Explanation

(a) [image:13_image29.emf]
When the piston is allowed to move the gases are kept separated but the pressure has to be equal.
$(P_{1} = P_{2})$ and final volume $x$ and $(6V - x),$ the no of moles are same in initial and final position at each parts.
$\because P_{1} = P_{2}\ \ \ \ \ \ \ \ \ \ \ \ P_{V} = n_{1}RT$
$\frac{n_{1}RT}{x} = \frac{n_{2}RT}{6V - x}\ \ \ n_{1} = \frac{5PV}{RT}$
$\frac{n_{1}}{x} = \frac{n_{2}}{6V - x}\ \ \ \ \ \ \ n_{2} = \frac{10PV}{RT}$
$\Rightarrow \frac{5PV}{xRT} = \frac{10PV}{(6V - x)RT} \Rightarrow \frac{1}{x} = \frac{2}{6V - x}$
$\Rightarrow 6V - x = 2x \Rightarrow x2V$ and $6V - x \Rightarrow 6V - 2V = 4V$
$\therefore(2V,4V)$