Question

Is there any example of a real-life system which violates the “third law” of thermodynamics while remaining at equilibrium?

Answer 1

I assume the following statement for the "third law" of thermodynamics:

limN→∞limT→0SN=0(1)(1)limN→∞limT→0SN=0

That is to say, I am considering those systems with a sub-exponential ground state degeneracy to satisfy the third law (see this answer of mine for more details about what I mean).

My question is: is there any real-life system that does not satisfy 11, while also remaining at equilibrium as T→0T→0?

Of course, there are examples of systems which don't satisfy 11, but all the examples I know concern non-equilibrium systems, like glasses (see residual entropy). For these system, however, no definition of entropy is in principle available, since SS can only be defined at equilibrium∗∗. Therefore, we cannot reallysay that they don't satisfy 11.

Note: I am not interested in model systems, but in real life systems, that can be studied experimentally.

Answer 2

$\sf\pink{Third \: law \: of \: Thermodynamics :}$

❥ Yes ; there are example of a real-life system which violates the “third law” of thermodynamics while remaining at equilibrium.

❥ At absolute zero the internal energy of the system would be zero since temperature is proportional to internal energy.

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$\sf \blue{Statement \: of \: This \: law :}$

❥ This law states that the entropy of a crystal of a pure substance reaches zero as the temperature reaches zero.

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