The third law of thermodynamics is the only one that is not generally given in simple mathematical form. Here is my version of the third law:

The entropy of a pure, perfectly-ordered crystalline solid is zero at absolute zero.

Notice that the law is about the absolute entropy (S) and not an entropy change(ΔS). It is the reason that we can assign absolute values to entropies of substances at higher temperatures, because if we measure or calculate the S that results when an element or compound is heated from T = 0 to the T

ΔS = S_T - S_{0 Kelvin} = S_T

we get the absolute entropy at that temperature.

Nobel Laureate Walther H. Nernst did formulate the third law in mathematical form

in 1906, but six years later came back with the caveat

Absolute zero is unattainable.

A more rigorous statement is that it is impossible to cool anything to absolute zero in any finite number of steps. While scientists have achieve temperatures as low as nanokelvin with records of picokelvin in the lab, no one has yet found this law to be incorrect. Here is a website that discusses how to get extremely low temperatures.

Our main use of the third law will be in working with absolute temperature values. However, there are some corollaries you might find interesting

• There are no thermodynamically defined temperatures below absolute zero.
• At absolute zero, all heat capacities are zero.
• At absolute zero, S for all reactions and phase transitions are zero.
• At absolute zero, all thermal molecular motion should stop.