13.6 Entropy and the second law of thermodynamics: disorder and  (Page 5/10)

Either way, the universe is destined for thermodynamic equilibrium—maximum entropy. This is often called the heat death of the universe , and will mean the end of all activity. However, whether the universe contracts and heats up, or continues to expand and cools down, the end is not near. Calculations of black holes suggest that entropy can easily continue for at least ${\text{10}}^{\text{100}}$  years.

Order to disorder

Entropy is related not only to the unavailability of energy to do work—it is also a measure of disorder. This notion was initially postulated by Ludwig Boltzmann in the 1800s. For example, melting a block of ice means taking a highly structured and orderly system of water molecules and converting it into a disorderly liquid in which molecules have no fixed positions. (See [link] .) There is a large increase in entropy in the process, as seen in the following example.

In another easily imagined example, suppose we mix equal masses of water originally at two different temperatures, say $\text{20.0º C}$ and $\text{40.0º C}$ . The result is water at an intermediate temperature of $\text{30.0º C}$ . Three outcomes have resulted: entropy has increased, some energy has become unavailable to do work, and the system has become less orderly. Let us think about each of these results.

First, entropy has increased for the same reason that it did in the example above. Mixing the two bodies of water has the same effect as heat transfer from the hot one and the same heat transfer into the cold one. The mixing decreases the entropy of the hot water but increases the entropy of the cold water by a greater amount, producing an overall increase in entropy.

Second, once the two masses of water are mixed, there is only one temperature—you cannot run a heat engine with them. The energy that could have been used to run a heat engine is now unavailable to do work.