Question

In an adiabatic expansion of air the volume increases by 5%. The percentage change in pressure is

Easy

Solution

We know that
${PV}^{γ} = constant$
Differentiating, we get
$P \cdot {γV}^{γ - 1} dV + V^{γ} dP = 0$
or $γ \frac{dV}{V} = - \frac{dP}{P} . . . . (1)$
Given $\frac{dV}{V} \times 100 = 5 or \frac{dV}{V} = \frac{1}{20}$
From eq. (1), $1 \cdot 4 \times (\frac{1}{20}) = - \frac{dP}{P}$
or $\frac{dP}{P} \times 100 = 100 \times 1 \cdot 4 \times (1 / 20) = 7 %$

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