Question

There are n connected container having volume V, 2V, 3V, ......, nV separated by stopcock. All container have same moles of gas at same temperature. If pressure of first container is P, then final pressure when all stop cocks are opened is ?

Answer 1

The number of moles present in one container is PV/RT.

Total number of moles present in n containers is nPV/RT.

Letn $P_f$ be the final pressure. The final volume is $\frac{n(n+1)V}{2}$.

Total number of moles when all the stopcocks are opened is $\frac{P_{f}n(n+1)v/2}{RT}$.

Since the number of moles remains same,

$\frac{P_{f}n(n+1)V/2}{=}n\left(PV\right)$

Hence, $P_f=\frac{2P}{n+1}$. This is the final pressure when all the stopcocks are opened.