Third law of thermodynamics and mixtures

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At absolute zero (0K), the entropy of a mixture of two different ideal quantum gases is indeed considered to be zero, aligning with the third law of thermodynamics, which states that the entropy of a perfect crystal is zero at this temperature. This raises questions about the entropy of mixing, as one might expect multiple arrangements of particles A and B to contribute to entropy. However, the third law primarily applies to one-component systems and assumes a perfect crystalline structure, which complicates the application to mixtures. Additionally, isotopic variations in pure substances challenge the absoluteness of the zero entropy statement. The formulation of entropy also involves constants of integration, indicating that the assertion is not entirely straightforward.
paweld
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Is it true that entropy of mixture of twodifferent ideal quantum gases
at 0K temperature is equal 0 that is the entropy of mixing is 0 at 0K
(two pure gases would have also 0 entropy).
 
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Why would the entropy of mixing be zero when there are many ways to arrange the mixture of particles A and B?
 
I suppose then that the third law works only for one component system.
But I don't know if these assumption is made usually in formulation of this law.
If not entropy of mixing should be 0. But I have no idea why?
 
The third law is (was) meant to apply only to perfect crystals.

Even this has its issues because even pure substances have isotopic variation in composition.

Even the statement "The entropy of a perfect crystal at absolute zero is zero" is not absolute. It relies on setting to zero the constant of integration inherent in

S = kln(Z) + U/T + Constant
 

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