A metre long narrow bore held horizontal | Class 11 Physics Chapter Kinetic Theory, Kinetic Theory NCERT Solutions

Question:

A metre 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:

Length of the narrow bore, L= 1 m = 100 cm

Length of the mercury thread, l= 76 cm

Length of the air column between mercury and the closed end, la= 15 cm

Since the boreis held vertically in air with the open end at the bottom, the mercury length that occupies the air space is: 100 - (76 + 15) = 9 cm

Hence, the total length of the air column = 15 + 9 = 24 cm

Let h cm of mercury flow out as a result of atmospheric pressure.

∴Length of the air column in the bore= 24 + hcm

And, length of the mercury column = 76 - hcm

Initial pressure, P1= 76 cm of mercury

Initial volume, V1= 15 cm3

Final pressure, P2= 76 - (76 - h) = h cm of mercury

Final volume, V2= (24 + h) cm3

Temperature remains constant throughout the process.

∴P1V1= P2V2

= 76 × 15 = h (24 + h)

h2+ 24h - 1140 = 0

∴ h  =  - 24 +- underroot [(24)+ 4 x 1 x 1140]  / 2 x 1

= 23.8 cm or -47.8 cm

Height cannot be negative.

Hence, 23.8 cm of mercurywill flow out from the boreand 52.2 cm of mercury will remain in it.

The length of the air column will be 24 + 23.8 = 47.8 cm.


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Welcome to the NCERT Solutions for Class 11 Physics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 11: A metre long narrow bore held horizontally (and closed at one end) contains a 76 cm long mercury thr....