The 3rd law of thermodynamics

What's the absolute value of entropy?

$$dS=\frac{\delta Q_r}{T},$$

So,

$$S=\int \frac{\delta Q_r}{T} +S_0.$$ But what's $S_0$? Often we don't care, since often we only care about changes in quantities. (Think about gravitational potential energy...)

But there's a problem: $$dG=-S\,dT+V\,dP ?$$

Even to find a change in $G$ we need the absolute entropy.

Note, from this Pfaffian relation, that $$-S = $\frac{\partial G}{\partial T}$_P.$$

The 3rd law refers to attempts to address the absolute value of entropy...

Formulations of the 3rd law

Planck's later (1911) statement of the third law was that

The entropy of a true equilibrium state at absolute zero is zero

But, what *is* a "true" equilibrium state?

One could think a bit about glasses with regard to this one...

Nernst' slightly earlier formulation of the third law was not so, errm, absolute, and therefore more widely agreed on...

All reactions in a liquid or solid in thermal equilibrium take place with no change of entropy in the neighborhood of absolute zero.

Or

$$\lim_{T\rightarrow 0} \Delta S = 0 = $\frac{\partial G}{\partial T}$_P.$$

This means that the Gibbs energy is "coming in flat" on approaching absolute zero:

This will apply more nearly to liquids or solids (not as well for gases) near absolute zero.