Temperature remaining constant, the pressure of gas is decreased by $20 \%$. The percentage change in volume

Temperature remaining constant, the pressure of gas is decreased by $20 \%$. The percentage change in volume
  1. increases by $29 \%$
  2. decreases by $20 \%$
  3. increases by $25 \%$
  4. decreases by $25 \%$

Solution

$\begin{aligned} & \text { Using, } \mathrm{P}_1 \mathrm{~V}_1=\mathrm{P}_2 \mathrm{~V}_2 \text { we get, } \\ \mathrm{PV}=\mathrm{P}^{\prime} \times \frac{80 \mathrm{~V}}{100} & \Rightarrow \frac{\mathrm{P}^{\prime}}{\mathrm{P}}=\frac{10}{8} \\ \therefore \quad \frac{\mathrm{P}^{\prime}-\mathrm{P}}{\mathrm{P}} \times 100 & =\left(\frac{10}{8}-1\right) \times 100 \\ & =\left(\frac{2}{8} \times 100\right)=\frac{1}{4} \times 100=25 \%\end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 2)

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