In an adiabatic expansion of air, the volume is increased by $6.2 \%$. The percentage change in pressure is $(\gamma=1.4)$

For an adiabatic process, the relation between pressure $P$ and volume $V$ is given by $PV^{\gamma} = \text{constant}$.

Taking the logarithmic differentiation of the equation $PV^{\gamma} = C$, we get $\ln P + \gamma \ln V = \ln C$.

Differentiating both sides, we obtain $\dfrac{dP}{P} + \gamma \dfrac{dV}{V} = 0$, which implies $\dfrac{dP}{P} = -\gamma \dfrac{dV}{V}$.

Given that the volume increases by $6.2 \%$, we have $\dfrac{dV}{V} = 0.062$.

Substituting the values $\gamma = 1.4$ and $\dfrac{dV}{V} = 0.062$ into the expression for the fractional change in pressure:

$\dfrac{dP}{P} = -1.4 \times 0.062 = -0.0868$.

The percentage change in pressure is $\dfrac{dP}{P} \times 100 = -0.0868 \times 100 = -8.68 \%$.

The magnitude of the percentage change in pressure is $8.68 \%$.

Answer: 8.68