Question

The volume of a vessel is V. The volume of the barrel of pump is v. After n strokes of the exhaust pump, what the pressure of air inside the vessel if the original pressure inside the vessel is P${}_0$?

• A. $P_0{\left(\frac{V}{V+v}\right)}^n$
• B. $P_0{\left(\frac{V+v}{V}\right)}^n$
• C. $\frac{P_{0}V}{V+v}$
• D. $\frac{P_0(V+v)}{v}$

Answer 1

The correct option is B $P_0{\left(\frac{V+v}{V}\right)}^n$

The gas in barrel of pump and vessel is being compressed into volume of vessel in each stroke.

After first stroke,

$P_{1}V=P_0(V+v)$

$⟹P_1=P_0\left(\frac{V+v}{V}\right)$

After second stroke, P_2V=P_1(V+v)$

$⟹P_2=P_0(\frac{V+v}{V}{)}^2$

Similarly after n strokes,

$P_n=P_0(\frac{V+v}{V}{)}^n$