 Different type of processes
Question

# Two identical containers A and B with frictionless positions contain the same ideal gas at the same temperature and the same volume V.  The mass of the gas in A is mA and that of B is mB. The gas in each cylinder is now allowed to expand isothermally to the same final volume 3V. The change in the pressure in A and B are found to be $∆\mathrm{P}$ and 2.5  $∆\mathrm{P}$ respectively. Then

Moderate
Solution

## T = Constant,  $\mathrm{P\alpha }\frac{1}{\mathrm{V}}$For Chamber A,  $\mathrm{\Delta P}={\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{t}}=\frac{{\mathrm{n}}_{\mathrm{A}}\mathrm{RT}}{\mathrm{V}}-\frac{{\mathrm{n}}_{\mathrm{A}}\mathrm{RT}}{3\mathrm{V}}=\frac{2\mathrm{nART}}{3\mathrm{V}}$  ------(I)For Chamber B,  $2.5\mathrm{\Delta P}={\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{t}}=\frac{{\mathrm{n}}_{\mathrm{B}}\mathrm{RT}}{\mathrm{V}}-\frac{{\mathrm{n}}_{\mathrm{B}}\mathrm{RT}}{3\mathrm{V}}=\frac{2}{3}\frac{{\mathrm{n}}_{\mathrm{s}}\mathrm{RT}}{\mathrm{V}}$ ------(II)From equations   (I)  and (II)$\begin{array}{l}\frac{{\mathrm{n}}_{\mathrm{A}}}{{\mathrm{n}}_{\mathrm{s}}}=\frac{1}{2.5}=\frac{2}{5}\\ ⇒\frac{{\mathrm{m}}_{\mathrm{A}}/\mathrm{M}}{{\mathrm{m}}_{\mathrm{B}}/\mathrm{M}}=\frac{2}{5}⇒5{\mathrm{m}}_{A}=2{\mathrm{m}}_{B}\end{array}$

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