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 and another movable stopper $S$ which can move freely without friction inside the ring. What is the value of the angle $\alpha$ (in degree) at equilibrium?

Answer 1

Answer: 192

Pressure on both sides will be equal.
i.e., $p_1=p_2$
$\frac{{\text{n}}_1\text{RT}}{{\text{V}}_1}=\frac{{\text{n}}_2\text{RT}}{{\text{V}}_2}$ $\left(\text{n}=\frac{\text{m}}{\text{M}}\right)$
or $\frac{\text{m}}{{\text{M}}_1{\text{V}}_1}=\frac{\text{m}}{{\text{M}}_2{\text{V}}_2}\text{ or }\frac{{\text{V}}_2}{{\text{V}}_1}=\frac{{\text{M}}_1}{{\text{M}}_2}=\frac{32}{28}=\frac{8}{7}$
$\therefore$ $\alpha =\left(\frac{360^{\circ }}{8+7}\right)\times 8=192^{\circ }$