Calculation of pressure

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Question

A ring shaped tube contains two ideal gases with equal masses and relative molar masses $M_{1} = 32$ and $M_{2} = 28$ . The gases are separated by one fixed partition p and another movable stopper S which can move freely without friction inside the ring. The angle $α$ in equilibrium as shown in the figure (in degrees) is

Moderate

Solution

For equilibrium,
$\begin{array}{l} P_{1} = P_{2} \\ \frac{n_{1} RT}{V_{1}} = \frac{n_{2} RT}{V_{2}} \\ \frac{m}{M_{1} Arα} = \frac{m}{M_{2} Ar (360^{0} - α)} \\ 32 α = 28 (360^{0} - α) \\ α = 168^{0} \end{array}$

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