Question

An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the Hg level as shown in Fig. The open end of the tube is then closed and sealed and the tube is raised vertically by an additional 46 cm. The length of the air column above mercury in the tube now will be

(1) 38 cm

(2) 6 cm

(3) 16 cm

(4) 22 cm

Answer 1

(3) 16 cm

Let A be the area of cross–section of the tube. P₁ , V₁ denote pressure and volume of air in tube intially. P₂ , V₂ are corresponding quantities when one end of tube has been scaled. Under isothermal conditions

P₁V₁ = P₂V₂

or P₀ 8 x A = P₂ x (54-x)A

where x is length of mercury inside tube as shown in Fig.

From Eqns (i) and (ii) we have

The length of air column in closed tube = 54 - 38 = 16 cm