# 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.