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Question
Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is 0.465 N m–1. Density of mercury = 13.6 × 103 kg m–3
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Solution 1
Angle of contact between mercury and soda lime glass, θ = 140°
Radius of the narrow tube, r = 1 mm = 1 × 10–3 m
Surface tension of mercury at the given temperature, s = 0.465 N m–1
Density of mercury, ρ =13.6 × 103 kg/m3
Dip in the height of mercury = h
Acceleration due to gravity, g = 9.8 m/s2
Surface tension is related with the angle of contact and the dip in the height as:
`s = (hrhogr)/(2costheta)`
`:.h = (2s cos theta)/(rrhog)`
` = (2xx0.465xxcos 140)/(1xx10^(-3)xx13.6xx10^3xx 9.8)`
= - 0.00534 m
= -5.34 mm
Here, the negative sign shows the decreasing level of mercury. Hence, the mercury level dips by 5.34 mm
Solution 2
Radius or tube = r = 1.00 mm = `10^(-3) m`
Surface tension of mercury, `sigma = 0.465 Nm^(-1)`
Density of mercury, `sigma = 13.6 xx 10^3 kg m6(-3)`
Angle of contact, `theta = 140^@`
`:. h = (2sigma cos theta)/(rrhog) = (2xx0.465xxcos 140^@)/(10^(-3)xx 13.6xx10^3xx 9.8)`
`= (2xx0.465xx(-0.7660))/(10^(-3)xx13.6xx10^3xx9.8)`
`= -5.34 xx 10^(-3) m = -5.34 mm`
Negative sign shows that the mercury level is deprssedin the tube
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