An ideal gas (with C_p / C_V = γ ) undergoes a process where its...

The specific heat capacity of a gas is zero when no heat is exchanged with the surroundings during the process, which means $dQ = 0$.

This condition corresponds to an adiabatic process.

The equation for an adiabatic process is $pV^{\gamma} = \text{constant}$.

The given process equation is $p = aV^b$, which can be rewritten as $pV^{-b} = a$.

Comparing this with the equation of an adiabatic process, we get $-b = \gamma$.

Therefore, $b = -\gamma$.