Gibbs equation and third law of thermodynamics

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

Ah, OK, I misread your question slightly. The reason the equation you cite holds for all processes is that every quantity in it is a state variable, so overall the equation is an equation of state. That means it doesn't matter how you got from $(V_1, T_1)$ to $(V_2, T_2)$, reversible or irreversible, the entropy change will be the same.