A mercury thread of length 10 cm is contained in the middle of a narrow horizontal tube of length 100 cm. and sealed at both the ends. The air in both halves of the tube is under a pressure of 76 cm of Hg, What distance will the mercury column move if the tube is placed vertically ?

A mercury thread of length 10 cm is contained in the middle of a narro

1.	A mercury thread of length 10 cm is contained in the middle of a narrow horizontal tube of length 100 cm. and sealed at both the ends. The air in both halves of the tube is under a pressure of 76 cm of Hg, What distance will the mercury column move if the tube is placed vertically ?
Answer» SOLUTION :When the tube is horizontal, in fig., length of air COLUMN on either sideof 10 cm mercury THREAD, `V =(100-10)/(2) = 45 cm` Pressure of air in both halves of tube , P= 76 cm of Hg. when the tube is held vertically, LET the mercury column move down through a distance x as shown in fig. Let `P_(1), P_(2)` be the pressures and `V_(1), V_(2)` be the volume half respectively. Applying Boyle's Law to upper half `P_(1) V_(1) = PV` `P_(1) (54 +x) = 76 xx 45` `P_(1) = (76 xx 45)/(45 + x)` ...(i) Applying Boyle's Law to LOWER half `P_(2)V_(2) = PV` `P_(2) = (PV)/(V^2) = (76 xx 45)/(45-x)` ..(ii) Now ,`P_(2)` = pressure of air in upper half+ length of Hg col. `=(P_1) + 10` `:.` From (i) and (ii) ` (76 xx45)/(45 - x) = (76 xx45)/(45+x) +10` On solving we get `x = 2.948 cm`.