b
(b)
Adiabatic bulk modulus for an ideal gas is
$\quad K=\frac{d p}{-d V / V}=-V\left(\frac{d p}{d V}\right)$
$\quad=\gamma P \quad \dots(i)$
Now given,
$\quad K \propto p^n \quad \dots(ii)$
$\therefore$ From Eqs. $(i)$ and $(ii)$, we have
$\Rightarrow \quad n=1$