5.5.1: The Second Law of Thermodynamics

Whereas the first law of thermodynamics states that you cannot get more energy out of a system than is already present in some form, the second law of thermodynamics tells us that we cannot even get back the energy that we use to bring about a change in a system. The idea in the second law is captured by the phrase “for any change in a system, the total entropy of the universe must increase.” As we will see, this means that some of the energy is changed into a form that is no longer useful (that is, it cannot do work).

There are lots of subtle and not so subtle implications captured by this statement and we will need to look at them carefully to identify them. You may already have some idea of what entropy means, but can you define it? As you might imagine it is not a simple idea. The word entropy is often used to designate randomness or disorder but this is not a very useful or accurate way to define entropy (although randomly disordered systems do have high entropy). A better way to think about entropy is in terms of probabilities: how to measure, calculate, and predict outcomes. Thermal energy transfers from hot to cold systems because the outcome is the most probable outcome. A drop of dye disperses in water because the resulting dispersed distribution of dye molecules is the most probable. Osmosis occurs when water passes through a membrane from a dilute to a more concentrated solution because the resulting system is more probable. In fact whenever a change occurs, the overall entropy of the universe always increases.¹⁰² The second law has (as far as we know) never, ever been violated. In fact the direction of entropy change has been called “time’s arrow”; the forward direction of time is determined by the entropy change. At this point you should be shaking your head. All this cannot possibly be true! First of all, if entropy is always increasing, then was there a time in the past when entropy was 0?¹⁰³ Second, are there not situations where entropy decreases and things become more ordered, like when you clean up a room? Finally, given that common sense tells us that time flows in only one direction (to the future), how is it possible that at the atomic and molecular scale all events are reversible?

References

¹⁰² This is another example of the different ways that the same process is described. In chemistry we usually describe osmosis as movement from a solution of low concentration to high (where we are referring to the concentration of the solute). In biology osmosis is often described as movement from high concentration (of water) to low. These two statements mean exactly the same thing even though they appear to be saying the opposite of each other.

¹⁰³ One of many speculations about the relationship between the big bang and entropy; http://chronicle.uchicago.edu/041118/entropy.shtml