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  4. In an adiabatic expansion, the volume of air is increased by 5 % , then the approximate percentage decrease in its pressure will be

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Q. In an adiabatic expansion, the volume of air is increased by $5\%$ , then the approximate percentage decrease in its pressure will be

NTA AbhyasNTA Abhyas 2022

Solution:

$\frac{\Delta P}{\Delta V}=-\gamma \frac{P}{V} \, \rightarrow $ Air $ \rightarrow$ diatomic $\left(\gamma = \, 1.4\right)$
$\therefore \frac{\Delta P}{P}\times 100=-\gamma \frac{\Delta V}{V}\times 100$
$=-1.4\times 5=7\%$