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A narrow uniform glass tube 80 cm long a...

A narrow uniform glass tube 80 cm long and open at both ends is half immersed in mercurry. Then the top of the tube is closed and it is taken out of mercury. A column of mercury 22 cm long then remains in the tube. What is the atmospheric pressure?

Text Solution

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Suppose A is the area of cross section of the tube and P is the atmosphere pressure. When half tube is inside mercury then volume of air in the tube.
`V_(1)=Axx40=40Acm^(3)`
`P_(1)=P`

When the tube is taken out of mercury, the volume of air
`V_(2)=Axx58=58A`
If `P_(2)` is the pressure of air in the tube then
`P_(2)+22=P`
or `P_(2)=P-22`
Now by Boyle.s law we have
`P_(1)V_(1)=P_(2)V_(2)`
`Pxx40A=(P-22)xx58A`
or `18P=22xx58`
`:.P=70.9cm`
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