A meter long narrow bore held horizontally

cbse
kinetictheoryofgases

#1

A meter long narrow bore held horizontally (and closed at one end) contains a 76 cm long mercury thread which traps a 15 cm column of air. What happens, if the tube is held vertically with the open end at the bottom?


#2

If the tube is held horizontally, the mercury thread of length 76 cm traps a length of air = 15 cm. A length of 9 cm of the tube will be at the open end, Fig. (a). The pressure of air enclosed in tube will be atmospheric pressure. Let area of cross-section of the tube be 1 sq. cm.

If the tube is held vertically, 15 cm air gets another 9 cm of air (filled in the right handside in the horizontal position) and let h cm of mercury flow out to balance the atmospheric pressure, Fig. (b). Then, the heights of air column and mercury column are {24 + h) cm and (76 - h) cm respectively.
The pressure of air =76(76-h) = h cm of mercury
${ V }{ 2 }$ = (24+h) ${{cm}^{3}}$ and
${ p }
{ 2 }$ = h cm
If we assume that temperature remains constant, then

Since h cannot be negative (because more mercury cannot flow into the tube), therefore h = 23.8 cm. Thus, in the vertical position of the tube, 23.8 cm of mercury flows out.