Third law of thermodynamics?!?

Question

Based on the third law of thermodynamics, we know that perfect crystals at absolute zero have
A. same enthalpy
B. differing deltaA values
C, same entropy
D. same crystal lattices
E. both A and C.
im leaning towards A, or C..or both.
im not sure.
anyone???
any help is greatly appreciated!!! THANKS!

Answer 1

Correct answer should be E

Answer 2

The third law of thermodynamics is an axiom of nature regarding entropy and the impossibility of reaching absolute zero of temperature. The most common enunciation of third law of thermodynamics is:

As a system approaches absolute zero of temperature all processes cease and the entropy of the system approaches a minimum value.

In simple terms, the Third Law states that the entropy of a pure substance at absolute zero temperature approaches zero. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy.

A special case of this is systems with a unique ground state, such as crystal lattices. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero (since log(1) = 0). However this disregards the fact that real crystals must be grown at a finite temperature and possess an equilibrium defect concentration. When cooled down they are generally unable to achieve complete perfection. This, of course, is in line with the observation that entropy must always increase since no real process is reversible.

Another application of the third law is with respect to the magnetic moments of a material. Paramagnetic materials (moments random) will order as T approaches 0 K. They may order in a ferromagnetic sense, with all moments parallel to each other, or they may order in an antiferromagnetic sense, with all moments antiparallel to each other.

Yet another application of the third law is the fact that at 0 K no solid solutions should exist. Phases in equilibrium at 0 K should either be pure elements or atomically ordered phases. See J.P. Abriata and D.E. Laughlin, “The Third Law of Thermodynamics and low temperature phase stability,” Progress in Materials Science 49, 367-387, 2004.

This law, of course, is applicable only to classical systems. For classical systems, one expects the ground state energy of the system to be equal to zero. When one considers the full quantum mechanical description of any system, the entropy at 0 K is nonzero. The reason for this is that unlike classical systems, quantum mechanical systems do have a certain amount of energy even at 0 K known as the zero point energy of the system. There are also classical exceptions such as frustrated systems which contain degenerate ground states, yielding a non-zero entropy arbitrarily close to 0 K.

It can be shown (for any system) that the quantum mechanical description is a superset of the classical description. One can also show that the quantum mechanical approach approximates to the classical approach when certain conditions (usually high quantum number or temperature) are satisfied. This is the so called correspondence principle.

Answer 3

E for sure.