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 $n$-stroke of the pump? (assume temperature remains same)

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

Answer 1

Answer: (A)

After stroke $P V=$ constant
$P V=P_{1}(V+v)$
$P_{1}=\frac{P V}{(V+v)}$
Similarly after ${ }^{2^{\text {nd }}}$ stroke
$P_{2}=P\left(\frac{V}{V+v}\right)^{2}$
After $n^{\text {th }}$ stroke
$P_{n}=P\left(\frac{V}{V+v}\right)^{n}$