Well, I've had my coffee, and I've stretched mentally, so let us get the ball rolling on this paper.
The Third Law of Thermodynamics intrigues me. The zeroth law has been around since before Thermodynamics had been called Thermodynamics. There are miles of writing on the first and second laws. But the third one is just there.
Just think for a moment. If there is energy is in a system, what is the temperature of the system when there is no energy? I mean absolutely no energy. The lowest temperature on the Celsius scale is -273.15 degrees. When you can measure a state at that temperature, then there is no energy. There is no processes that the energy can create. And there is temperature scale that uses this point as zero. The Kelvin scale measures the absolute temperature of a system.
The story goes that heat is created by the movement of molecules. As a state cools, the molecules begin to move less and less, thereby creating less heat and less entropy. They begin line themselves up into a structure, creating a crystal. In a perfect crystal, the entropy is equal to zero.
Here's where the fun begins. Mathematically speaking, you can't reach zero using a finite number of processes. If there was a gas at 310 K and we want to cool it down, we could introduce a cooler state for the heat to transfer to. So, let us whip out our perfect crystal. The problem is, the crystal will only help bring the gas down to equilibrium, it won't cool it down to Absolute zero completely. Ignoring entropy for the moment, let us say that equilibrium is the mean of the two temperatures, or 155 K. To actually bring it down to 0 K, you would need a state lower than Absolute zero; in this case it would need to be -310 K. As stated, it can't go lower than zero, because there is no heat due to complete inactivity from the molecules.
So, let us instead figure that we have a cabinet full of these damn crystals. And we keep dividing the gas in half over and over. The problem is 0 multiplied by any number is still zero, and no number can be divided to equal zero.
As I'm writing this, I'm also catching up on convergent series. Quite honestly, this will by stopping point because this is my limit. According to most of what I can find, a series can not converge to zero. And since I'm learning as much as I am sharing, I've hit my confusion point because it seems there are some proofs that claim I can reach zero. Goodbye, my imagiary friends. Dinners calls.