1st law of thermodynamics and statevariables

edington

Hello,

My book gives the equation du=Tds-pdV as for the first law of thermodyanmics. The book derives this for a reversible process, but then makes the comment that u,p,V,T,s are all states variables, therefore this equation is valid for any irreversible processes as well. What confuses me is that I accept the fact that those variables are all state variables, but pdV is work which is not a state variable. So, how can this equation be valid for an irreversible process?

Thank you very much