The Second Law Is Better Than The Zeroth Law By Two Units

On Wednesday, we finally made it to possibly the most powerful and darkly beautiful statement in all of thermodynamics: the Second Law. But, before that, we examined how we might calculate some entropy changes using the Clausius relation [dS = dq_rev/T], underscoring how this equation only works while tracing reversible paths. The irreversible heat transfer from a hot to cold reservoir can, for example, be broken into three reversible -- and calculable -- steps. It is from this simple system that leads us to the 2nd Law conjecture:

∆S_univ ≥ 0 [= for equil/reversible, > for spont/irreversible]

Unfortunately, abuses of this statement are many and takes but a moment's googling to find them. For many scientists, it holds a special place:

The law that entropy always increases-the second law of thermodynamics-holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations-then so much the worse for Maxwell's equations. If it is found to be contradicted by observation-well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." – Sir Arthur Eddington [1928]

And to reiterate some general statements from class, which will hopefully help you more fully grasp spontaneity and reversibility:

All spontaneous processes are irreversible.
For all irreversible processes, ∆S_univ > 0.
All reversible processes are at equilibrium.
For all reversible processes, ∆S_univ = 0.

Some common misstatements about the Second Law:

All systems tend to greater disorder.
False: Not only is "disorder" a poorly constructed idea and overly dependent on human interpretation, the underlying premise is wrong.
All systems tend towards greater entropy.
False: Some systems tend towards greater entropy while others don't. The restriction rests on ∆S_univ, not on ∆S.

Before moving onto specific applications of the Clausius relation, we paused, for bookkeeping's sake, to mention the Zeroth Law: If systems A and B are in equilibrium, and systems B and C are in equilibrium, then systems A and C are in equilibrium. Not only does this establish that a state property common to them must be equal (the temperature), it also allows for the possibility that two systems could be in equilibrium without in direct contact.

Lastly we began our march of calculating entropy changes for ten processes, finishing four:
01. cyclic
02. reversible adiabatic
03. reversible isothermal
04. reversible phase transition [at const T, P]

On Friday, we will finish this list of ten, visit the revolutionary work of Boltzmann and, if time permits, elucidate the Third Law of Thermodynamics.