Question

An ideal gas is trapped between Hg thread of $12cm$ and the closed lower end of a narrow vertical tube of uniform cross section. Length of the air column is $20.5cm$, when the open end is kept upward. If the tube is making ${30}^0$with the horizontal then the length of the air column is (assuming temperature to be constant and atmospheric pressure = $76cm$ of $Hg$)

• A. $22cm$
• B. $18\ cm
• C. $24cm$
• D. $20.2cm$

Answer 1

The correct option is A $22cm$

Assuming the process to be isothermal, we can sa for an ideal gas,

$P_1{V}_1=P_2{V}_2$

$(76+12)\left(20.5\right)=(76+12sin({30}^0\left)\right)l$, since in second case, the vertical height of mercury column will be $12sin\left({30}^0\right)$.

This gives $l=22cm$.