I have seen a discussion of what would happen for an ideal gas expands irreversibly and adiabatically until absolute zero degree K. The entropy change is like that:
$\Delta S=C_v \ln(T_2/T_1)+R \ln(V_2/V_1)$
It is impossible for T2 to be zero K in the equation and so it becomes one justification of the third law. I wonder whether it is valid and whether an irreversible process can be represented by the above equation. For irreversible process the heat exchange is not equal to Tds so can the Gibbs equation be applied?
The video is in https://www.youtube.com/watch?v=r4fGG_7NQr8 , 46:12