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A heat conducting and movable piston separates the container containing an ideal gas into two parts as shown in the figure. If the walls are insulating then find the displacement observed by the piston in (cm) before the equilibrium is again reached.(width of the piston is negligible). Final temperature is same in both parts.

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answer is 4.

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Detailed Solution

For chamber (1)
Equation number of moles
$\frac{P_{0} (10) (A)}{R (2 T_{0})} = \frac{P_{1} x (A)}{R T_{1}} .... (1)$

For chamber (2)

$\frac{P_{0} (20) (A)}{R T_{0}} = \frac{P_{1} (30 - x) A}{R T_{1}} .... (2)$

Dividing (1) by (2)

$\frac{1}{4} = \frac{x}{30 - x} \Rightarrow 30 - x = 4 x$

$5 x = 30$

Thus piston moves by 10 - 6 = 4cm

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