Question

why is the entropy for irreversible adiabatic process not zero? Provide a mathematical proof.

Answer 1

mperatures A simple answer to your question is "by definition". One of possible entropy definition is that it is a value, which for an isolated system does not change in course of any reversible process (not only adiabatic). It changes only if a system is not isolated or a process is inreversible. All quantitative formulas for the enthropy should satisfy these conditions. Hope it helps you.