The Second Law of Thermodynamics

The second law of thermodynamics describes the flow of energy in nature in processes which are irreversible. The physical significance of the second law of thermodynamics is that the energy flow in such processes is always toward a more uniform distribution of the energy of the universe. Anyone who has had to pay utility bills for long has become aware that too much of the warm air in his or her home during winter escapes to the outside. This flow of energy from the house to the cold outside in winter, or the flow of energy from the hot outdoors into the air-conditioned home in the summer, is a process described by the second law of thermodynamics. The burning of gasoline, converting energy “rich” compounds (hydrocarbons) into energy “lean” compounds, carbon dioxide (CO2) and water (H20), is a second illustration of this principle.

The concept of entropy (S) gives us a more quantitative way to describe the tendency for energy to flow in a particular direction. The entropy change for a system is defined mathematically as the flow of energy divided by the temperature, or,

S [Q / T] (7-2)

where S is the change in entropy, Q is the heat flow into or out of a system, and T is the absolute temperature in degrees Kelvin (K).

[Note: For a reversible flow of energy such as occurs under equilibrium conditions, the equality sign applies. For irreversible energy flow, the inequality applies.]

A Driving Force

If we consider heat flow from a warm house to the outdoors on a cold winter night, we may apply equation 7-2 as follows:

ST = Shouse + Soutdoors - Q / T1 + Q / T2 (7-3)

where Sr is the total entropy change associated with this irreversible heat flow, T1 is the temperature inside the house, and T2 is the temperature outdoors. The negative sign of the first term notes loss of heat from the house, while the positive sign on the second term recognizes heat gained by the outdoors. Since it is warmer in the house than outdoors (T1 > T2), the total entropy will increase (Sr > 0) as a result of this heat flow. If we turn off the heater in the house, it will gradually cool until the temperature approaches that of the outdoors, i.e., T1 = T2. When this occurs, the entropy change (S) associated with heat flow (Q) goes to zero. Since there is no further driving force for heat flow to the outdoors, it ceases; equilibrium conditions have been established.

As this simple example shows, energy flow occurs in a direction that causes the total energy to be more uniformly distributed. If we think about it, we can also see that the entropy increase associated with such energy flow is proportional to the driving force for such energy flow to occur. The second law of thermodynamics says that the entropy of the universe (or any isolated system therein) is increasing; i.e., the energy of the universe is becoming more uniformly distributed.

It is often noted that the second law indicates that nature tends to go from order to disorder, from complexity to simplicity. If the most random arrangement of energy is a uniform distribution, then the present arrangement of the energy in the universe is nonrandom, since some matter is very rich in chemical energy, some in thermal energy, etc., and other matter is very poor in these kinds of energy. In a similar way, the arrangements of mass in the universe tend to go from order to disorder due to the random motion on an atomic scale produced by thermal energy. The diffusional processes in the solid, liquid, or gaseous states are examples of increasing entropy due to random atomic movements. Thus, increasing entropy in a system corresponds to increasingly random arrangements of mass and/or energy.