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 ?

A meter long narrow bore held horizontally (and closed at one end) con

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 ?
Answer» Solution :When the tube is HELD horizontally, the mercurythread of length of air `= 15 cm`. A lenght of `9 cm` of the tube will be LEFT at teh open end, fig., The pressure of air enclosed in tube will be atmospheric pressure. Let area of cross-section of teh tube be `1 SQ. cm`, `:. P_(1) 76 cm` and `V_(1)=15cm^(3)` When 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 tobalance the atmospheric pressure. 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 `P_(1)V_(1) =P_(2)V_(2) or 76 xx 15 = h xx (24+h)`or `h^(2) + 24h - 1140 = 0 or h= -24 +- sqrt((24)^((2)+4 xx 1140))/(2) = 23.8 cm or -47.8 cm`.