Question

What is Gibb's paradox ?

Answer 1

The Gibbs paradox involves the contrast between mixing two quantities of (ideal) gases of a different kind and that of mixing two quantities of the same gas.

In the case of different gases, mixing is accompanied by an entropy increase

$\Delta S=2R\ln{2}$,  in the case of same gases there is no entropy change: $\Delta S=0$.