# Equivalence of the various statements of Third law of Thermodynamics

The Third Law of Thermodynamics is stated as:

The entropy of a perfect crystal at absolute zero is exactly equal to zero.

or alternately as:

It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations.

[Both statements sourced from Wikipedia]

Can somebody tell me why they are equivalent without a lot of mathematics [coz I will not understand it anyways] ?? Any kind of intuition for at least why these may be equivalent ??

The most basic process of cooling something that has temperature $T$ is to put it in contact with something that has temperature $t<T$. Now, $t>0$ since negative temperatures are not the case of this discussion, and $t=0$ was considered above. Cooling by using any $t>0$ and $t<T$ will give a final temperature $t<\hat t<T$. In order for this to work, you will have to apply this method of cooling an infinite number of times before you get to 0K. So the equivalent in entropy is that you need an infinite number of processes to get to 0 entropy.