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 opened end is kept upward. If the tube is making ${30}^o$ 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. $18cm$
• C. $24cm$
• D. $20.2cm$

Answer 1

Answer: (A)

$22cm$

Assuming the process to be isothermal, PV= constant

or $P_1{V}_1$ = $P_2{V}_2$ (Boyle's Law)

Given, $P_1$ = 76 + 12 = 88 cm

$V_1$ = 20.5

$P_2$ will be = 76 + 12 sin30⁰ = 82 cm

Thus, length of the air column = $\frac{P_1{V}_1}{P_2}$ = $\frac{88\times 20.5}{82}$ = 22 cm.