If the pressure of an ideal gas is decreased by $10 \%$ isothermally, then its volume will

If the pressure of an ideal gas is decreased by $10 \%$ isothermally, then its volume will
  1. decrease by $8 \%$
  2. decrease by $9 \%$
  3. increase by $8 \%$
  4. increase by $11 \%$

Solution

For isothermal process, $\mathrm{P}_1 \mathrm{~V}_1=\mathrm{P}_2 \mathrm{~V}_2$ $\begin{aligned} & \mathrm{P}_2=\mathrm{P}_1-\frac{\mathrm{P}_1}{10}=\frac{9}{10} \mathrm{P}_1 \\ & \therefore \mathrm{P}_1 \mathrm{~V}_1=\frac{9}{10} \mathrm{P}_1 \mathrm{~V}_2 \\ & \therefore \mathrm{V}_2=\frac{10}{9} \mathrm{~V}_1 \\ & =1.11 \mathrm{~V}_1 \\ & =\mathrm{V}_1+0.11 \mathrm{~V}_1 \end{aligned}$ Volume increase by $11 \%$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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