# Entropy change in adiabatic process

Why is entropy not zero for an irreversible adiabatic process though q=0? Ideally entropy is a state function so entropy should be zero.

The 2nd law is

$d S \ge \displaystyle \frac{d q}{T}$

so the best you can do is zero for a reversible process. Or if you don't like inequalities,

$d S = \displaystyle \frac{d q}{T} + d S_{irr}$

where $d S_{irr}$ is the entropy production due to the irreversible processes within the system.

You can find a intuitive in depth discussion in Prigogine's book:

Modern Thermodynamics: From Heat Engines to Dissipative Structures

$$\mathrm{d}U = - \delta W$$