For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $$\gamma$$ is the ratio of specific heats):

For an adiabatic process involving an ideal gas, we have $$PV^\gamma = \text{constant}$$.

Taking the differential of both sides: $$V^\gamma \, dP + P \cdot \gamma V^{\gamma - 1} \, dV = 0$$.

Dividing throughout by $$PV^\gamma$$: $$\frac{dP}{P} + \gamma \frac{dV}{V} = 0$$.

Therefore, the fractional change in pressure is $$\frac{dP}{P} = -\gamma \frac{dV}{V}$$.

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