<Thermo Pages

What observations about the world can be explained using the the Second Law of Thermodynamics?  How does the very general statement about probabilities and states that we developed in the previous readings explain why cold objects don't spontaneously transfer heat to hot objects, or why resting chairs don't spontaneously pick up heat from the floor and start moving?

Let's consider the case of a system composed of a hot object placed in contact with a cold object, and let's be very specific about the distribution of energy that we are considering.  Let's say that the cold object starts with 2 "units" of energy and the hot object starts with 8 "units" of energy, and let's assume that one "unit" of heat is transferred from the cold object toward the hot one.  The result, of course, is that the hot object now has 9 "units" of energy and the cold object is left with just 1 "unit."  What does such a process do to the entropy of the system?  Clearly, the entropy of the system has gone down!  There are fewer arrangements consistent with the 9/1 energy distribution than there are arrangements consistent with 8/2 energy distribution.  Now consider, instead, that the hot object transfers one "unit" of heat to the cold object.  In this case, the system's entropy has gone UP, since the 7/3 distribution is consistent with more arrangements than is the 8/2 distribution.  We see, then, that in this simple case of a hot object placed next to a cold object, the probabilistic statement of the Second Law of Thermodynamics tells us the direction in which heat is likely to transfer.  As the temperature difference between the objects gets greater, the Second Law says that the direction of heat flow becomes almost solely toward the colder object.

There is another, more mechanistic way of understanding what happens when a hot object is placed in contact with a cold object.  Instead of considering probabilities, think for a moment about what happens when a hot molecule comes in contact with a cold molecule via a collision.  In such a collision, the hot molecule transfers some of its kinetic energy to the cold molecule, thereby producing two molecules whose temperatures (energies) are more similar to each other than they were prior to the collision.  The result, therefore, is the same as what one would obtain using probabilistic considerations of entropy alone:  the two objects move toward an equilibrium temperature lying somewhere between the two extreme temperatures.

Consider now the case of the chair sliding across a floor with friction and coming to a stop, which we introduced earlier as an example of a process that exhibited unidirectionality that was unexplained using just the First Law of Thermodyamics.  How can we understand this irreversibility in light of the Second Law statement about entropy?  Well, what would have to happen for the chair to collect heat from the floor and start sliding across the room in a straight line?  All of the molecules that were vibrating randomly about their equilibrium positions in the floor would have to, for at least a moment, all start vibrating in the same direction, so that the legs of the chair would develop motion in a particular direction.  As we saw when discussing diffusion, the likelihood that all of the floor molecules will suddenly align themselves in a particular direction is incredibly small.  Put another way, the entropy of the floor's molecules is MUCH larger when they are vibrating randomly than when they are all moving in a single direction.  So while it is exceedingly likely that the floor will cause the sliding chair to stop moving, it is exceedingly UNlikely that the floor will act in reverse, causing the chair to start moving again.

Can you now do this analysis yourself for the case of smoke diffusing out through a room?  You are now in a position to understand, at both a mechanistic and probabilistic level, why it is that smoke emanating from the corner of a room spreads out to fill the room while the reverse process does not spontaneously occur.  The randomly oscillating air molecules in the room are incredibly unlikely to direct their vibrating efforts in only one spatial direction; in doing so they would be lowering their own entropy tremendously.  Do you see why this makes it incredibly unlikely that the smoke will re-coalesce in the corner?

Our probabilistic version of the Second Law of Thermodynamics has gotten us pretty far down the road toward understanding why some thermodynamic processes occur and others do not.  We've unpacked a number of mysteries and seen why, at least at the macroscopic world we all inhabit, certain processes do not occur because they would violate the Second Law of Thermodynamics.  Before we conclude our discussion of the Second Law, let's look at what we might expect to see in the micro-world, where the number of particles might be quite small.

Ben Geller