Heat and Thermodynamics 6 Question 23
28. 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. The angle $\alpha$ as shown in the figure is …… degrees.
(1997, 2M)
Show Answer
Answer:
Correct Answer: 28. $192^{\circ}$
Solution:
- Pressure on both sides will be equal i.e.
$$ \begin{aligned} p _1 & =p _2 \\ \frac{n _1 R T}{V _1} & =\frac{n _2 R T}{V _2} \quad\left(n=\frac{m}{M}\right) \end{aligned} $$
$$ \begin{array}{rlrl} \text { or } & \frac{m}{M _1 V _1} & =\frac{m}{M _2 V _2} \\ \text { or } & \frac{V _2}{V _1} & =\frac{M _1}{M _2}=\frac{32}{28}=\frac{8}{7} \\ & \therefore & \alpha & =\left(\frac{360^{\circ}}{8+7}\right) \times 8=192^{\circ} \end{array} $$
