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  4. A ring shaped tube contains two ideal gases with equal masses and relative molar masses M1= 32 and M2= 28. The gases arc separated by one fixed partition and another movable stopper S which can move freely without friction inside the ring. The angle a as shown in the figure is ....... degrees.

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Q. A ring shaped tube contains two ideal gases with equal masses and relative molar masses $M_1= 32$ and $M_2= 28$. The gases arc separated by one fixed partition and another movable stopper $S$ which can move freely without friction inside the ring. The angle a as shown in the figure is ....... degrees.Physics Question Image

IIT JEEIIT JEE 1997Thermodynamics

Solution:

Pressure on both sides will be equal
$i.e.,,p_1 =p_2$
$\frac{n_1RT}{V_1} =\frac{n_2RT}{V_2} \left(n=\frac{m}{M}\right)$
or $ \frac{m}{M_1V_1} =\frac{m}{M_2V_2}$
or $\frac{V_2}{V_1}=\frac{M_1}{M_2}=\frac{32}{28}=\frac{8}{7}$
$\therefore \alpha =\left(\frac{360^{\circ}}{8+7}\right) \, \times 8 =192^{\circ}$