In an adiabatic process, the pressure is increased by 23%. If γ=32, if the decrease in volume is n9% then find the value of n.

dPdV=−γPV⇒dPP=−γdVV 23=−32dVV⇒dVV=−49∴ Decreases in volume = 4/9%

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In an adiabatic process, the pressure is increased by $\frac{2}{3} % .$ If $γ = \frac{3}{2},$ if the decrease in volume is $\frac{n}{9} %$ then find the value of $n .$

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Detailed Solution

$\frac{d P}{d V} = - γ \frac{P}{V} \Rightarrow \frac{d P}{P} = - γ \frac{d V}{V} \frac{2}{3} = - \frac{3}{2} \frac{d V}{V} \Rightarrow \frac{d V}{V} = - \frac{4}{9}$

$∴$ Decreases in volume = 4/9%

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