. As a result, the molecules have greater freedom of movement and move/vibrate/rotate faster. An increase of temperature, therefore, also can lead to an increase in the number of microstates. S is also proportional to the number of microstates.