1. 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?
Answers
Length of narrow bore = 1 m (100 cm)
Length of Mercury (Hg) thread = 76 cm
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.
So, the air between the narrow bore and Mercury thread is 15 cm.
Given condition is: “If the tube is held vertically with the open end at the bottom.”
Now, mercury thread occupies space = 100 - (76 + 15) = 100 - 91 = 9 cm
Also, total length of air column = 24 cm (15 + 9)
Let us assume that due to atmospheric pressure 'x' cm (length) of mercury flows out.
Now,
Length of mercury column = (76 - x) cm
Length of the air column in a bore = (24 + x) cm
Temperature is constant. Then,
P1V1 = P2V2
Here, P1 = Initial Pressure, P2 = Final Pressure, V1 = Initial Volume and V2 = Final Volume
Also, P1 = 76 cm, P2 = h cm [76 - (76 - h)]
V1 = 15 cm³ and V2 = (24 + h) cm³
=> 76(15) = h(24 + h)
=> 1140 = 24h + h²
=> h² + 24h - 1140 = 0
On solving we get,
=> h = -47.8, 23.8
As height can't be negative. So, the negative one is neglected.
Therefore, 23.8 cm of mercury flows out due to atmospheric pressure.
