• # question_answer A vessel of volume $V$ is evacuated by means of a piston air pump. One piston stroke captures the volume ${{V}_{0}}$. The pressure in the vessel is to be reduced to $\left( \frac{1}{n} \right)$ of its original pressure ${{P}_{0}}.$ If the process is assumed to be isothermal and air is considered an ideal gas the number of strokes needed in the process is A) $\left[ \frac{\ell nn}{\ell n\left( 1-\frac{{{v}_{0}}}{V} \right)} \right]$ B) $\left[ \frac{\ell nn}{\ell n\left( 1+\frac{{{v}_{0}}}{V} \right)} \right]$ C) $\left[ \frac{\ell n\left( 1-\frac{{{v}_{0}}}{V} \right)}{\ell n} \right]$           D) none of these

 $VP-(V+{{v}_{0}}){{P}_{1}}$$\Rightarrow$${{P}_{1}}=\left[ \frac{VP}{V+{{v}_{0}}} \right]$ and       $V{{P}_{1}}=\left( V+{{v}_{0}} \right){{P}_{2}}$$\Rightarrow$         ${{P}_{2}}={{\left[ \frac{V}{V+{{v}_{0}}} \right]}^{2}}P$ Therefore ${{\left[ \frac{V}{V+{{v}_{0}}} \right]}^{n}}P=\frac{P}{n}$ After simplifying, we get $n=\left[ \frac{\ell n\,\,n}{\ell n\left( 1+\frac{{{v}_{0}}}{V} \right)} \right]$