question_answer 11)

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:

When 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 left at the open end. Fig. 9(NCT).2(a). The pressure of air enclosed in tube will be atmospheric pressure. Let area of cross-section of the tube be 1 sq. cm.                             cm and   When the tube is held vertically, 15 cm air gets another9 cm of air (filled in the right hand side in the horizontal position) and let h cm of mercury flow out to balance             Mercury the atmospheric pressure. Fig. 9 (NCT). 2(b). Then the (24 + h) cm 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.       If we assume that temperature remains constant, then                                   or            76 x 15 = h x (24 + h) or            or            or            Since h cannot be negative (because more mercury cannot flow into the tube),therefore h =cm. Thus, in the vertical position of the tube, cm of mercury flows out.