A) \[4{{m}_{A}}=9{{m}_{B}}\]
B) \[2{{m}_{A}}=3{{m}_{B}}\]
C) \[3{{m}_{A}}=2{{m}_{B}}\]
D) \[9{{m}_{A}}=3{{m}_{B}}\]
Correct Answer: C
Solution :
Process is isothermal. There fore, T = constant, \[\left( P\propto \frac{1}{V} \right)\] volume is increasing, therefore pressure will decreases. In chamber A : \[\Delta P={{P}_{i}}-{{P}_{f}}=\frac{{{\mu }_{A}}RT}{V}-\frac{{{\mu }_{A}}RT}{2V}=\frac{{{\mu }_{A}}RT}{2V}\] ?..(i) In chamber B : \[1.5\Delta P={{P}_{i}}-{{P}_{f}}=\frac{{{\mu }_{B}}RT}{V}-\frac{{{\mu }_{B}}RT}{2V}=\frac{{{\mu }_{B}}RT}{2V}\] ?..(ii) from equations (i) and (ii) \[\frac{{{\mu }_{A}}}{{{\mu }_{B}}}=\frac{1}{1.5}=\frac{2}{3}\] Þ \[\frac{{{m}_{A}}/M}{{{m}_{B}}/M}=\frac{2}{3}\]Þ \[3{{m}_{A}}=2{{m}_{B}}.\]You need to login to perform this action.
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