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$P\left(\frac{V}{V-v}\right)^n$
Medium
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A$P\left(\frac{V}{V+v}\right)^n$
a (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
$P_n=P\left(\frac{V}{V+V}\right)^n$
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