Question

A ring shaped tube contains two ideal gases with equal masses and molar masses $M_1=32$ and $M_2=28.$The gases are separated by one fixed partition and another movable stopper S which can move freely without friction inside the ring. Both the partitions are thermally conducting. The angle $\alpha$ as shown in the figure is degrees.

Answer 1

Pressure on both sides will be equal
$p_1=p_2$
i.e., $\frac{n_{1}RT}{V_1}=\frac{n_{2}RT}{V_2}(n=\frac{m}{M})$
$\frac{m}{M_1{V}_1}=\frac{m}{M_1{V}_2}$ or $\frac{V_2}{V_1}=\frac{M_1}{M_2}=\frac{32}{28}=\frac{8}{7}$
but $\frac{V_2}{V_1}=\frac{\alpha }{360-\alpha }$
Solve to get $\alpha =\left(\frac{{360}^{\circ }}{8+7}\right)8={192}^{\circ }$