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Calculate the diameter of a capillary tu...

Calculate the diameter of a capillary tube in which mercury is derpessed by 1.21 cm. Given surface tension for mercury is `540 xx 10^(-3) "Nm"^(-1).` the angle of contact with glass is `140^(@)` and density of mercury is `13.6 xx 10^(3) "kg" m^(-3).`

Text Solution

Verified by Experts

The correct Answer is:
`1.03`
Here h = -1.21cm `= -1.21xx10^(-2)m, theta = 140^@`
`sigma= 540 xx 10^(-3)Nm^(-1)`,
`cos140^(@) = cos(180^(@) - 40^(@) = -cos 40^(@) = -0.7660 `
Diameter, `2 r = (4 sigma cos theta)/(h rhog) = (4xx540xx10^(-3)xx (0.7660))/(-1.21 xx 10^(-2)xx 13.6 xx 10^(3) xx 9.8)`
`= 1.026 xx10^(-3) ~~ 1.03 xx 10^(-3) m`
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