Question

A 10-cm column of air is trapped by an 8-cm-long column of Hg in a capillary tube horizontally fixed as shown in the figure at 1 atm pressure.
(a) vertically with open end up
(b) vertically with open end down
(c) at ${45}^0$ from horizontal with the open end up

Answer 1

(a) At the horizontal position of tube, air pressure is 1 atm, i.e., 76 cmHg. If the tube is now held in different given positions at the same temperature, the length of air column will vary. Applying Boyle's law, we have,
$p_1{V}_1=p_2{V}_2$
or $p_1{l}_{1}a=p_2{l}_{2}a$
or $p_1{l}_1=p_2{l}_2$.
Now when the tube is held vertically with open end up,
air pressure $p_2=76cm\left(Hg\right)+8cm\left(Hg\right)$
= 84 cm (Hg).
$\therefore l_2=\frac{p_1{l}_1}{p_2}=\frac{76\times 10}{84}=9.04cm$
(b) When the tube is held vertically with open end down,