Scientists use the term entropy to quantify the spread or dispersal of thermal energy. A system in which energy is concentrated—not spread out—has low entropy. The initial situations in Figures 20.16 and 20.17 are states of low entropy. In each case, the system spontaneously evolves to a state in which the energy is more spread out. These are states of higher entropy; the entropy increases as thermal energy becomes more dispersed. Because equilibrium is a state in which thermal energy is maximally dispersed, or shared among all the constituents, the entropy of a system is maximum when the system is in equilibrium.
This observation about how thermal energy spreads and how macroscopic systems evolve irreversibly toward equilibrium is a new law of physics, the second law of thermodynamics, that is usually stated in terms of entropy:
NOTE The qualifier “isolated” is crucial. We could reduce a system’s entropy by reaching in from the outside, perhaps using tiny tweezers to give most of the thermal energy to a few fast molecules while freezing the others in place. Similarly, we can transfer heat from cold to hot by using a refrigerator. The second law is about what a system can or cannot do spontaneously, on its own, without outside intervention.
The second law of thermodynamics is often stated in several equivalent but more informal versions. One of these, and the one most relevant to our discussion, is
This version of the second law will be used in Chapter 21 to understand the thermodynamics of engines.
Thermodynamics is a science of energy, and we need two laws of energy to understand how macroscopic systems behave. We can restate the two laws of energy as follows:
First law of thermodynamics: Energy is conserved. It can be transferred or transformed, but the total amount does not change.
Second law of thermodynamics: Energy spreads out. An isolated system evolves until the thermal energy is maximally dispersed among all the system’s constituents.
It is the second law that creates the “arrow of time” that we observe in irreversible processes. Stirring blends your coffee and cream; it never unmixes them. Systems evolve over time only in ways that continue to spread out thermal energy, thus increasing entropy, not in ways that concentrate thermal energy, which would decrease entropy.
Thus another statement of the second law is
Establishing the arrow of time is one of the most profound implications of the second law of thermodynamics.