Question

An ideal gas is enclosed in a container of volume $V$ at a pressure $P$. It is being pumped out of the container by using a pump with stroke volume $v$. What is final pressure in container after $n-strokes$ of the pump? (assume temperature remains same).

• A. $P{\left(\frac{V}{V+v}\right)}^n$
• B. $\frac{PV}{(V-v{)}^n}$
• C. $P\frac{V^n}{v^n}$
• D. $P{\left(\frac{V}{V-v}\right)}^n$

Answer 1

The correct option is D $P{\left(\frac{V}{V-v}\right)}^n$

Given:

Initial pressure = P, Volume = V

Let the initial temperature be T

$PV=nRT⟹P\propto \frac{1}{V}$

stroke volume of the pump = v (let $v<<V$)

Assuming an isothermal process:

After the pumping out gas of volume v out of V, the number of moles of the given gas left in the container = $n\times \frac{(V-v)}{V}$

As Volume V of the container is constant,

$P_1=P\left(\frac{V}{V-v}\right)$

Again when gas is pumped out pressure will become

$P_2=P_1\left(\frac{V}{V-v}\right)=P{\left(\frac{V}{V-v}\right)}^2$

After n pumpings, Pressure inside the container = $P{\left(\frac{V}{V-v}\right)}^n$

is the final pressure in the container after n strokes.

The correct answer is option(D).