"Two boxes of gas in thermal equilibrium are most likely to divide their energy in a way the equalizes their temperature"
This fact has been known to me since high school, but I've never actually heard of it referred to as the Zeroth Law of Thermodynamics (by the way, does anyone know exactly why they called it the Zeroth Law, as opposed to the Fourth Law etc? The closest reasonings I can think of are that it's importance preceeds the well known 3, and that their order couldn't be rearranged, or that it's been labelled in the same way that computer data is, starting at position 0)
So, despite this being quite an easy concept to grasp, it did however open up a series of discussions in the text, so I felt it wise to bring up in a blog. The fundamental definition of temperature (the focus of part of our homework) is T = (dS/dE)^-1
From the text, "we define temperature abstractly as the quantity that comes to equal values when two subsystems exchanging energy come to equilibrium." This is where the equation came from, and it makes sense, since we'd expect for two systems that are at a point of zero net energy flux, we would need to have a defined shared temperature as well.
Moving on from here, the text led us into the ideas of extensive qualities (such as entropy, which can double if a system is double, halved if a system is halved etc) and intensive properties (such as temperature, which can remain the same, even if a system is doubled, halved etc).
My last point to make about temperature equilibrium however, is that size matters (that's right, to all who say that size doesn't matter, they obviously haven't come across thermal equilibrium before). It's important to remember that just because two objects of different temperature are going to come to equilibrium, it's not going to be the average of their two temperatures, it's going to be the average of their two temperatures relative to their respectives sizes. So if you had two of those medical packs that you can either heat up or freeze, and you put them together after heating up one and cooling down the other, they will find that approximate average of their temperatues. However, if you took the heated pack and placed in on an iceberg, then the hot pack will cool down to a temperature almost that of the iceberg, and the temperatue of the iceberg will be minimally raised.